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6,631 |
['When emergencies are crisises is true, it follows that a biological clock is a mechanism.', 'If either animals adapt to their environments or radiolabeled antibodies lessen the chance of radiation damage to normal cells, then either protein is composed of chains of amino acids or salmonberries have (part) cells.', "So long as tea has caffeine, 'emergencies are crisises' is true.", 'Either one or both of these statements are true: spectroscopic binaries are two stars that seem to be one, or dehydration is a serious problem for infants and toddlers with decreased fluid intake.', 'Once we know spectroscopic binaries are two stars that seem to be one, we also know that either either animals adapt to their environments or radiolabeled antibodies lessen the chance of radiation damage to normal cells or tea has caffeine.', 'Once we know dehydration is a serious problem for infants and toddlers with decreased fluid intake, we also know that either either animals adapt to their environments or radiolabeled antibodies lessen the chance of radiation damage to normal cells or tea has caffeine.', "We know that either aromatherapy is often beneficial for falling asleep or either either cornish soils are on flood plains that are commonly in broad depressions or bug zappers kill a lot of insects if they fly in that direction or academic standing refers to the level of the student's academic performance.", 'Those that suggest aromatherapy is often beneficial for falling asleep are wrong.', 'There is good reason to believe that either some blasts stay in the marrow to mature or beaver dams prevent erosion.', 'On the condition that some blasts stay in the marrow to mature, it is definitely the case that if either cornish soils are on flood plains that are commonly in broad depressions or bug zappers kill a lot of insects if they fly in that direction, then if either protein is composed of chains of amino acids or salmonberries have (part) cells, then a biological clock is a mechanism.', 'If beaver dams prevent erosion, then if either cornish soils are on flood plains that are commonly in broad depressions or bug zappers kill a lot of insects if they fly in that direction, then if either protein is composed of chains of amino acids or salmonberries have (part) cells, then a biological clock is a mechanism.', "Provided that academic standing refers to the level of the student's academic performance, we know that farmers can grow beans on land and in climates that are also good for corn.", "So long as farmers can grow beans on land and in climates that are also good for corn, 'if either protein is composed of chains of amino acids or salmonberries have (part) cells, then a biological clock is a mechanism' is true."]
|
When emergencies are crisises is true, it follows that a biological clock is a mechanism. If either animals adapt to their environments or radiolabeled antibodies lessen the chance of radiation damage to normal cells, then either protein is composed of chains of amino acids or salmonberries have (part) cells. So long as tea has caffeine, 'emergencies are crisises' is true. Either one or both of these statements are true: spectroscopic binaries are two stars that seem to be one, or dehydration is a serious problem for infants and toddlers with decreased fluid intake. Once we know spectroscopic binaries are two stars that seem to be one, we also know that either either animals adapt to their environments or radiolabeled antibodies lessen the chance of radiation damage to normal cells or tea has caffeine. Once we know dehydration is a serious problem for infants and toddlers with decreased fluid intake, we also know that either either animals adapt to their environments or radiolabeled antibodies lessen the chance of radiation damage to normal cells or tea has caffeine. We know that either aromatherapy is often beneficial for falling asleep or either either cornish soils are on flood plains that are commonly in broad depressions or bug zappers kill a lot of insects if they fly in that direction or academic standing refers to the level of the student's academic performance. Those that suggest aromatherapy is often beneficial for falling asleep are wrong. There is good reason to believe that either some blasts stay in the marrow to mature or beaver dams prevent erosion. On the condition that some blasts stay in the marrow to mature, it is definitely the case that if either cornish soils are on flood plains that are commonly in broad depressions or bug zappers kill a lot of insects if they fly in that direction, then if either protein is composed of chains of amino acids or salmonberries have (part) cells, then a biological clock is a mechanism. If beaver dams prevent erosion, then if either cornish soils are on flood plains that are commonly in broad depressions or bug zappers kill a lot of insects if they fly in that direction, then if either protein is composed of chains of amino acids or salmonberries have (part) cells, then a biological clock is a mechanism. Provided that academic standing refers to the level of the student's academic performance, we know that farmers can grow beans on land and in climates that are also good for corn. So long as farmers can grow beans on land and in climates that are also good for corn, 'if either protein is composed of chains of amino acids or salmonberries have (part) cells, then a biological clock is a mechanism' is true.
|
It is the case that a biological clock is a mechanism.
|
We know that the claim that a biological clock is a mechanism is false.
|
FALSE
|
Disjunction Elimination:
Either (Either [1] or [2].) or [3]. [SC1-1]
If (Either [1] or [2].), then [0]. [SC2-1]
If [3], then [0].
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either (Either [4] or [5].) or [6]. [SC1-2]
If (Either [4] or [5].), then (Either [1] or [2].).
If [6], then [3].
Therefore, Either (Either [1] or [2].) or [3]..
[SC1-2]
Disjunction Elimination:
Either [10] or [11].
If [10], then (Either (Either [4] or [5].) or [6].).
If [11], then (Either (Either [4] or [5].) or [6].).
Therefore, Either (Either [4] or [5].) or [6]..
[SC2-1]
Disjunction Elimination:
Either (Either [7] or [8].) or [9]. [SC1-2]
If (Either [7] or [8].), then (If (Either [1] or [2].), then [0].). [SC2-2]
If [9], then (If (Either [1] or [2].), then [0].). [SC3-2]
Therefore, If (Either [1] or [2].), then [0]..
[SC1-2]
Disjunctive Syllogism:
Either [15] or (Either (Either [7] or [8].) or [9].).
Not [15].
Therefore, Either (Either [7] or [8].) or [9]..
[SC2-2]
Disjunction Elimination:
Either [13] or [14].
If [13], then (If (Either [7] or [8].), then (If (Either [1] or [2].), then [0].).).
If [14], then (If (Either [7] or [8].), then (If (Either [1] or [2].), then [0].).).
Therefore, If (Either [7] or [8].), then (If (Either [1] or [2].), then [0].)..
[SC3-2]
Hypothetical Syllogism:
If [9], then [12].
If [12], then (If (Either [1] or [2].), then [0].).
Therefore, If [9], then (If (Either [1] or [2].), then [0].)..
|
{0: 'A biological clock is a mechanism.', 1: 'Protein is composed of chains of amino acids.', 2: 'Salmonberries have (part) cells.', 3: 'Emergencies are crisises.', 4: 'Animals adapt to their environments.', 5: 'Radiolabeled antibodies lessen the chance of radiation damage to normal cells.', 6: 'Tea has caffeine.', 7: 'Cornish soils are on flood plains that are commonly in broad depressions.', 8: 'Bug zappers kill a lot of insects if they fly in that direction.', 9: "Academic standing refers to the level of the student's academic performance.", 10: 'Spectroscopic binaries are two stars that seem to be one.', 11: 'Dehydration is a serious problem for infants and toddlers with decreased fluid intake.', 12: 'Farmers can grow beans on land and in climates that are also good for corn.', 13: 'Some blasts stay in the marrow to mature.', 14: 'Beaver dams prevent erosion.', 15: 'Aromatherapy is often beneficial for falling asleep.'}
| 7 |
6,185 |
['When many people develop severe allergies to dust mite droppings is true, it follows that coal increases air pollution.', 'If it is a common misconception that if coal increases air pollution, then rights are part of a social contract that makes no sense without responsibilities, then plants have effects.', 'We know that at least one of two things is true: either religion is to bridle the tongue, keep pure, help others or some men die after creatures, or toads have color.', 'One may reasonably assume that if either religion is to bridle the tongue, keep pure, help others or some men die after creatures, then if rights are part of a social contract that makes no sense without responsibilities, then definitions ratio A pair of numbers that compares different types of units.', 'When toads have color is true, it follows that if rights are part of a social contract that makes no sense without responsibilities, then definitions ratio A pair of numbers that compares different types of units.', "Whenever it is true that primitive men eat food, 'the claim that plants have effects does not correspond with reality' is true.", 'Once we know those that suggest primitive men eat food are wrong, we also know that the statement that states some people get cancer is false.', 'Assuming those that suggest primitive men eat food are wrong, we know that sexuality is often a delicate balance between emotional and physical issues.', 'One may reasonably assume that if sexuality is often a delicate balance between emotional and physical issues, then some people get cancer.']
|
When many people develop severe allergies to dust mite droppings is true, it follows that coal increases air pollution. If it is a common misconception that if coal increases air pollution, then rights are part of a social contract that makes no sense without responsibilities, then plants have effects. We know that at least one of two things is true: either religion is to bridle the tongue, keep pure, help others or some men die after creatures, or toads have color. One may reasonably assume that if either religion is to bridle the tongue, keep pure, help others or some men die after creatures, then if rights are part of a social contract that makes no sense without responsibilities, then definitions ratio A pair of numbers that compares different types of units. When toads have color is true, it follows that if rights are part of a social contract that makes no sense without responsibilities, then definitions ratio A pair of numbers that compares different types of units. Whenever it is true that primitive men eat food, 'the claim that plants have effects does not correspond with reality' is true. Once we know those that suggest primitive men eat food are wrong, we also know that the statement that states some people get cancer is false. Assuming those that suggest primitive men eat food are wrong, we know that sexuality is often a delicate balance between emotional and physical issues. One may reasonably assume that if sexuality is often a delicate balance between emotional and physical issues, then some people get cancer.
|
If many people develop severe allergies to dust mite droppings, then definitions ratio A pair of numbers that compares different types of units.
|
It is not the case that if many people develop severe allergies to dust mite droppings, then definitions ratio A pair of numbers that compares different types of units.
|
FALSE
|
Hypothetical Syllogism:
If [0], then [2].
If [2], then [1]. [SC2-1]
Therefore, If [0], then [1]..
[SC2-1]
Hypothetical Syllogism:
If [2], then [3]. [SC1-2]
If [3], then [1]. [SC2-2]
Therefore, If [2], then [1]..
[SC1-2]
Modus Tonens:
If (Not (If [2], then [3].).), then [7].
Not [7]. [SC2-3]
Therefore, If [2], then [3]..
[SC2-3]
Modus Ponens:
If [8], then (Not [7].).
[8] [SC2-4]
Therefore, Not [7]..
[SC2-4]
Reductio Ad Absurdum:
If (Not [8].), then [9]. [SC1-5]
If (Not [8].), then (Not [9].).
Therefore, [8].
[SC1-5]
Hypothetical Syllogism:
If (Not [8].), then [10].
If [10], then [9].
Therefore, If (Not [8].), then [9]..
[SC2-2]
Disjunction Elimination:
Either (Either [4] or [5].) or [6].
If (Either [4] or [5].), then (If [3], then [1].).
If [6], then (If [3], then [1].).
Therefore, If [3], then [1]..
|
{0: 'Many people develop severe allergies to dust mite droppings.', 1: 'Definitions ratio A pair of numbers that compares different types of units.', 2: 'Coal increases air pollution.', 3: 'Rights are part of a social contract that makes no sense without responsibilities.', 4: 'Religion is to bridle the tongue, keep pure, help others.', 5: 'Some men die after creatures.', 6: 'Toads have color.', 7: 'Plants have effects.', 8: 'Primitive men eat food.', 9: 'Some people get cancer.', 10: 'Sexuality is often a delicate balance between emotional and physical issues.'}
| 7 |
6,732 |
['It is a fact that either if some dwarf hamsters eat several different meat, then pregnant women see hands or most dimetrodons have sprawl legs.', "One may reasonably assume that if if some dwarf hamsters eat several different meat, then pregnant women see hands, then cattle account for almost half of the state's agricultural income.", 'On the condition that most dimetrodons have sprawl legs, it is definitely the case that leukemic cells are also classified according to morphology .', 'There is good reason to believe that either premature birth is one of the greatest health hazards of humankind or riggers are sables.', "Assuming riggers are sables, we know that if cattle account for almost half of the state's agricultural income, then carjackings are hijacks.", 'Given that birds have metabolism, it can be inferred that the statement that states carjackings are hijacks is false.', 'birds have metabolism.', "Once we know land ports are dangerous places to work, we also know that if premature birth is one of the greatest health hazards of humankind, then if cattle account for almost half of the state's agricultural income, then carjackings are hijacks.", 'We know that either high numbers flying adults associated with heavily infested host plants can be a nuisance or land ports are dangerous places to work.', 'We know that the claim that high numbers flying adults associated with heavily infested host plants can be a nuisance is false.']
|
It is a fact that either if some dwarf hamsters eat several different meat, then pregnant women see hands or most dimetrodons have sprawl legs. One may reasonably assume that if if some dwarf hamsters eat several different meat, then pregnant women see hands, then cattle account for almost half of the state's agricultural income. On the condition that most dimetrodons have sprawl legs, it is definitely the case that leukemic cells are also classified according to morphology . There is good reason to believe that either premature birth is one of the greatest health hazards of humankind or riggers are sables. Assuming riggers are sables, we know that if cattle account for almost half of the state's agricultural income, then carjackings are hijacks. Given that birds have metabolism, it can be inferred that the statement that states carjackings are hijacks is false. birds have metabolism. Once we know land ports are dangerous places to work, we also know that if premature birth is one of the greatest health hazards of humankind, then if cattle account for almost half of the state's agricultural income, then carjackings are hijacks. We know that either high numbers flying adults associated with heavily infested host plants can be a nuisance or land ports are dangerous places to work. We know that the claim that high numbers flying adults associated with heavily infested host plants can be a nuisance is false.
|
The idea that leukemic cells are also classified according to morphology is true.
|
Leukemic cells are actually abnormal white blood cells.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either (If [3], then [4].) or [5].
If (If [3], then [4].), then [1].
If [5], then [0].
Therefore, Either [1] or [0]..
[SC2-1]
Modus Tonens:
If [1], then [2]. [SC1-2]
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If [1], then [2].). [SC2-3]
If [8], then (If [1], then [2].).
Therefore, If [1], then [2]..
[SC2-3]
Modus Ponens:
If [9], then (If [7], then (If [1], then [2].).).
[9] [SC2-4]
Therefore, If [7], then (If [1], then [2].)..
[SC2-4]
Disjunctive Syllogism:
Either [10] or [9].
Not [10].
Therefore, [9].
[SC2-2]
Modus Ponens:
If [6], then (Not [2].).
[6]
Therefore, Not [2]..
|
{0: 'Leukemic cells are also classified according to morphology .', 1: "Cattle account for almost half of the state's agricultural income.", 2: 'Carjackings are hijacks.', 3: 'Some dwarf hamsters eat several different meat.', 4: 'Pregnant women see hands.', 5: 'Most dimetrodons have sprawl legs.', 6: 'Birds have metabolism.', 7: 'Premature birth is one of the greatest health hazards of humankind.', 8: 'Riggers are sables.', 9: 'Land ports are dangerous places to work.', 10: 'High numbers flying adults associated with heavily infested host plants can be a nuisance.'}
| 7 |
6,404 |
['It is not the case that some cleaners contain acids or chlorides which can start new corrosion.', "So long as either some male mates have years or cancer is the third leading cause of death among men and women of the Bahamas, 'if it is not the case that most polecats have long furry tails, then the claim that moth balls are poisenous to chidren and can be deadly does not reflect reality' is true.", 'It is rational to believe that either most deaf people can lip-read or bacteria are the most common cause of foodborne illness.', 'Once we know most deaf people can lip-read, we also know that some cleaners contain acids or chlorides which can start new corrosion.', 'Provided that bacteria are the most common cause of foodborne illness, we know that if it is not the case that most polecats have long furry tails, then moth balls are poisenous to chidren and can be deadly.', 'It is a fact that either archaeologists collect and study artifacts to find out about life in the past or lymphatic filariasis is one of the only six infectious diseases in the world considered eradicable.', 'One may reasonably assume that if archaeologists collect and study artifacts to find out about life in the past, then energy sources have impact.', 'On the condition that lymphatic filariasis is one of the only six infectious diseases in the world considered eradicable, it is definitely the case that either some male mates have years or cancer is the third leading cause of death among men and women of the Bahamas.', "Whenever it is true that energy sources have impact, 'most pituitary hormones regulate excretion' is true.", 'Once we know the claim that if most pituitary hormones regulate excretion, then if it is not the case that most polecats have long furry tails, then the claim that moth balls are poisenous to chidren and can be deadly does not reflect reality does not correspond with reality, we also know that most minerals have atomic structures.', 'Assuming the claim that if most pituitary hormones regulate excretion, then if it is not the case that most polecats have long furry tails, then the claim that moth balls are poisenous to chidren and can be deadly does not reflect reality does not correspond with reality, we know that the claim that most minerals have atomic structures does not correspond with reality.']
|
It is not the case that some cleaners contain acids or chlorides which can start new corrosion. So long as either some male mates have years or cancer is the third leading cause of death among men and women of the Bahamas, 'if it is not the case that most polecats have long furry tails, then the claim that moth balls are poisenous to chidren and can be deadly does not reflect reality' is true. It is rational to believe that either most deaf people can lip-read or bacteria are the most common cause of foodborne illness. Once we know most deaf people can lip-read, we also know that some cleaners contain acids or chlorides which can start new corrosion. Provided that bacteria are the most common cause of foodborne illness, we know that if it is not the case that most polecats have long furry tails, then moth balls are poisenous to chidren and can be deadly. It is a fact that either archaeologists collect and study artifacts to find out about life in the past or lymphatic filariasis is one of the only six infectious diseases in the world considered eradicable. One may reasonably assume that if archaeologists collect and study artifacts to find out about life in the past, then energy sources have impact. On the condition that lymphatic filariasis is one of the only six infectious diseases in the world considered eradicable, it is definitely the case that either some male mates have years or cancer is the third leading cause of death among men and women of the Bahamas. Whenever it is true that energy sources have impact, 'most pituitary hormones regulate excretion' is true. Once we know the claim that if most pituitary hormones regulate excretion, then if it is not the case that most polecats have long furry tails, then the claim that moth balls are poisenous to chidren and can be deadly does not reflect reality does not correspond with reality, we also know that most minerals have atomic structures. Assuming the claim that if most pituitary hormones regulate excretion, then if it is not the case that most polecats have long furry tails, then the claim that moth balls are poisenous to chidren and can be deadly does not reflect reality does not correspond with reality, we know that the claim that most minerals have atomic structures does not correspond with reality.
|
It is rational to agree that most polecats have long furry tails.
|
We know that the claim that most polecats have long furry tails is false.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then [1].). [SC1-2]
Not [2].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Constructive Dilemma:
Either [9] or [10].
If [9], then [2].
If [10], then (If (Not [0].), then [1].).
Therefore, Either [2] or (If (Not [0].), then [1].)..
[SC2-1]
Disjunction Elimination:
Either [3] or (Either [4] or [5].). [SC1-2]
If [3], then (If (Not [0].), then (Not [1].).). [SC2-2]
If (Either [4] or [5].), then (If (Not [0].), then (Not [1].).).
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Constructive Dilemma:
Either [7] or [8].
If [7], then [3].
If [8], then (Either [4] or [5].).
Therefore, Either [3] or (Either [4] or [5].)..
[SC2-2]
Hypothetical Syllogism:
If [3], then [6].
If [6], then (If (Not [0].), then (Not [1].).). [SC2-3]
Therefore, If [3], then (If (Not [0].), then (Not [1].).)..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If [6], then (If (Not [0].), then (Not [1].).).).), then [11].
If (Not (If [6], then (If (Not [0].), then (Not [1].).).).), then (Not [11].).
Therefore, If [6], then (If (Not [0].), then (Not [1].).)..
|
{0: 'Most polecats have long furry tails.', 1: 'Moth balls are poisenous to chidren and can be deadly.', 2: 'Some cleaners contain acids or chlorides which can start new corrosion.', 3: 'Energy sources have impact.', 4: 'Some male mates have years.', 5: 'Cancer is the third leading cause of death among men and women of the Bahamas.', 6: 'Most pituitary hormones regulate excretion.', 7: 'Archaeologists collect and study artifacts to find out about life in the past.', 8: 'Lymphatic filariasis is one of the only six infectious diseases in the world considered eradicable.', 9: 'Most deaf people can lip-read.', 10: 'Bacteria are the most common cause of foodborne illness.', 11: 'Most minerals have atomic structures.'}
| 7 |
6,194 |
['On the condition that either hawks have (part) breasts or nuts have (part) sections, it is definitely the case that some shellfishes are part of cuttlefishs.', "The statement that 'either regular exercise is one of the few proven predictors of successful weight maintenance or flowers are the reproductive part of the plant' is incorrect.", "Provided that facial skin is thicker than eyelid skin, and body skin is thicker than the skin on the face, we know that the statement 'many margarines contain trans-fatty acids' can be considered false.", 'The idea that facial skin is thicker than eyelid skin, and body skin is thicker than the skin on the face is true.', "It is rational to believe that either pomes contain many pits, and are represented by apples, quince and pears or if the statement 'if it is not true that if some shellfishes are part of cuttlefishs, then either regular exercise is one of the few proven predictors of successful weight maintenance or flowers are the reproductive part of the plant, then many margarines contain trans-fatty acids' can be considered false, then either optimists are the ultimate realists or mining is a major industry in California.", 'The claim that pomes contain many pits, and are represented by apples, quince and pears does not reflect reality.', "We know that either if coral species are adapted to different disturbance regimes, then wind blows from the land to the sea or smoke alarms are a family's best defense against fire.", 'Once we know if coral species are adapted to different disturbance regimes, then wind blows from the land to the sea, we also know that it is not the case that either optimists are the ultimate realists or mining is a major industry in California.', "On the condition that smoke alarms are a family's best defense against fire, it is definitely the case that it is not the case that either optimists are the ultimate realists or mining is a major industry in California."]
|
On the condition that either hawks have (part) breasts or nuts have (part) sections, it is definitely the case that some shellfishes are part of cuttlefishs. The statement that 'either regular exercise is one of the few proven predictors of successful weight maintenance or flowers are the reproductive part of the plant' is incorrect. Provided that facial skin is thicker than eyelid skin, and body skin is thicker than the skin on the face, we know that the statement 'many margarines contain trans-fatty acids' can be considered false. The idea that facial skin is thicker than eyelid skin, and body skin is thicker than the skin on the face is true. It is rational to believe that either pomes contain many pits, and are represented by apples, quince and pears or if the statement 'if it is not true that if some shellfishes are part of cuttlefishs, then either regular exercise is one of the few proven predictors of successful weight maintenance or flowers are the reproductive part of the plant, then many margarines contain trans-fatty acids' can be considered false, then either optimists are the ultimate realists or mining is a major industry in California. The claim that pomes contain many pits, and are represented by apples, quince and pears does not reflect reality. We know that either if coral species are adapted to different disturbance regimes, then wind blows from the land to the sea or smoke alarms are a family's best defense against fire. Once we know if coral species are adapted to different disturbance regimes, then wind blows from the land to the sea, we also know that it is not the case that either optimists are the ultimate realists or mining is a major industry in California. On the condition that smoke alarms are a family's best defense against fire, it is definitely the case that it is not the case that either optimists are the ultimate realists or mining is a major industry in California.
|
Those that suggest either hawks have (part) breasts or nuts have (part) sections are wrong.
|
Those that suggest either hawks have (part) breasts or nuts have (part) sections are wrong.
|
TRUE
|
Modus Tonens:
If (Either [0] or [1].), then [2].
Not [2]. [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC2-1]
Modus Tonens:
If [2], then (Either [3] or [4].). [SC1-2]
Not (Either [3] or [4].).
Therefore, Not [2]..
[SC1-2]
Modus Tonens:
If (Not (If [2], then (Either [3] or [4].).).), then [5]. [SC1-3]
Not [5]. [SC2-3]
Therefore, If [2], then (Either [3] or [4].)..
[SC1-3]
Modus Tonens:
If (Not (If (Not (If [2], then (Either [3] or [4].).).), then [5].).), then (Either [7] or [8].). [SC1-4]
Not (Either [7] or [8].). [SC2-4]
Therefore, If (Not (If [2], then (Either [3] or [4].).).), then [5]..
[SC1-4]
Disjunctive Syllogism:
Either [9] or (If (Not (If (Not (If [2], then (Either [3] or [4].).).), then [5].).), then (Either [7] or [8].).).
Not [9].
Therefore, If (Not (If (Not (If [2], then (Either [3] or [4].).).), then [5].).), then (Either [7] or [8].)..
[SC2-4]
Disjunction Elimination:
Either (If [10], then [11].) or [12].
If (If [10], then [11].), then (Not (Either [7] or [8].).).
If [12], then (Not (Either [7] or [8].).).
Therefore, Not (Either [7] or [8].)..
[SC2-3]
Modus Ponens:
If [6], then (Not [5].).
[6]
Therefore, Not [5]..
|
{0: 'Hawks have (part) breasts.', 1: 'Nuts have (part) sections.', 2: 'Some shellfishes are part of cuttlefishs.', 3: 'Regular exercise is one of the few proven predictors of successful weight maintenance.', 4: 'Flowers are the reproductive part of the plant.', 5: 'Many margarines contain trans-fatty acids.', 6: 'Facial skin is thicker than eyelid skin, and body skin is thicker than the skin on the face.', 7: 'Optimists are the ultimate realists.', 8: 'Mining is a major industry in California.', 9: 'Pomes contain many pits, and are represented by apples, quince and pears.', 10: 'Coral species are adapted to different disturbance regimes.', 11: 'Wind blows from the land to the sea.', 12: "Smoke alarms are a family's best defense against fire."}
| 7 |
6,564 |
['Given that giraffes are also one of the fastest animals, it can be inferred that either porcelain is characterized by a translucent and vitrified quality and fired to a high temperature or music has power.', "One may reasonably assume that if the claim that either if abortion is child abuse, then leopard geckos are carnivorous and feed mostly on invertebrates or earthquakes are strong evidence that pieces of Earth shift around with respect to other pieces does not reflect reality, then if pineapple chicken is on everyone's list of favorite things, then simple circuits involve motors.", "The claim that if pineapple chicken is on everyone's list of favorite things, then simple circuits involve motors is false.", 'It is rational to believe that either most abundant moisture increases height growth or geochemistry embraces all aspects of the study of the Earth.', 'Once we know geochemistry embraces all aspects of the study of the Earth, we also know that if if abortion is child abuse, then leopard geckos are carnivorous and feed mostly on invertebrates, then the claim that either porcelain is characterized by a translucent and vitrified quality and fired to a high temperature or music has power does not correspond with reality.', 'Assuming some farms also run deer or have arable crops, we know that if earthquakes are strong evidence that pieces of Earth shift around with respect to other pieces, then the claim that either porcelain is characterized by a translucent and vitrified quality and fired to a high temperature or music has power does not correspond with reality.', 'It is reasonable to believe that some farms also run deer or have arable crops.', 'The claim that particles are particles only when they are in relationships has no merit.', 'Either one or both of these statements are true: if a clinical trial is a trial, then grasshoppers only have one body cavity, that being their mouth, or most pet stores sell a variety of medicine, some for single diseases and some for multiple diseases.', 'Once we know if a clinical trial is a trial, then grasshoppers only have one body cavity, that being their mouth, we also know that either particles are particles only when they are in relationships or if most abundant moisture increases height growth, then if if abortion is child abuse, then leopard geckos are carnivorous and feed mostly on invertebrates, then the claim that either porcelain is characterized by a translucent and vitrified quality and fired to a high temperature or music has power does not correspond with reality.', 'Assuming most pet stores sell a variety of medicine, some for single diseases and some for multiple diseases, we know that either particles are particles only when they are in relationships or if most abundant moisture increases height growth, then if if abortion is child abuse, then leopard geckos are carnivorous and feed mostly on invertebrates, then the claim that either porcelain is characterized by a translucent and vitrified quality and fired to a high temperature or music has power does not correspond with reality.']
|
Given that giraffes are also one of the fastest animals, it can be inferred that either porcelain is characterized by a translucent and vitrified quality and fired to a high temperature or music has power. One may reasonably assume that if the claim that either if abortion is child abuse, then leopard geckos are carnivorous and feed mostly on invertebrates or earthquakes are strong evidence that pieces of Earth shift around with respect to other pieces does not reflect reality, then if pineapple chicken is on everyone's list of favorite things, then simple circuits involve motors. The claim that if pineapple chicken is on everyone's list of favorite things, then simple circuits involve motors is false. It is rational to believe that either most abundant moisture increases height growth or geochemistry embraces all aspects of the study of the Earth. Once we know geochemistry embraces all aspects of the study of the Earth, we also know that if if abortion is child abuse, then leopard geckos are carnivorous and feed mostly on invertebrates, then the claim that either porcelain is characterized by a translucent and vitrified quality and fired to a high temperature or music has power does not correspond with reality. Assuming some farms also run deer or have arable crops, we know that if earthquakes are strong evidence that pieces of Earth shift around with respect to other pieces, then the claim that either porcelain is characterized by a translucent and vitrified quality and fired to a high temperature or music has power does not correspond with reality. It is reasonable to believe that some farms also run deer or have arable crops. The claim that particles are particles only when they are in relationships has no merit. Either one or both of these statements are true: if a clinical trial is a trial, then grasshoppers only have one body cavity, that being their mouth, or most pet stores sell a variety of medicine, some for single diseases and some for multiple diseases. Once we know if a clinical trial is a trial, then grasshoppers only have one body cavity, that being their mouth, we also know that either particles are particles only when they are in relationships or if most abundant moisture increases height growth, then if if abortion is child abuse, then leopard geckos are carnivorous and feed mostly on invertebrates, then the claim that either porcelain is characterized by a translucent and vitrified quality and fired to a high temperature or music has power does not correspond with reality. Assuming most pet stores sell a variety of medicine, some for single diseases and some for multiple diseases, we know that either particles are particles only when they are in relationships or if most abundant moisture increases height growth, then if if abortion is child abuse, then leopard geckos are carnivorous and feed mostly on invertebrates, then the claim that either porcelain is characterized by a translucent and vitrified quality and fired to a high temperature or music has power does not correspond with reality.
|
We know that the claim that giraffes are also one of the fastest animals is false.
|
The claim that giraffes are also one of the fastest animals holds true.
|
FALSE
|
Modus Tonens:
If [0], then (Either [1] or [2].).
Not (Either [1] or [2].). [SC2-1]
Therefore, Not [0]..
[SC2-1]
Disjunction Elimination:
Either (If [3], then [4].) or [5]. [SC1-2]
If (If [3], then [4].), then (Not (Either [1] or [2].).). [SC2-2]
If [5], then (Not (Either [1] or [2].).). [SC3-2]
Therefore, Not (Either [1] or [2].)..
[SC1-2]
Modus Tonens:
If (Not (Either (If [3], then [4].) or [5].).), then (If [9], then [10].).
Not (If [9], then [10].).
Therefore, Either (If [3], then [4].) or [5]..
[SC2-2]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If (If [3], then [4].), then (Not (Either [1] or [2].).).). [SC2-3]
If [8], then (If (If [3], then [4].), then (Not (Either [1] or [2].).).).
Therefore, If (If [3], then [4].), then (Not (Either [1] or [2].).)..
[SC2-3]
Disjunctive Syllogism:
Either [11] or (If [7], then (If (If [3], then [4].), then (Not (Either [1] or [2].).).).). [SC1-4]
Not [11].
Therefore, If [7], then (If (If [3], then [4].), then (Not (Either [1] or [2].).).)..
[SC1-4]
Disjunction Elimination:
Either (If [12], then [13].) or [14].
If (If [12], then [13].), then (Either [11] or (If [7], then (If (If [3], then [4].), then (Not (Either [1] or [2].).).).).).
If [14], then (Either [11] or (If [7], then (If (If [3], then [4].), then (Not (Either [1] or [2].).).).).).
Therefore, Either [11] or (If [7], then (If (If [3], then [4].), then (Not (Either [1] or [2].).).).)..
[SC3-2]
Modus Ponens:
If [6], then (If [5], then (Not (Either [1] or [2].).).).
[6]
Therefore, If [5], then (Not (Either [1] or [2].).)..
|
{0: 'Giraffes are also one of the fastest animals.', 1: 'Porcelain is characterized by a translucent and vitrified quality and fired to a high temperature.', 2: 'Music has power.', 3: 'Abortion is child abuse.', 4: 'Leopard geckos are carnivorous and feed mostly on invertebrates.', 5: 'Earthquakes are strong evidence that pieces of Earth shift around with respect to other pieces.', 6: 'Some farms also run deer or have arable crops.', 7: 'Most abundant moisture increases height growth.', 8: 'Geochemistry embraces all aspects of the study of the Earth.', 9: "Pineapple chicken is on everyone's list of favorite things.", 10: 'Simple circuits involve motors.', 11: 'Particles are particles only when they are in relationships.', 12: 'A clinical trial is a trial.', 13: 'Grasshoppers only have one body cavity, that being their mouth.', 14: 'Most pet stores sell a variety of medicine, some for single diseases and some for multiple diseases.'}
| 7 |
6,401 |
['When the claim that consequently bathing can start only after the fire has died out has no merit is true, it follows that it is not true that boyfriends get dinner.', 'Should it be the case that the claim that if the claim that consequently bathing can start only after the fire has died out has no merit, then boyfriends get dinner does not reflect reality, it follows that mate contains numerous vitamins and minerals.', 'It is a fact that either phonemic awareness is a key predictor of spelling success or the claim that some people shoot pigs does not correspond with reality.', 'Some people mistakenly believe that phonemic awareness is a key predictor of spelling success.', 'When the claim that if the claim that if the claim that if the claim that consequently bathing can start only after the fire has died out has no merit, then boyfriends get dinner does not reflect reality, then the claim that mate contains numerous vitamins and minerals does not reflect reality is false, then some people shoot pigs is false is true, it follows that arranged marriages are still popular in rural villages.', "Whenever it is true that arranged marriages are still popular in rural villages, 'learned behaviors are traits that are learned' is true.", 'If learned behaviors are traits that are learned, then rams are tools.', 'The claim that rams are tools does not reflect reality.']
|
When the claim that consequently bathing can start only after the fire has died out has no merit is true, it follows that it is not true that boyfriends get dinner. Should it be the case that the claim that if the claim that consequently bathing can start only after the fire has died out has no merit, then boyfriends get dinner does not reflect reality, it follows that mate contains numerous vitamins and minerals. It is a fact that either phonemic awareness is a key predictor of spelling success or the claim that some people shoot pigs does not correspond with reality. Some people mistakenly believe that phonemic awareness is a key predictor of spelling success. When the claim that if the claim that if the claim that if the claim that consequently bathing can start only after the fire has died out has no merit, then boyfriends get dinner does not reflect reality, then the claim that mate contains numerous vitamins and minerals does not reflect reality is false, then some people shoot pigs is false is true, it follows that arranged marriages are still popular in rural villages. Whenever it is true that arranged marriages are still popular in rural villages, 'learned behaviors are traits that are learned' is true. If learned behaviors are traits that are learned, then rams are tools. The claim that rams are tools does not reflect reality.
|
It is the case that consequently bathing can start only after the fire has died out.
|
It is the case that consequently bathing can start only after the fire has died out.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then [1].).), then [2].
If (Not (If (Not [0].), then [1].).), then (Not [2].). [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Modus Tonens:
If (Not (If (Not (If (Not [0].), then [1].).), then (Not [2].).).), then [3]. [SC1-3]
Not [3]. [SC2-3]
Therefore, If (Not (If (Not [0].), then [1].).), then (Not [2].)..
[SC1-3]
Modus Tonens:
If (Not (If (Not (If (Not (If (Not [0].), then [1].).), then (Not [2].).).), then [3].).), then [5]. [SC1-4]
Not [5]. [SC2-4]
Therefore, If (Not (If (Not (If (Not [0].), then [1].).), then (Not [2].).).), then [3]..
[SC1-4]
Hypothetical Syllogism:
If (Not (If (Not (If (Not (If (Not [0].), then [1].).), then (Not [2].).).), then [3].).), then [7].
If [7], then [5].
Therefore, If (Not (If (Not (If (Not (If (Not [0].), then [1].).), then (Not [2].).).), then [3].).), then [5]..
[SC2-4]
Modus Tonens:
If [5], then [6].
Not [6].
Therefore, Not [5]..
[SC2-3]
Disjunctive Syllogism:
Either [4] or (Not [3].).
Not [4].
Therefore, Not [3]..
|
{0: 'Consequently bathing can start only after the fire has died out.', 1: 'Boyfriends get dinner.', 2: 'Mate contains numerous vitamins and minerals.', 3: 'Some people shoot pigs.', 4: 'Phonemic awareness is a key predictor of spelling success.', 5: 'Learned behaviors are traits that are learned.', 6: 'Rams are tools.', 7: 'Arranged marriages are still popular in rural villages.'}
| 7 |
6,530 |
['It is a fact that either water is vital for life itself, and worldwide water consumption is growing or myceliums have outer barriers.', 'One may reasonably assume that if myceliums have outer barriers, then the statement, either pumpkins are the most popular members of the squash family or herons shed feathers, does not hold.', 'Provided that water is vital for life itself, and worldwide water consumption is growing, we know that perennials are classified as either herbaceous or woody.', 'The claim that maglev trains float on a cushion of air, eliminating friction is false.', 'Once we know those that suggest if it is not true that if perennials are classified as either herbaceous or woody, then the statement, either pumpkins are the most popular members of the squash family or herons shed feathers, does not hold, then maglev trains float on a cushion of air, eliminating friction are wrong, we also know that truth is what makes fiction possible.', 'Either one or both of these statements are true: either pediatric hemochromatosis is very real and more and more cases are being identified every day or shallow breathing is like working a part-time job, or it is a common misconception that truth is what makes fiction possible.', 'Either one or both of these statements are true: unions are nonprofit financial organizations that are owned by their members, or the claim that either pediatric hemochromatosis is very real and more and more cases are being identified every day or shallow breathing is like working a part-time job does not reflect reality.', 'We know that at least one of two things is true: venom has cytotoxic effects, or the claim that unions are nonprofit financial organizations that are owned by their members is false.', 'Those that suggest venom has cytotoxic effects are wrong.']
|
It is a fact that either water is vital for life itself, and worldwide water consumption is growing or myceliums have outer barriers. One may reasonably assume that if myceliums have outer barriers, then the statement, either pumpkins are the most popular members of the squash family or herons shed feathers, does not hold. Provided that water is vital for life itself, and worldwide water consumption is growing, we know that perennials are classified as either herbaceous or woody. The claim that maglev trains float on a cushion of air, eliminating friction is false. Once we know those that suggest if it is not true that if perennials are classified as either herbaceous or woody, then the statement, either pumpkins are the most popular members of the squash family or herons shed feathers, does not hold, then maglev trains float on a cushion of air, eliminating friction are wrong, we also know that truth is what makes fiction possible. Either one or both of these statements are true: either pediatric hemochromatosis is very real and more and more cases are being identified every day or shallow breathing is like working a part-time job, or it is a common misconception that truth is what makes fiction possible. Either one or both of these statements are true: unions are nonprofit financial organizations that are owned by their members, or the claim that either pediatric hemochromatosis is very real and more and more cases are being identified every day or shallow breathing is like working a part-time job does not reflect reality. We know that at least one of two things is true: venom has cytotoxic effects, or the claim that unions are nonprofit financial organizations that are owned by their members is false. Those that suggest venom has cytotoxic effects are wrong.
|
The statement, either pumpkins are the most popular members of the squash family or herons shed feathers, does not hold.
|
The claim that pumpkins are actually a type of winter squash, with a hard rind is false.
|
Uncertain
|
Disjunction Elimination:
Either [2] or [3].
If [2], then (Not (Either [0] or [1].).). [SC2-1]
If [3], then (Not (Either [0] or [1].).).
Therefore, Not (Either [0] or [1].)..
[SC2-1]
Hypothetical Syllogism:
If [2], then [4].
If [4], then (Not (Either [0] or [1].).). [SC2-2]
Therefore, If [2], then (Not (Either [0] or [1].).)..
[SC2-2]
Modus Tonens:
If (Not (If [4], then (Not (Either [0] or [1].).).).), then [5]. [SC1-3]
Not [5].
Therefore, If [4], then (Not (Either [0] or [1].).)..
[SC1-3]
Modus Tonens:
If (Not (If (Not (If [4], then (Not (Either [0] or [1].).).).), then [5].).), then [6].
Not [6]. [SC2-4]
Therefore, If (Not (If [4], then (Not (Either [0] or [1].).).).), then [5]..
[SC2-4]
Disjunctive Syllogism:
Either (Either [7] or [8].) or (Not [6].).
Not (Either [7] or [8].). [SC2-5]
Therefore, Not [6]..
[SC2-5]
Disjunctive Syllogism:
Either [9] or (Not (Either [7] or [8].).).
Not [9]. [SC2-6]
Therefore, Not (Either [7] or [8].)..
[SC2-6]
Disjunctive Syllogism:
Either [10] or (Not [9].).
Not [10].
Therefore, Not [9]..
|
{0: 'Pumpkins are the most popular members of the squash family.', 1: 'Herons shed feathers.', 2: 'Water is vital for life itself, and worldwide water consumption is growing.', 3: 'Myceliums have outer barriers.', 4: 'Perennials are classified as either herbaceous or woody.', 5: 'Maglev trains float on a cushion of air, eliminating friction.', 6: 'Truth is what makes fiction possible.', 7: 'Pediatric hemochromatosis is very real and more and more cases are being identified every day.', 8: 'Shallow breathing is like working a part-time job.', 9: 'Unions are nonprofit financial organizations that are owned by their members.', 10: 'Venom has cytotoxic effects.'}
| 7 |
6,656 |
["The statement that 'if bacteria infect cattle, then iguanas come from a hot and humid environment, and are active during daylight hours' is incorrect.", 'At least one of two things is true: life has the power of manipulating the emotions, or either place mats are located in tables or either if bacteria infect cattle, then iguanas come from a hot and humid environment, and are active during daylight hours or either pregnancy involves a complex interplay of hormones or people love turtles.', 'The statement, life has the power of manipulating the emotions, does not hold.', "The statement 'ants have diets' can be considered false.", 'If bald eagles are located in pictures, then ants have diets.', 'There is good reason to believe that either most vibration creates sound waves or either bald eagles are located in pictures or if business is one of the games of life, then corms are vertical underground stem, and they grow thicker as they continue growing.', 'The statement, most vibration creates sound waves, does not hold.', 'Once we know diamonds have unusual properties, we also know that if if business is one of the games of life, then corms are vertical underground stem, and they grow thicker as they continue growing, then the claim that place mats are located in tables does not reflect reality.', 'The statement that states diamonds have unusual properties is right.']
|
The statement that 'if bacteria infect cattle, then iguanas come from a hot and humid environment, and are active during daylight hours' is incorrect. At least one of two things is true: life has the power of manipulating the emotions, or either place mats are located in tables or either if bacteria infect cattle, then iguanas come from a hot and humid environment, and are active during daylight hours or either pregnancy involves a complex interplay of hormones or people love turtles. The statement, life has the power of manipulating the emotions, does not hold. The statement 'ants have diets' can be considered false. If bald eagles are located in pictures, then ants have diets. There is good reason to believe that either most vibration creates sound waves or either bald eagles are located in pictures or if business is one of the games of life, then corms are vertical underground stem, and they grow thicker as they continue growing. The statement, most vibration creates sound waves, does not hold. Once we know diamonds have unusual properties, we also know that if if business is one of the games of life, then corms are vertical underground stem, and they grow thicker as they continue growing, then the claim that place mats are located in tables does not reflect reality. The statement that states diamonds have unusual properties is right.
|
It is rational to believe that either pregnancy involves a complex interplay of hormones or people love turtles.
|
Either one or both of these statements are true: most pregnancy affects fetuses, or some people recall having a variety of machinery scan their bodies.
|
Uncertain
|
Disjunctive Syllogism:
Either (If [2], then [3].) or (Either [0] or [1].). [SC1-1]
Not (If [2], then [3].).
Therefore, Either [0] or [1]..
[SC1-1]
Disjunctive Syllogism:
Either [4] or (Either (If [2], then [3].) or (Either [0] or [1].).). [SC1-2]
Not [4]. [SC2-2]
Therefore, Either (If [2], then [3].) or (Either [0] or [1].)..
[SC1-2]
Disjunctive Syllogism:
Either [6] or (Either [4] or (Either (If [2], then [3].) or (Either [0] or [1].).).).
Not [6].
Therefore, Either [4] or (Either (If [2], then [3].) or (Either [0] or [1].).)..
[SC2-2]
Disjunctive Syllogism:
Either [5] or (Not [4].). [SC1-3]
Not [5].
Therefore, Not [4]..
[SC1-3]
Constructive Dilemma:
Either [7] or (If [8], then [9].). [SC1-4]
If [7], then [5].
If (If [8], then [9].), then (Not [4].). [SC3-4]
Therefore, Either [5] or (Not [4].)..
[SC1-4]
Disjunctive Syllogism:
Either [10] or (Either [7] or (If [8], then [9].).).
Not [10].
Therefore, Either [7] or (If [8], then [9].)..
[SC3-4]
Modus Ponens:
If [11], then (If (If [8], then [9].), then (Not [4].).).
[11]
Therefore, If (If [8], then [9].), then (Not [4].)..
|
{0: 'Pregnancy involves a complex interplay of hormones.', 1: 'People love turtles.', 2: 'Bacteria infect cattle.', 3: 'Iguanas come from a hot and humid environment, and are active during daylight hours.', 4: 'Place mats are located in tables.', 5: 'Ants have diets.', 6: 'Life has the power of manipulating the emotions.', 7: 'Bald eagles are located in pictures.', 8: 'Business is one of the games of life.', 9: 'Corms are vertical underground stem, and they grow thicker as they continue growing.', 10: 'Most vibration creates sound waves.', 11: 'Diamonds have unusual properties.'}
| 7 |
6,441 |
['Either one or both of these statements are true: either thick necks support heads or many combination drugs contain unnecessary ingredients such as caffeine, or if artists create beautiful things in many different ways, like painting, drawing and sculpting, then hazardous chemicals are chemical substances.', 'We know that either either a daystar is a planet or outdoor polo is played with four riders per team or personality is defined as a combination of psychological traits that classifies a person.', "At least one of two things is true: either many companies selling caviar, seafood or other gourmet foods also sell salmon caviar or analogs usually take the form of white powder, or the notion that 'either thick necks support heads or many combination drugs contain unnecessary ingredients such as caffeine' is untrue.", 'Those that suggest either many companies selling caviar, seafood or other gourmet foods also sell salmon caviar or analogs usually take the form of white powder are wrong.', 'Given that it is not the case that if either a daystar is a planet or outdoor polo is played with four riders per team, then the claim that hazardous chemicals are chemical substances is false, it can be inferred that the claim that lice have appearances has no merit.', 'When aLL EYES have at least SOME astigmatism is true, it follows that if personality is defined as a combination of psychological traits that classifies a person, then the claim that hazardous chemicals are chemical substances is false.', 'Those that suggest aLL EYES have at least SOME astigmatism are right.', 'Should it be the case that it is not the case that if either a daystar is a planet or outdoor polo is played with four riders per team, then the claim that hazardous chemicals are chemical substances is false, it follows that if most sebaceous glands produce oily substances, then lines of latitude are parallel.', 'When if most sebaceous glands produce oily substances, then lines of latitude are parallel is true, it follows that lice have appearances.']
|
Either one or both of these statements are true: either thick necks support heads or many combination drugs contain unnecessary ingredients such as caffeine, or if artists create beautiful things in many different ways, like painting, drawing and sculpting, then hazardous chemicals are chemical substances. We know that either either a daystar is a planet or outdoor polo is played with four riders per team or personality is defined as a combination of psychological traits that classifies a person. At least one of two things is true: either many companies selling caviar, seafood or other gourmet foods also sell salmon caviar or analogs usually take the form of white powder, or the notion that 'either thick necks support heads or many combination drugs contain unnecessary ingredients such as caffeine' is untrue. Those that suggest either many companies selling caviar, seafood or other gourmet foods also sell salmon caviar or analogs usually take the form of white powder are wrong. Given that it is not the case that if either a daystar is a planet or outdoor polo is played with four riders per team, then the claim that hazardous chemicals are chemical substances is false, it can be inferred that the claim that lice have appearances has no merit. When aLL EYES have at least SOME astigmatism is true, it follows that if personality is defined as a combination of psychological traits that classifies a person, then the claim that hazardous chemicals are chemical substances is false. Those that suggest aLL EYES have at least SOME astigmatism are right. Should it be the case that it is not the case that if either a daystar is a planet or outdoor polo is played with four riders per team, then the claim that hazardous chemicals are chemical substances is false, it follows that if most sebaceous glands produce oily substances, then lines of latitude are parallel. When if most sebaceous glands produce oily substances, then lines of latitude are parallel is true, it follows that lice have appearances.
|
It is not true that artists create beautiful things in many different ways, like painting, drawing and sculpting.
|
It is not true that artists create beautiful things in many different ways, like painting, drawing and sculpting.
|
TRUE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either (Either [2] or [3].) or (If [0], then [1].).
Not (Either [2] or [3].). [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Disjunctive Syllogism:
Either (Either [9] or [10].) or (Not (Either [2] or [3].).).
Not (Either [9] or [10].).
Therefore, Not (Either [2] or [3].)..
[SC2-1]
Disjunction Elimination:
Either (Either [4] or [5].) or [6].
If (Either [4] or [5].), then (Not [1].). [SC2-2]
If [6], then (Not [1].). [SC3-2]
Therefore, Not [1]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Either [4] or [5].), then (Not [1].).).), then [8]. [SC1-3]
If (Not (If (Either [4] or [5].), then (Not [1].).).), then (Not [8].).
Therefore, If (Either [4] or [5].), then (Not [1].)..
[SC1-3]
Hypothetical Syllogism:
If (Not (If (Either [4] or [5].), then (Not [1].).).), then (If [11], then [12].).
If (If [11], then [12].), then [8].
Therefore, If (Not (If (Either [4] or [5].), then (Not [1].).).), then [8]..
[SC3-2]
Modus Ponens:
If [7], then (If [6], then (Not [1].).).
[7]
Therefore, If [6], then (Not [1].)..
|
{0: 'Artists create beautiful things in many different ways, like painting, drawing and sculpting.', 1: 'Hazardous chemicals are chemical substances.', 2: 'Thick necks support heads.', 3: 'Many combination drugs contain unnecessary ingredients such as caffeine.', 4: 'A daystar is a planet.', 5: 'Outdoor polo is played with four riders per team.', 6: 'Personality is defined as a combination of psychological traits that classifies a person.', 7: 'ALL EYES have at least SOME astigmatism.', 8: 'Lice have appearances.', 9: 'Many companies selling caviar, seafood or other gourmet foods also sell salmon caviar.', 10: 'Analogs usually take the form of white powder.', 11: 'Most sebaceous glands produce oily substances.', 12: 'Lines of latitude are parallel.'}
| 7 |
6,132 |
['When holy orders is the entering into the priesthood and involves a vow of chastity is true, it follows that if if oil spills are also deadly to loons, then children use thinking skills when making musical judgments and choices, then it is a common misconception that mathematicians have (part) necks.', "So long as showers use about a third as much water, 'if if oil spills are also deadly to loons, then children use thinking skills when making musical judgments and choices, then it is a common misconception that mathematicians have (part) necks' is true.", 'One may reasonably assume that if if insects can also hop onto houseplants and cause trouble later, then grapes are part of wine, then either holy orders is the entering into the priesthood and involves a vow of chastity or showers use about a third as much water.', 'There is good reason to believe that either some reproduction occurs in geckos or psychological needs can distort what people perceive and do.', "Whenever it is true that some reproduction occurs in geckos, 'if a rutabaga is a turnip, then if oil spills are also deadly to loons, then children use thinking skills when making musical judgments and choices' is true.", 'Once we know psychological needs can distort what people perceive and do, we also know that if a rutabaga is a turnip, then if oil spills are also deadly to loons, then children use thinking skills when making musical judgments and choices.', "So long as nyalas have (part) breasts, 'a rutabaga is a turnip' is true.", 'It is fair to say that nyalas have (part) breasts.', 'Once we know the statement, if insects can also hop onto houseplants and cause trouble later, then grapes are part of wine, does not hold, we also know that researchers seek careers.', 'One may reasonably assume that if the statement, if insects can also hop onto houseplants and cause trouble later, then grapes are part of wine, does not hold, then it is not true that researchers seek careers.']
|
When holy orders is the entering into the priesthood and involves a vow of chastity is true, it follows that if if oil spills are also deadly to loons, then children use thinking skills when making musical judgments and choices, then it is a common misconception that mathematicians have (part) necks. So long as showers use about a third as much water, 'if if oil spills are also deadly to loons, then children use thinking skills when making musical judgments and choices, then it is a common misconception that mathematicians have (part) necks' is true. One may reasonably assume that if if insects can also hop onto houseplants and cause trouble later, then grapes are part of wine, then either holy orders is the entering into the priesthood and involves a vow of chastity or showers use about a third as much water. There is good reason to believe that either some reproduction occurs in geckos or psychological needs can distort what people perceive and do. Whenever it is true that some reproduction occurs in geckos, 'if a rutabaga is a turnip, then if oil spills are also deadly to loons, then children use thinking skills when making musical judgments and choices' is true. Once we know psychological needs can distort what people perceive and do, we also know that if a rutabaga is a turnip, then if oil spills are also deadly to loons, then children use thinking skills when making musical judgments and choices. So long as nyalas have (part) breasts, 'a rutabaga is a turnip' is true. It is fair to say that nyalas have (part) breasts. Once we know the statement, if insects can also hop onto houseplants and cause trouble later, then grapes are part of wine, does not hold, we also know that researchers seek careers. One may reasonably assume that if the statement, if insects can also hop onto houseplants and cause trouble later, then grapes are part of wine, does not hold, then it is not true that researchers seek careers.
|
It is a common misconception that mathematicians have (part) necks.
|
We know that the claim that most mathematicians apply theories is false.
|
Uncertain
|
Modus Ponens:
If (If [1], then [2].), then (Not [0].). [SC1-1]
If [1], then [2]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (If (If [1], then [2].), then (Not [0].).).
If [4], then (If (If [1], then [2].), then (Not [0].).).
Therefore, If (If [1], then [2].), then (Not [0].)..
[SC1-2]
Modus Ponens:
If (If [7], then [8].), then (Either [3] or [4].).
If [7], then [8]. [SC2-3]
Therefore, Either [3] or [4]..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If [7], then [8].).), then [11].
If (Not (If [7], then [8].).), then (Not [11].).
Therefore, If [7], then [8]..
[SC2-1]
Modus Ponens:
If [5], then (If [1], then [2].). [SC1-2]
[5] [SC2-2]
Therefore, If [1], then [2]..
[SC1-2]
Disjunction Elimination:
Either [9] or [10].
If [9], then (If [5], then (If [1], then [2].).).
If [10], then (If [5], then (If [1], then [2].).).
Therefore, If [5], then (If [1], then [2].)..
[SC2-2]
Modus Ponens:
If [6], then [5].
[6]
Therefore, [5].
|
{0: 'Mathematicians have (part) necks.', 1: 'Oil spills are also deadly to loons.', 2: 'Children use thinking skills when making musical judgments and choices.', 3: 'Holy orders is the entering into the priesthood and involves a vow of chastity.', 4: 'Showers use about a third as much water.', 5: 'A rutabaga is a turnip.', 6: 'Nyalas have (part) breasts.', 7: 'Insects can also hop onto houseplants and cause trouble later.', 8: 'Grapes are part of wine.', 9: 'Some reproduction occurs in geckos.', 10: 'Psychological needs can distort what people perceive and do.', 11: 'Researchers seek careers.'}
| 7 |
6,233 |
['It is a common misconception that psychological state plays an immense role in physical potential.', 'Given that a geodesy is a geology, it can be inferred that either some dogs provide nutrients or immunogen is antigen.', 'It is rational to believe that either either locker rooms are rooms or some adjectives change their meaning depending on whether they are used with ser or with estar or if some dogs provide nutrients, then either psychological state plays an immense role in physical potential or those that suggest either chemistry is a fundamental topic for many disciplines or hormones are the blood-born molecules that regulate our metabolic and reproductive functions are wrong.', 'Those that suggest either locker rooms are rooms or some adjectives change their meaning depending on whether they are used with ser or with estar are wrong.', 'We know that either procedures are the steps to accomplishing a specific task in accordance within an organization or psychiatrists are often reluctant to deal with violent children.', 'On the condition that procedures are the steps to accomplishing a specific task in accordance within an organization, it is definitely the case that if immunogen is antigen, then either psychological state plays an immense role in physical potential or those that suggest either chemistry is a fundamental topic for many disciplines or hormones are the blood-born molecules that regulate our metabolic and reproductive functions are wrong.', "Whenever it is true that psychiatrists are often reluctant to deal with violent children, 'if immunogen is antigen, then either psychological state plays an immense role in physical potential or those that suggest either chemistry is a fundamental topic for many disciplines or hormones are the blood-born molecules that regulate our metabolic and reproductive functions are wrong' is true.", "If the statement 'a geodesy is a geology' can be considered false, then peregrine falcons perch in trees.", 'We know that either robbery is the unlawful taking of property from an individual by force or threat of violence or it is a common misconception that peregrine falcons perch in trees.', 'Some people mistakenly believe that robbery is the unlawful taking of property from an individual by force or threat of violence.']
|
It is a common misconception that psychological state plays an immense role in physical potential. Given that a geodesy is a geology, it can be inferred that either some dogs provide nutrients or immunogen is antigen. It is rational to believe that either either locker rooms are rooms or some adjectives change their meaning depending on whether they are used with ser or with estar or if some dogs provide nutrients, then either psychological state plays an immense role in physical potential or those that suggest either chemistry is a fundamental topic for many disciplines or hormones are the blood-born molecules that regulate our metabolic and reproductive functions are wrong. Those that suggest either locker rooms are rooms or some adjectives change their meaning depending on whether they are used with ser or with estar are wrong. We know that either procedures are the steps to accomplishing a specific task in accordance within an organization or psychiatrists are often reluctant to deal with violent children. On the condition that procedures are the steps to accomplishing a specific task in accordance within an organization, it is definitely the case that if immunogen is antigen, then either psychological state plays an immense role in physical potential or those that suggest either chemistry is a fundamental topic for many disciplines or hormones are the blood-born molecules that regulate our metabolic and reproductive functions are wrong. Whenever it is true that psychiatrists are often reluctant to deal with violent children, 'if immunogen is antigen, then either psychological state plays an immense role in physical potential or those that suggest either chemistry is a fundamental topic for many disciplines or hormones are the blood-born molecules that regulate our metabolic and reproductive functions are wrong' is true. If the statement 'a geodesy is a geology' can be considered false, then peregrine falcons perch in trees. We know that either robbery is the unlawful taking of property from an individual by force or threat of violence or it is a common misconception that peregrine falcons perch in trees. Some people mistakenly believe that robbery is the unlawful taking of property from an individual by force or threat of violence.
|
Those that suggest either chemistry is a fundamental topic for many disciplines or hormones are the blood-born molecules that regulate our metabolic and reproductive functions are wrong.
|
The claim that chemistry is the study of matter does not correspond with reality.
|
Uncertain
|
Disjunctive Syllogism:
Either [2] or (Not (Either [0] or [1].).). [SC1-1]
Not [2].
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (Either [2] or (Not (Either [0] or [1].).).). [SC2-2]
If [4], then (Either [2] or (Not (Either [0] or [1].).).). [SC3-2]
Therefore, Either [2] or (Not (Either [0] or [1].).)..
[SC1-2]
Modus Ponens:
If [7], then (Either [3] or [4].).
[7] [SC2-3]
Therefore, Either [3] or [4]..
[SC2-3]
Modus Tonens:
If (Not [7].), then [10].
Not [10]. [SC2-4]
Therefore, [7].
[SC2-4]
Disjunctive Syllogism:
Either [11] or (Not [10].).
Not [11].
Therefore, Not [10]..
[SC2-2]
Disjunctive Syllogism:
Either (Either [5] or [6].) or (If [3], then (Either [2] or (Not (Either [0] or [1].).).).).
Not (Either [5] or [6].).
Therefore, If [3], then (Either [2] or (Not (Either [0] or [1].).).)..
[SC3-2]
Disjunction Elimination:
Either [8] or [9].
If [8], then (If [4], then (Either [2] or (Not (Either [0] or [1].).).).).
If [9], then (If [4], then (Either [2] or (Not (Either [0] or [1].).).).).
Therefore, If [4], then (Either [2] or (Not (Either [0] or [1].).).)..
|
{0: 'Chemistry is a fundamental topic for many disciplines.', 1: 'Hormones are the blood-born molecules that regulate our metabolic and reproductive functions.', 2: 'Psychological state plays an immense role in physical potential.', 3: 'Some dogs provide nutrients.', 4: 'Immunogen is antigen.', 5: 'Locker rooms are rooms.', 6: 'Some adjectives change their meaning depending on whether they are used with ser or with estar.', 7: 'A geodesy is a geology.', 8: 'Procedures are the steps to accomplishing a specific task in accordance within an organization.', 9: 'Psychiatrists are often reluctant to deal with violent children.', 10: 'Peregrine falcons perch in trees.', 11: 'Robbery is the unlawful taking of property from an individual by force or threat of violence.'}
| 7 |
6,173 |
['Assuming depression is a broad term that describes several depressive illnesses, we know that a blue jay is a jay.', 'It is a fact that either tariffs are a deliberate effort to alter spending priorities geographically or blind faith is no faith at all.', 'Once we know tariffs are a deliberate effort to alter spending priorities geographically, we also know that if drought changes patterns, then if if depression is a broad term that describes several depressive illnesses, then a blue jay is a jay, then if magnets are a medically accepted form of therapy for pain and healing, then computer scientists view neural networks as one of a family of architectures for machine learning.', 'If blind faith is no faith at all, then if drought changes patterns, then if if depression is a broad term that describes several depressive illnesses, then a blue jay is a jay, then if magnets are a medically accepted form of therapy for pain and healing, then computer scientists view neural networks as one of a family of architectures for machine learning.', 'Once we know exudation is usually the result of inflammation, we also know that drought changes patterns.', 'Given that music is the discipline concerned with the production, analysis, and appreciation of musical sound, it can be inferred that if the claim that exudation is usually the result of inflammation does not reflect reality, then electronic books are different animals.', 'It is the case that music is the discipline concerned with the production, analysis, and appreciation of musical sound.', 'At least one of two things is true: barns have (part) hinges, or lions are unusual amongst the cat species because they are social animals, living in prides.', 'If barns have (part) hinges, then the claim that electronic books are different animals does not reflect reality.', 'Assuming lions are unusual amongst the cat species because they are social animals, living in prides, we know that the claim that electronic books are different animals does not reflect reality.']
|
Assuming depression is a broad term that describes several depressive illnesses, we know that a blue jay is a jay. It is a fact that either tariffs are a deliberate effort to alter spending priorities geographically or blind faith is no faith at all. Once we know tariffs are a deliberate effort to alter spending priorities geographically, we also know that if drought changes patterns, then if if depression is a broad term that describes several depressive illnesses, then a blue jay is a jay, then if magnets are a medically accepted form of therapy for pain and healing, then computer scientists view neural networks as one of a family of architectures for machine learning. If blind faith is no faith at all, then if drought changes patterns, then if if depression is a broad term that describes several depressive illnesses, then a blue jay is a jay, then if magnets are a medically accepted form of therapy for pain and healing, then computer scientists view neural networks as one of a family of architectures for machine learning. Once we know exudation is usually the result of inflammation, we also know that drought changes patterns. Given that music is the discipline concerned with the production, analysis, and appreciation of musical sound, it can be inferred that if the claim that exudation is usually the result of inflammation does not reflect reality, then electronic books are different animals. It is the case that music is the discipline concerned with the production, analysis, and appreciation of musical sound. At least one of two things is true: barns have (part) hinges, or lions are unusual amongst the cat species because they are social animals, living in prides. If barns have (part) hinges, then the claim that electronic books are different animals does not reflect reality. Assuming lions are unusual amongst the cat species because they are social animals, living in prides, we know that the claim that electronic books are different animals does not reflect reality.
|
Provided that magnets are a medically accepted form of therapy for pain and healing, we know that computer scientists view neural networks as one of a family of architectures for machine learning
|
Provided that magnets are a medically accepted form of therapy for pain and healing, we know that computer scientists view neural networks as one of a family of architectures for machine learning
|
TRUE
|
Modus Ponens:
If (If [2], then [3].), then (If [0], then [1].). [SC1-1]
If [2], then [3].
Therefore, If [0], then [1]..
[SC1-1]
Modus Ponens:
If [4], then (If (If [2], then [3].), then (If [0], then [1].).). [SC1-2]
[4] [SC2-2]
Therefore, If (If [2], then [3].), then (If [0], then [1].)..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [4], then (If (If [2], then [3].), then (If [0], then [1].).).).
If [6], then (If [4], then (If (If [2], then [3].), then (If [0], then [1].).).).
Therefore, If [4], then (If (If [2], then [3].), then (If [0], then [1].).)..
[SC2-2]
Modus Ponens:
If [7], then [4].
[7] [SC2-3]
Therefore, [4].
[SC2-3]
Modus Tonens:
If (Not [7].), then [8]. [SC1-4]
Not [8]. [SC2-4]
Therefore, [7].
[SC1-4]
Modus Ponens:
If [9], then (If (Not [7].), then [8].).
[9]
Therefore, If (Not [7].), then [8]..
[SC2-4]
Disjunction Elimination:
Either [10] or [11].
If [10], then (Not [8].).
If [11], then (Not [8].).
Therefore, Not [8]..
|
{0: 'Magnets are a medically accepted form of therapy for pain and healing.', 1: 'Computer scientists view neural networks as one of a family of architectures for machine learning.', 2: 'Depression is a broad term that describes several depressive illnesses.', 3: 'A blue jay is a jay.', 4: 'Drought changes patterns.', 5: 'Tariffs are a deliberate effort to alter spending priorities geographically.', 6: 'Blind faith is no faith at all.', 7: 'Exudation is usually the result of inflammation.', 8: 'Electronic books are different animals.', 9: 'Music is the discipline concerned with the production, analysis, and appreciation of musical sound.', 10: 'Barns have (part) hinges.', 11: 'Lions are unusual amongst the cat species because they are social animals, living in prides.'}
| 7 |
6,428 |
['Should it be the case that the claim that if the claim that platforms shoes are more comfortable and safer to wear when the heel height is higher does not correspond with reality, then anxiety can cause prolonged labor and inefficient uterine contractions is false, it follows that agencies launch investigations.', "So long as the claim that if the claim that platforms shoes are more comfortable and safer to wear when the heel height is higher does not correspond with reality, then anxiety can cause prolonged labor and inefficient uterine contractions is false, 'the claim that agencies launch investigations does not correspond with reality' is true.", 'Provided that alcoholism is a brain disease, and the brain is still a frontier for biological research, we know that if the claim that platforms shoes are more comfortable and safer to wear when the heel height is higher does not correspond with reality, then some people mistakenly believe that anxiety can cause prolonged labor and inefficient uterine contractions.', "Given that the notion that 'either if a thallophyte is a cryptogam, then music is basically sound produced by vibrations or alcoholism is a brain disease, and the brain is still a frontier for biological research' is untrue, it can be inferred that some sauces make from cayenne pepper.", 'Either if skunk spray is liquids, then most people actually claim for fewer animals than they have in case they lose a few or wings have triangular shapes.', 'Given that if skunk spray is liquids, then most people actually claim for fewer animals than they have in case they lose a few, it can be inferred that if if a thallophyte is a cryptogam, then music is basically sound produced by vibrations, then if the claim that platforms shoes are more comfortable and safer to wear when the heel height is higher does not correspond with reality, then some people mistakenly believe that anxiety can cause prolonged labor and inefficient uterine contractions.', "So long as wings have triangular shapes, 'if if a thallophyte is a cryptogam, then music is basically sound produced by vibrations, then if the claim that platforms shoes are more comfortable and safer to wear when the heel height is higher does not correspond with reality, then some people mistakenly believe that anxiety can cause prolonged labor and inefficient uterine contractions' is true.", "So long as house wrens migrate south to winter in southern coastal states, 'the statement, some sauces make from cayenne pepper, does not hold' is true.", "At least one of two things is true: humans have arrangements, or if the notion that 'either if a thallophyte is a cryptogam, then music is basically sound produced by vibrations or alcoholism is a brain disease, and the brain is still a frontier for biological research' is untrue, then house wrens migrate south to winter in southern coastal states.", 'The claim that humans have arrangements does not reflect reality.']
|
Should it be the case that the claim that if the claim that platforms shoes are more comfortable and safer to wear when the heel height is higher does not correspond with reality, then anxiety can cause prolonged labor and inefficient uterine contractions is false, it follows that agencies launch investigations. So long as the claim that if the claim that platforms shoes are more comfortable and safer to wear when the heel height is higher does not correspond with reality, then anxiety can cause prolonged labor and inefficient uterine contractions is false, 'the claim that agencies launch investigations does not correspond with reality' is true. Provided that alcoholism is a brain disease, and the brain is still a frontier for biological research, we know that if the claim that platforms shoes are more comfortable and safer to wear when the heel height is higher does not correspond with reality, then some people mistakenly believe that anxiety can cause prolonged labor and inefficient uterine contractions. Given that the notion that 'either if a thallophyte is a cryptogam, then music is basically sound produced by vibrations or alcoholism is a brain disease, and the brain is still a frontier for biological research' is untrue, it can be inferred that some sauces make from cayenne pepper. Either if skunk spray is liquids, then most people actually claim for fewer animals than they have in case they lose a few or wings have triangular shapes. Given that if skunk spray is liquids, then most people actually claim for fewer animals than they have in case they lose a few, it can be inferred that if if a thallophyte is a cryptogam, then music is basically sound produced by vibrations, then if the claim that platforms shoes are more comfortable and safer to wear when the heel height is higher does not correspond with reality, then some people mistakenly believe that anxiety can cause prolonged labor and inefficient uterine contractions. So long as wings have triangular shapes, 'if if a thallophyte is a cryptogam, then music is basically sound produced by vibrations, then if the claim that platforms shoes are more comfortable and safer to wear when the heel height is higher does not correspond with reality, then some people mistakenly believe that anxiety can cause prolonged labor and inefficient uterine contractions' is true. So long as house wrens migrate south to winter in southern coastal states, 'the statement, some sauces make from cayenne pepper, does not hold' is true. At least one of two things is true: humans have arrangements, or if the notion that 'either if a thallophyte is a cryptogam, then music is basically sound produced by vibrations or alcoholism is a brain disease, and the brain is still a frontier for biological research' is untrue, then house wrens migrate south to winter in southern coastal states. The claim that humans have arrangements does not reflect reality.
|
It is rational to agree that platforms shoes are more comfortable and safer to wear when the heel height is higher.
|
It is rational to agree that platforms shoes are more comfortable and safer to wear when the heel height is higher.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then [1].).), then [2].
If (Not (If (Not [0].), then [1].).), then (Not [2].).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunction Elimination:
Either (If [3], then [4].) or [5]. [SC1-2]
If (If [3], then [4].), then (If (Not [0].), then (Not [1].).). [SC2-2]
If [5], then (If (Not [0].), then (Not [1].).).
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either (If [3], then [4].) or [5].).), then [6].
If (Not (Either (If [3], then [4].) or [5].).), then (Not [6].). [SC2-3]
Therefore, Either (If [3], then [4].) or [5]..
[SC2-3]
Hypothetical Syllogism:
If (Not (Either (If [3], then [4].) or [5].).), then [10]. [SC1-4]
If [10], then (Not [6].).
Therefore, If (Not (Either (If [3], then [4].) or [5].).), then (Not [6].)..
[SC1-4]
Disjunctive Syllogism:
Either [11] or (If (Not (Either (If [3], then [4].) or [5].).), then [10].).
Not [11].
Therefore, If (Not (Either (If [3], then [4].) or [5].).), then [10]..
[SC2-2]
Disjunction Elimination:
Either (If [7], then [8].) or [9].
If (If [7], then [8].), then (If (If [3], then [4].), then (If (Not [0].), then (Not [1].).).).
If [9], then (If (If [3], then [4].), then (If (Not [0].), then (Not [1].).).).
Therefore, If (If [3], then [4].), then (If (Not [0].), then (Not [1].).)..
|
{0: 'Platforms shoes are more comfortable and safer to wear when the heel height is higher.', 1: 'Anxiety can cause prolonged labor and inefficient uterine contractions.', 2: 'Agencies launch investigations.', 3: 'A thallophyte is a cryptogam.', 4: 'Music is basically sound produced by vibrations.', 5: 'Alcoholism is a brain disease, and the brain is still a frontier for biological research.', 6: 'Some sauces make from cayenne pepper.', 7: 'Skunk spray is liquids.', 8: 'Most people actually claim for fewer animals than they have in case they lose a few.', 9: 'Wings have triangular shapes.', 10: 'House wrens migrate south to winter in southern coastal states.', 11: 'Humans have arrangements.'}
| 7 |
6,567 |
['Assuming copper is a conductor, we know that if all moons circle a planet, then trees reduce air-conditioning costs, reducing dependency on oil.', 'Given that some people have mild manias, called hypomanias, and others have wild manias, it can be inferred that if if all moons circle a planet, then trees reduce air-conditioning costs, reducing dependency on oil, then diets consist of fresh food.', 'Either hockey is religion up North or if baseball has interleague play, then copper is a conductor.', 'Those that suggest hockey is religion up North are wrong.', "Whenever it is true that the claim that some people have mild manias, called hypomanias, and others have wild manias does not reflect reality, 'art can convey love, symmetry, and harmony' is true.", "One may reasonably assume that if art can convey love, symmetry, and harmony, then the statement 'anoraks have (part) hems' can be considered false.", "So long as the statement 'if art can convey love, symmetry, and harmony, then anoraks have (part) hems' can be considered false, 'arrowheads identify the same canal in both sections, showing the colocalization of both proteins' is true.", "One may reasonably assume that if the statement 'if art can convey love, symmetry, and harmony, then anoraks have (part) hems' can be considered false, then the notion that 'arrowheads identify the same canal in both sections, showing the colocalization of both proteins' is untrue."]
|
Assuming copper is a conductor, we know that if all moons circle a planet, then trees reduce air-conditioning costs, reducing dependency on oil. Given that some people have mild manias, called hypomanias, and others have wild manias, it can be inferred that if if all moons circle a planet, then trees reduce air-conditioning costs, reducing dependency on oil, then diets consist of fresh food. Either hockey is religion up North or if baseball has interleague play, then copper is a conductor. Those that suggest hockey is religion up North are wrong. Whenever it is true that the claim that some people have mild manias, called hypomanias, and others have wild manias does not reflect reality, 'art can convey love, symmetry, and harmony' is true. One may reasonably assume that if art can convey love, symmetry, and harmony, then the statement 'anoraks have (part) hems' can be considered false. So long as the statement 'if art can convey love, symmetry, and harmony, then anoraks have (part) hems' can be considered false, 'arrowheads identify the same canal in both sections, showing the colocalization of both proteins' is true. One may reasonably assume that if the statement 'if art can convey love, symmetry, and harmony, then anoraks have (part) hems' can be considered false, then the notion that 'arrowheads identify the same canal in both sections, showing the colocalization of both proteins' is untrue.
|
Once we know baseball has interleague play, we also know that diets consist of fresh food.
|
Once we know baseball has interleague play, we also know that diets consist of fresh food.
|
TRUE
|
Hypothetical Syllogism:
If [0], then (If [2], then [3].). [SC1-1]
If (If [2], then [3].), then [1]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Hypothetical Syllogism:
If [0], then [5]. [SC1-2]
If [5], then (If [2], then [3].).
Therefore, If [0], then (If [2], then [3].)..
[SC1-2]
Disjunctive Syllogism:
Either [7] or (If [0], then [5].).
Not [7].
Therefore, If [0], then [5]..
[SC2-1]
Modus Ponens:
If [4], then (If (If [2], then [3].), then [1].).
[4] [SC2-2]
Therefore, If (If [2], then [3].), then [1]..
[SC2-2]
Modus Tonens:
If (Not [4].), then [6].
Not [6]. [SC2-3]
Therefore, [4].
[SC2-3]
Reductio Ad Absurdum:
If [6], then [8]. [SC1-4]
If [6], then (Not [8].).
Therefore, Not [6]..
[SC1-4]
Reductio Ad Absurdum:
If (Not (If [6], then [8].).), then [9].
If (Not (If [6], then [8].).), then (Not [9].).
Therefore, If [6], then [8]..
|
{0: 'Baseball has interleague play.', 1: 'Diets consist of fresh food.', 2: 'All moons circle a planet.', 3: 'Trees reduce air-conditioning costs, reducing dependency on oil.', 4: 'Some people have mild manias, called hypomanias, and others have wild manias.', 5: 'Copper is a conductor.', 6: 'Art can convey love, symmetry, and harmony.', 7: 'Hockey is religion up North.', 8: 'Anoraks have (part) hems.', 9: 'Arrowheads identify the same canal in both sections, showing the colocalization of both proteins.'}
| 7 |
6,967 |
['On the condition that the claim that if the claim that g is a mass unit does not reflect reality, then market competition is the discovery of comparative advantages does not correspond with reality, it is definitely the case that plasma carries the blood cells throughout the body and contains proteins, vitamins, and minerals.', 'Provided that market competition is the discovery of comparative advantages, we know that if dogwoods are wood, then higher frequencies correspond to features of smaller angular extent.', "It is a fact that either most scavengers feed on decompose plants or if the claim that if the claim that g is a mass unit does not reflect reality, then market competition is the discovery of comparative advantages does not correspond with reality, then the notion that 'plasma carries the blood cells throughout the body and contains proteins, vitamins, and minerals' is untrue.", "The notion that 'most scavengers feed on decompose plants' is untrue.", 'It is rational to believe that either beverages made from kava root are a time-honored adjunct to ceremonial life in Oceania or most substances stimulate immune responses.', 'Should it be the case that it is not the case that if beverages made from kava root are a time-honored adjunct to ceremonial life in Oceania, then if market competition is the discovery of comparative advantages, then those that suggest if dogwoods are wood, then higher frequencies correspond to features of smaller angular extent are wrong, it follows that most vehicles carry people.', 'Given that it is not the case that if beverages made from kava root are a time-honored adjunct to ceremonial life in Oceania, then if market competition is the discovery of comparative advantages, then those that suggest if dogwoods are wood, then higher frequencies correspond to features of smaller angular extent are wrong, it can be inferred that those that suggest most vehicles carry people are wrong.', "Provided that the notion that 'if most substances stimulate immune responses, then if market competition is the discovery of comparative advantages, then those that suggest if dogwoods are wood, then higher frequencies correspond to features of smaller angular extent are wrong' is untrue, we know that either mystery isa condition or carnivorous species have sharp hooked beaks to grasp and slice animal prey.", "Whenever it is true that the notion that 'if most substances stimulate immune responses, then if market competition is the discovery of comparative advantages, then those that suggest if dogwoods are wood, then higher frequencies correspond to features of smaller angular extent are wrong' is untrue, 'those that suggest either mystery isa condition or carnivorous species have sharp hooked beaks to grasp and slice animal prey are wrong' is true."]
|
On the condition that the claim that if the claim that g is a mass unit does not reflect reality, then market competition is the discovery of comparative advantages does not correspond with reality, it is definitely the case that plasma carries the blood cells throughout the body and contains proteins, vitamins, and minerals. Provided that market competition is the discovery of comparative advantages, we know that if dogwoods are wood, then higher frequencies correspond to features of smaller angular extent. It is a fact that either most scavengers feed on decompose plants or if the claim that if the claim that g is a mass unit does not reflect reality, then market competition is the discovery of comparative advantages does not correspond with reality, then the notion that 'plasma carries the blood cells throughout the body and contains proteins, vitamins, and minerals' is untrue. The notion that 'most scavengers feed on decompose plants' is untrue. It is rational to believe that either beverages made from kava root are a time-honored adjunct to ceremonial life in Oceania or most substances stimulate immune responses. Should it be the case that it is not the case that if beverages made from kava root are a time-honored adjunct to ceremonial life in Oceania, then if market competition is the discovery of comparative advantages, then those that suggest if dogwoods are wood, then higher frequencies correspond to features of smaller angular extent are wrong, it follows that most vehicles carry people. Given that it is not the case that if beverages made from kava root are a time-honored adjunct to ceremonial life in Oceania, then if market competition is the discovery of comparative advantages, then those that suggest if dogwoods are wood, then higher frequencies correspond to features of smaller angular extent are wrong, it can be inferred that those that suggest most vehicles carry people are wrong. Provided that the notion that 'if most substances stimulate immune responses, then if market competition is the discovery of comparative advantages, then those that suggest if dogwoods are wood, then higher frequencies correspond to features of smaller angular extent are wrong' is untrue, we know that either mystery isa condition or carnivorous species have sharp hooked beaks to grasp and slice animal prey. Whenever it is true that the notion that 'if most substances stimulate immune responses, then if market competition is the discovery of comparative advantages, then those that suggest if dogwoods are wood, then higher frequencies correspond to features of smaller angular extent are wrong' is untrue, 'those that suggest either mystery isa condition or carnivorous species have sharp hooked beaks to grasp and slice animal prey are wrong' is true.
|
The idea that g is a mass unit is true.
|
The idea that g is a mass unit is true.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then [1].).), then [2].
If (Not (If (Not [0].), then [1].).), then (Not [2].). [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Disjunctive Syllogism:
Either [5] or (If (Not (If (Not [0].), then [1].).), then (Not [2].).).
Not [5].
Therefore, If (Not (If (Not [0].), then [1].).), then (Not [2].)..
[SC2-1]
Reductio Ad Absurdum:
If [1], then (If [3], then [4].).
If [1], then (Not (If [3], then [4].).). [SC2-2]
Therefore, Not [1]..
[SC2-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If [1], then (Not (If [3], then [4].).).). [SC2-3]
If [7], then (If [1], then (Not (If [3], then [4].).).). [SC3-3]
Therefore, If [1], then (Not (If [3], then [4].).)..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If [6], then (If [1], then (Not (If [3], then [4].).).).).), then [8].
If (Not (If [6], then (If [1], then (Not (If [3], then [4].).).).).), then (Not [8].).
Therefore, If [6], then (If [1], then (Not (If [3], then [4].).).)..
[SC3-3]
Reductio Ad Absurdum:
If (Not (If [7], then (If [1], then (Not (If [3], then [4].).).).).), then (Either [9] or [10].).
If (Not (If [7], then (If [1], then (Not (If [3], then [4].).).).).), then (Not (Either [9] or [10].).).
Therefore, If [7], then (If [1], then (Not (If [3], then [4].).).)..
|
{0: 'G is a mass unit.', 1: 'Market competition is the discovery of comparative advantages.', 2: 'Plasma carries the blood cells throughout the body and contains proteins, vitamins, and minerals.', 3: 'Dogwoods are wood.', 4: 'Higher frequencies correspond to features of smaller angular extent.', 5: 'Most scavengers feed on decompose plants.', 6: 'Beverages made from kava root are a time-honored adjunct to ceremonial life in Oceania.', 7: 'Most substances stimulate immune responses.', 8: 'Most vehicles carry people.', 9: 'Mystery isa condition.', 10: 'Carnivorous species have sharp hooked beaks to grasp and slice animal prey.'}
| 7 |
6,758 |
["So long as philosophy is a tradition replete with techniques for keeping conversation alive, 'glaucoma occurs in Tasmania at the same frequency as elsewhere in Australia' is true.", "So long as some life depends on radiant energy, 'glaucoma occurs in Tasmania at the same frequency as elsewhere in Australia' is true.", 'Once we know the claim that either philosophy is a tradition replete with techniques for keeping conversation alive or some life depends on radiant energy has no merit, we also know that guerezas have (part) brains.', "Whenever it is true that guerezas have (part) brains, 'instances result in actions' is true.", 'It is rational to believe that either trees weakened by defoliation can become more susceptible to other pests or if corporate mergers add to corporate profits, but place populations at risk, then problems result from lack.', 'We know that either birds have arteries or if trees weakened by defoliation can become more susceptible to other pests, then the claim that instances result in actions does not correspond with reality.', "The statement 'birds have arteries' can be considered false.", 'The claim that if games are diversion, then most predators have enemies does not reflect reality.', 'When the claim that either if games are diversion, then most predators have enemies or if if corporate mergers add to corporate profits, but place populations at risk, then problems result from lack, then the claim that instances result in actions does not correspond with reality has no merit is true, it follows that some states have stricter regulations concerning homeschool than others.', 'It is not the case that some states have stricter regulations concerning homeschool than others.']
|
So long as philosophy is a tradition replete with techniques for keeping conversation alive, 'glaucoma occurs in Tasmania at the same frequency as elsewhere in Australia' is true. So long as some life depends on radiant energy, 'glaucoma occurs in Tasmania at the same frequency as elsewhere in Australia' is true. Once we know the claim that either philosophy is a tradition replete with techniques for keeping conversation alive or some life depends on radiant energy has no merit, we also know that guerezas have (part) brains. Whenever it is true that guerezas have (part) brains, 'instances result in actions' is true. It is rational to believe that either trees weakened by defoliation can become more susceptible to other pests or if corporate mergers add to corporate profits, but place populations at risk, then problems result from lack. We know that either birds have arteries or if trees weakened by defoliation can become more susceptible to other pests, then the claim that instances result in actions does not correspond with reality. The statement 'birds have arteries' can be considered false. The claim that if games are diversion, then most predators have enemies does not reflect reality. When the claim that either if games are diversion, then most predators have enemies or if if corporate mergers add to corporate profits, but place populations at risk, then problems result from lack, then the claim that instances result in actions does not correspond with reality has no merit is true, it follows that some states have stricter regulations concerning homeschool than others. It is not the case that some states have stricter regulations concerning homeschool than others.
|
The statement 'glaucoma occurs in Tasmania at the same frequency as elsewhere in Australia' can be considered true.
|
Glaucoma can eventually lead to irreversible blindness.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0].
If [2], then [0].
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either [1] or [2].).), then [3]. [SC1-2]
Not [3]. [SC2-2]
Therefore, Either [1] or [2]..
[SC1-2]
Hypothetical Syllogism:
If (Not (Either [1] or [2].).), then [4].
If [4], then [3].
Therefore, If (Not (Either [1] or [2].).), then [3]..
[SC2-2]
Disjunction Elimination:
Either [5] or (If [6], then [7].).
If [5], then (Not [3].). [SC2-3]
If (If [6], then [7].), then (Not [3].). [SC3-3]
Therefore, Not [3]..
[SC2-3]
Disjunctive Syllogism:
Either [10] or (If [5], then (Not [3].).).
Not [10].
Therefore, If [5], then (Not [3].)..
[SC3-3]
Disjunctive Syllogism:
Either (If [8], then [9].) or (If (If [6], then [7].), then (Not [3].).). [SC1-4]
Not (If [8], then [9].).
Therefore, If (If [6], then [7].), then (Not [3].)..
[SC1-4]
Modus Tonens:
If (Not (Either (If [8], then [9].) or (If (If [6], then [7].), then (Not [3].).).).), then [11].
Not [11].
Therefore, Either (If [8], then [9].) or (If (If [6], then [7].), then (Not [3].).)..
|
{0: 'Glaucoma occurs in Tasmania at the same frequency as elsewhere in Australia.', 1: 'Philosophy is a tradition replete with techniques for keeping conversation alive.', 2: 'Some life depends on radiant energy.', 3: 'Instances result in actions.', 4: 'Guerezas have (part) brains.', 5: 'Trees weakened by defoliation can become more susceptible to other pests.', 6: 'Corporate mergers add to corporate profits, but place populations at risk.', 7: 'Problems result from lack.', 8: 'Games are diversion.', 9: 'Most predators have enemies.', 10: 'Birds have arteries.', 11: 'Some states have stricter regulations concerning homeschool than others.'}
| 7 |
6,626 |
["Whenever it is true that weevils have (part) sections, 'we know that the claim that if a denaturant is a substance, then wind speed is measured by an anemometer, of which there are many kinds is false' is true.", 'It is rational to believe that either african violets are very sensitive to a build-up of soluble salt which can damage plant roots or weevils have (part) sections.', 'It is a fact that either white spruce is a climax canopy tree in the boreal forests of Canada and Alaska or some pellets contain essential nutrients.', 'If if bluebottle isa angiosperm, then birds are principal agents of seed dissemination, with water a secondary agent, then if white spruce is a climax canopy tree in the boreal forests of Canada and Alaska, then the claim that african violets are very sensitive to a build-up of soluble salt which can damage plant roots does not correspond with reality.', 'Once we know bluebottle isa angiosperm, we also know that birds are principal agents of seed dissemination, with water a secondary agent.', 'There is good reason to believe that either registered mail is the safest way to send valuables or if some pellets contain essential nutrients, then the claim that african violets are very sensitive to a build-up of soluble salt which can damage plant roots does not correspond with reality.', 'The claim that earth has big oceans and a lot of water vapor in the air does not correspond with reality.', 'Provided that registered mail is the safest way to send valuables, we know that acidosis can create an unhealthy internal environment that leaves the body s health vulnerable.', 'Given that acidosis can create an unhealthy internal environment that leaves the body s health vulnerable, it can be inferred that earth has big oceans and a lot of water vapor in the air.']
|
Whenever it is true that weevils have (part) sections, 'we know that the claim that if a denaturant is a substance, then wind speed is measured by an anemometer, of which there are many kinds is false' is true. It is rational to believe that either african violets are very sensitive to a build-up of soluble salt which can damage plant roots or weevils have (part) sections. It is a fact that either white spruce is a climax canopy tree in the boreal forests of Canada and Alaska or some pellets contain essential nutrients. If if bluebottle isa angiosperm, then birds are principal agents of seed dissemination, with water a secondary agent, then if white spruce is a climax canopy tree in the boreal forests of Canada and Alaska, then the claim that african violets are very sensitive to a build-up of soluble salt which can damage plant roots does not correspond with reality. Once we know bluebottle isa angiosperm, we also know that birds are principal agents of seed dissemination, with water a secondary agent. There is good reason to believe that either registered mail is the safest way to send valuables or if some pellets contain essential nutrients, then the claim that african violets are very sensitive to a build-up of soluble salt which can damage plant roots does not correspond with reality. The claim that earth has big oceans and a lot of water vapor in the air does not correspond with reality. Provided that registered mail is the safest way to send valuables, we know that acidosis can create an unhealthy internal environment that leaves the body s health vulnerable. Given that acidosis can create an unhealthy internal environment that leaves the body s health vulnerable, it can be inferred that earth has big oceans and a lot of water vapor in the air.
|
We know that the claim that if a denaturant is a substance, then wind speed is measured by an anemometer, of which there are many kinds is false.
|
We know that the claim that if a denaturant is a substance, then wind speed is measured by an anemometer, of which there are many kinds is false.
|
TRUE
|
Modus Ponens:
If [2], then (Not (If [0], then [1].).).
[2] [SC2-1]
Therefore, Not (If [0], then [1].)..
[SC2-1]
Disjunctive Syllogism:
Either [3] or [2].
Not [3]. [SC2-2]
Therefore, [2].
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Not [3].). [SC2-3]
If [5], then (Not [3].). [SC3-3]
Therefore, Not [3]..
[SC2-3]
Modus Ponens:
If (If [7], then [8].), then (If [4], then (Not [3].).).
If [7], then [8].
Therefore, If [4], then (Not [3].)..
[SC3-3]
Disjunctive Syllogism:
Either [6] or (If [5], then (Not [3].).).
Not [6]. [SC2-4]
Therefore, If [5], then (Not [3].)..
[SC2-4]
Modus Tonens:
If [6], then [9]. [SC1-5]
Not [9].
Therefore, Not [6]..
[SC1-5]
Hypothetical Syllogism:
If [6], then [10].
If [10], then [9].
Therefore, If [6], then [9]..
|
{0: 'A denaturant is a substance.', 1: 'Wind speed is measured by an anemometer, of which there are many kinds.', 2: 'Weevils have (part) sections.', 3: 'African violets are very sensitive to a build-up of soluble salt which can damage plant roots.', 4: 'White spruce is a climax canopy tree in the boreal forests of Canada and Alaska.', 5: 'Some pellets contain essential nutrients.', 6: 'Registered mail is the safest way to send valuables.', 7: 'Bluebottle isa angiosperm.', 8: 'Birds are principal agents of seed dissemination, with water a secondary agent.', 9: 'Earth has big oceans and a lot of water vapor in the air.', 10: 'Acidosis can create an unhealthy internal environment that leaves the body s health vulnerable.'}
| 7 |
6,096 |
['Either one or both of these statements are true: power comes from electricity, or either onions keep aphids from harming lettuce, beets, tomatoes and cabbage or contact is junctions.', 'The claim that power comes from electricity has no merit.', "Whenever it is true that the statement 'if onions keep aphids from harming lettuce, beets, tomatoes and cabbage, then the statement that states some paws are part of dingos is false' can be considered false, 'some people mistakenly believe that ontologies provide an important resource to integrate information' is true.", "Provided that the statement 'if onions keep aphids from harming lettuce, beets, tomatoes and cabbage, then the statement that states some paws are part of dingos is false' can be considered false, we know that if eviction is a legal process that often times requires a court order, then seafood has proteins.", 'If if eviction is a legal process that often times requires a court order, then seafood has proteins, then ontologies provide an important resource to integrate information.', "Given that the statement 'if contact is junctions, then the statement that states some paws are part of dingos is false' can be considered false, it can be inferred that water is an essential ingredient for many human activities, notably including food production.", 'Should it be the case that water is an essential ingredient for many human activities, notably including food production, it follows that if acid sets dyes and alkaline releases dye, then oceanographers sometimes go underwater.', 'It is a fact that either water is the universal solvent or either most sweet nectar produces flowers or christians have a robust view of the body, both in life and in death.', "Once we know water is the universal solvent, we also know that if the statement 'if contact is junctions, then the statement that states some paws are part of dingos is false' can be considered false, then the statement 'if acid sets dyes and alkaline releases dye, then oceanographers sometimes go underwater' can be considered false.", "Once we know either most sweet nectar produces flowers or christians have a robust view of the body, both in life and in death, we also know that if the statement 'if contact is junctions, then the statement that states some paws are part of dingos is false' can be considered false, then the statement 'if acid sets dyes and alkaline releases dye, then oceanographers sometimes go underwater' can be considered false."]
|
Either one or both of these statements are true: power comes from electricity, or either onions keep aphids from harming lettuce, beets, tomatoes and cabbage or contact is junctions. The claim that power comes from electricity has no merit. Whenever it is true that the statement 'if onions keep aphids from harming lettuce, beets, tomatoes and cabbage, then the statement that states some paws are part of dingos is false' can be considered false, 'some people mistakenly believe that ontologies provide an important resource to integrate information' is true. Provided that the statement 'if onions keep aphids from harming lettuce, beets, tomatoes and cabbage, then the statement that states some paws are part of dingos is false' can be considered false, we know that if eviction is a legal process that often times requires a court order, then seafood has proteins. If if eviction is a legal process that often times requires a court order, then seafood has proteins, then ontologies provide an important resource to integrate information. Given that the statement 'if contact is junctions, then the statement that states some paws are part of dingos is false' can be considered false, it can be inferred that water is an essential ingredient for many human activities, notably including food production. Should it be the case that water is an essential ingredient for many human activities, notably including food production, it follows that if acid sets dyes and alkaline releases dye, then oceanographers sometimes go underwater. It is a fact that either water is the universal solvent or either most sweet nectar produces flowers or christians have a robust view of the body, both in life and in death. Once we know water is the universal solvent, we also know that if the statement 'if contact is junctions, then the statement that states some paws are part of dingos is false' can be considered false, then the statement 'if acid sets dyes and alkaline releases dye, then oceanographers sometimes go underwater' can be considered false. Once we know either most sweet nectar produces flowers or christians have a robust view of the body, both in life and in death, we also know that if the statement 'if contact is junctions, then the statement that states some paws are part of dingos is false' can be considered false, then the statement 'if acid sets dyes and alkaline releases dye, then oceanographers sometimes go underwater' can be considered false.
|
The statement that states some paws are part of dingos is false.
|
It is not true that some paws make noise.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].). [SC2-1]
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [5] or (Either [1] or [2].).
Not [5].
Therefore, Either [1] or [2]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [1], then (Not [0].).).), then [6]. [SC1-2]
If (Not (If [1], then (Not [0].).).), then (Not [6].).
Therefore, If [1], then (Not [0].)..
[SC1-2]
Hypothetical Syllogism:
If (Not (If [1], then (Not [0].).).), then (If [7], then [8].).
If (If [7], then [8].), then [6].
Therefore, If (Not (If [1], then (Not [0].).).), then [6]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then (Not [0].).).), then (If [3], then [4].). [SC1-2]
If (Not (If [2], then (Not [0].).).), then (Not (If [3], then [4].).). [SC2-2]
Therefore, If [2], then (Not [0].)..
[SC1-2]
Hypothetical Syllogism:
If (Not (If [2], then (Not [0].).).), then [12].
If [12], then (If [3], then [4].).
Therefore, If (Not (If [2], then (Not [0].).).), then (If [3], then [4].)..
[SC2-2]
Disjunction Elimination:
Either [9] or (Either [10] or [11].).
If [9], then (If (Not (If [2], then (Not [0].).).), then (Not (If [3], then [4].).).).
If (Either [10] or [11].), then (If (Not (If [2], then (Not [0].).).), then (Not (If [3], then [4].).).).
Therefore, If (Not (If [2], then (Not [0].).).), then (Not (If [3], then [4].).)..
|
{0: 'Some paws are part of dingos.', 1: 'Onions keep aphids from harming lettuce, beets, tomatoes and cabbage.', 2: 'Contact is junctions.', 3: 'Acid sets dyes and alkaline releases dye.', 4: 'Oceanographers sometimes go underwater.', 5: 'Power comes from electricity.', 6: 'Ontologies provide an important resource to integrate information.', 7: 'Eviction is a legal process that often times requires a court order.', 8: 'Seafood has proteins.', 9: 'Water is the universal solvent.', 10: 'Most sweet nectar produces flowers.', 11: 'Christians have a robust view of the body, both in life and in death.', 12: 'Water is an essential ingredient for many human activities, notably including food production.'}
| 7 |
6,781 |
['It is a common misconception that individual liberty is the freedom to act.', 'There is good reason to believe that either water is also vital to the unusual biota, or animal and plant life, of the region or if the statement that states cells showing intestinal dysplasia are one step closer to cancer is false, then modern meteorology focuses on weather patterns.', 'We know that the claim that water is also vital to the unusual biota, or animal and plant life, of the region is false.', 'It is the case that bicyclists have the same right to use the road as motorists.', "Whenever it is true that protists are the most diversified of all eukaryotes, 'if some people mistakenly believe that if the statement that states cells showing intestinal dysplasia are one step closer to cancer is false, then it is not the case that dealers are located in casinos, then individual liberty is the freedom to act' is true.", 'The claim that protists are the most diversified of all eukaryotes holds true.', "Given that the notion that 'if bicyclists have the same right to use the road as motorists, then if modern meteorology focuses on weather patterns, then dealers are located in casinos' is untrue, it can be inferred that dogs possess reaction.", "Should it be the case that the notion that 'if bicyclists have the same right to use the road as motorists, then if modern meteorology focuses on weather patterns, then dealers are located in casinos' is untrue, it follows that the claim that dogs possess reaction does not reflect reality."]
|
It is a common misconception that individual liberty is the freedom to act. There is good reason to believe that either water is also vital to the unusual biota, or animal and plant life, of the region or if the statement that states cells showing intestinal dysplasia are one step closer to cancer is false, then modern meteorology focuses on weather patterns. We know that the claim that water is also vital to the unusual biota, or animal and plant life, of the region is false. It is the case that bicyclists have the same right to use the road as motorists. Whenever it is true that protists are the most diversified of all eukaryotes, 'if some people mistakenly believe that if the statement that states cells showing intestinal dysplasia are one step closer to cancer is false, then it is not the case that dealers are located in casinos, then individual liberty is the freedom to act' is true. The claim that protists are the most diversified of all eukaryotes holds true. Given that the notion that 'if bicyclists have the same right to use the road as motorists, then if modern meteorology focuses on weather patterns, then dealers are located in casinos' is untrue, it can be inferred that dogs possess reaction. Should it be the case that the notion that 'if bicyclists have the same right to use the road as motorists, then if modern meteorology focuses on weather patterns, then dealers are located in casinos' is untrue, it follows that the claim that dogs possess reaction does not reflect reality.
|
The idea that cells showing intestinal dysplasia are one step closer to cancer is true.
|
It is not the case that cells showing intestinal dysplasia are one step closer to cancer.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [2]. [SC1-2]
If [2], then [1]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunctive Syllogism:
Either [6] or (If (Not [0].), then [2].).
Not [6].
Therefore, If (Not [0].), then [2]..
[SC2-2]
Modus Ponens:
If [4], then (If [2], then [1].). [SC1-3]
[4]
Therefore, If [2], then [1]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If [4], then (If [2], then [1].).).), then [7].
If (Not (If [4], then (If [2], then [1].).).), then (Not [7].).
Therefore, If [4], then (If [2], then [1].)..
[SC2-1]
Modus Tonens:
If (Not (If (Not [0].), then (Not [1].).).), then [3]. [SC1-2]
Not [3].
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Modus Ponens:
If [5], then (If (Not (If (Not [0].), then (Not [1].).).), then [3].).
[5]
Therefore, If (Not (If (Not [0].), then (Not [1].).).), then [3]..
|
{0: 'Cells showing intestinal dysplasia are one step closer to cancer.', 1: 'Dealers are located in casinos.', 2: 'Modern meteorology focuses on weather patterns.', 3: 'Individual liberty is the freedom to act.', 4: 'Bicyclists have the same right to use the road as motorists.', 5: 'Protists are the most diversified of all eukaryotes.', 6: 'Water is also vital to the unusual biota, or animal and plant life, of the region.', 7: 'Dogs possess reaction.'}
| 7 |
6,499 |
['We know that at least one of two things is true: a whey is a dairy product, or ecthyma lesions show dermal necrosis and inflammation.', 'Assuming a whey is a dairy product, we know that some physicians question classifications.', 'It is rational to believe that either if most coyotes resemble small dogs, then some women have infection or flounder is flatfishs.', 'When if most coyotes resemble small dogs, then some women have infection is true, it follows that if it is not the case that if ecthyma lesions show dermal necrosis and inflammation, then some physicians question classifications, then either stepfathers have (part) sections or heavier elements are less efficient nuclear fuel, so each cycle takes less time.', "So long as flounder is flatfishs, 'if it is not the case that if ecthyma lesions show dermal necrosis and inflammation, then some physicians question classifications, then either stepfathers have (part) sections or heavier elements are less efficient nuclear fuel, so each cycle takes less time' is true.", 'When either stepfathers have (part) sections or heavier elements are less efficient nuclear fuel, so each cycle takes less time is true, it follows that reconciliation is a two person act, which requires the full cooperation of the injurer.', 'Provided that reconciliation is a two person act, which requires the full cooperation of the injurer, we know that those that suggest forces cause net external torque are wrong.', 'Provided that a craton is a part, we know that forces cause net external torque.', 'Provided that reconciliation is a two person act, which requires the full cooperation of the injurer, we know that lobsters grow in size only when they discard their shell.', 'Given that lobsters grow in size only when they discard their shell, it can be inferred that a craton is a part.']
|
We know that at least one of two things is true: a whey is a dairy product, or ecthyma lesions show dermal necrosis and inflammation. Assuming a whey is a dairy product, we know that some physicians question classifications. It is rational to believe that either if most coyotes resemble small dogs, then some women have infection or flounder is flatfishs. When if most coyotes resemble small dogs, then some women have infection is true, it follows that if it is not the case that if ecthyma lesions show dermal necrosis and inflammation, then some physicians question classifications, then either stepfathers have (part) sections or heavier elements are less efficient nuclear fuel, so each cycle takes less time. So long as flounder is flatfishs, 'if it is not the case that if ecthyma lesions show dermal necrosis and inflammation, then some physicians question classifications, then either stepfathers have (part) sections or heavier elements are less efficient nuclear fuel, so each cycle takes less time' is true. When either stepfathers have (part) sections or heavier elements are less efficient nuclear fuel, so each cycle takes less time is true, it follows that reconciliation is a two person act, which requires the full cooperation of the injurer. Provided that reconciliation is a two person act, which requires the full cooperation of the injurer, we know that those that suggest forces cause net external torque are wrong. Provided that a craton is a part, we know that forces cause net external torque. Provided that reconciliation is a two person act, which requires the full cooperation of the injurer, we know that lobsters grow in size only when they discard their shell. Given that lobsters grow in size only when they discard their shell, it can be inferred that a craton is a part.
|
The statement 'some physicians question classifications' can be considered true.
|
We know that the claim that some physicians question classifications is false.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC3-1]
Modus Tonens:
If (Not (If [2], then [0].).), then (Either [3] or [4].). [SC1-2]
Not (Either [3] or [4].). [SC2-2]
Therefore, If [2], then [0]..
[SC1-2]
Disjunction Elimination:
Either (If [6], then [7].) or [8].
If (If [6], then [7].), then (If (Not (If [2], then [0].).), then (Either [3] or [4].).).
If [8], then (If (Not (If [2], then [0].).), then (Either [3] or [4].).).
Therefore, If (Not (If [2], then [0].).), then (Either [3] or [4].)..
[SC2-2]
Modus Tonens:
If (Either [3] or [4].), then [5].
Not [5]. [SC2-3]
Therefore, Not (Either [3] or [4].)..
[SC2-3]
Reductio Ad Absurdum:
If [5], then [9]. [SC1-4]
If [5], then (Not [9].).
Therefore, Not [5]..
[SC1-4]
Hypothetical Syllogism:
If [5], then [10]. [SC1-5]
If [10], then [9].
Therefore, If [5], then [9]..
[SC1-5]
Hypothetical Syllogism:
If [5], then [11].
If [11], then [10].
Therefore, If [5], then [10]..
|
{0: 'Some physicians question classifications.', 1: 'A whey is a dairy product.', 2: 'Ecthyma lesions show dermal necrosis and inflammation.', 3: 'Stepfathers have (part) sections.', 4: 'Heavier elements are less efficient nuclear fuel, so each cycle takes less time.', 5: 'Reconciliation is a two person act, which requires the full cooperation of the injurer.', 6: 'Most coyotes resemble small dogs.', 7: 'Some women have infection.', 8: 'Flounder is flatfishs.', 9: 'Forces cause net external torque.', 10: 'A craton is a part.', 11: 'Lobsters grow in size only when they discard their shell.'}
| 7 |
6,074 |
['Those that suggest military courts are an arm of the executive branch are wrong.', 'We know that at least one of two things is true: ideology is part of organizations, or if dogs like to stick close to their leaders, then articles provide additional details.', 'Provided that if dogs like to stick close to their leaders, then articles provide additional details, we know that if parathormone regulates the calcium level in the blood, then winged forms have two membranous pairs of wings, with the front pair larger than the hind pair.', 'Should it be the case that we know that the claim that if sandbars have (part) slopes, then winged forms have two membranous pairs of wings, with the front pair larger than the hind pair is false, it follows that if beetles eat the most when they are larvae, then some amoebas enter contractile vacuoles.', "Whenever it is true that we know that the claim that if sandbars have (part) slopes, then winged forms have two membranous pairs of wings, with the front pair larger than the hind pair is false, 'the notion that 'if beetles eat the most when they are larvae, then some amoebas enter contractile vacuoles' is untrue' is true.", "So long as it is not the case that if the statement that states either parathormone regulates the calcium level in the blood or sandbars have (part) slopes is false, then military courts are an arm of the executive branch, 'etymologists are lexicographers' is true.", "So long as it is not the case that if the statement that states either parathormone regulates the calcium level in the blood or sandbars have (part) slopes is false, then military courts are an arm of the executive branch, 'the statement, etymologists are lexicographers, does not hold' is true.", 'Those that suggest mustelids have well-developed anal scent glands wich produce a potent repellent smell are right.', 'Either either chicken laying mash or dry dog food is excellent feed for raising crickets or some cytokinesis is part of meiosis or some horses live to be fifty, though mares live less long.', 'One may reasonably assume that if either chicken laying mash or dry dog food is excellent feed for raising crickets or some cytokinesis is part of meiosis, then if mustelids have well-developed anal scent glands wich produce a potent repellent smell, then if ideology is part of organizations, then if parathormone regulates the calcium level in the blood, then winged forms have two membranous pairs of wings, with the front pair larger than the hind pair.', 'Given that some horses live to be fifty, though mares live less long, it can be inferred that if mustelids have well-developed anal scent glands wich produce a potent repellent smell, then if ideology is part of organizations, then if parathormone regulates the calcium level in the blood, then winged forms have two membranous pairs of wings, with the front pair larger than the hind pair.']
|
Those that suggest military courts are an arm of the executive branch are wrong. We know that at least one of two things is true: ideology is part of organizations, or if dogs like to stick close to their leaders, then articles provide additional details. Provided that if dogs like to stick close to their leaders, then articles provide additional details, we know that if parathormone regulates the calcium level in the blood, then winged forms have two membranous pairs of wings, with the front pair larger than the hind pair. Should it be the case that we know that the claim that if sandbars have (part) slopes, then winged forms have two membranous pairs of wings, with the front pair larger than the hind pair is false, it follows that if beetles eat the most when they are larvae, then some amoebas enter contractile vacuoles. Whenever it is true that we know that the claim that if sandbars have (part) slopes, then winged forms have two membranous pairs of wings, with the front pair larger than the hind pair is false, 'the notion that 'if beetles eat the most when they are larvae, then some amoebas enter contractile vacuoles' is untrue' is true. So long as it is not the case that if the statement that states either parathormone regulates the calcium level in the blood or sandbars have (part) slopes is false, then military courts are an arm of the executive branch, 'etymologists are lexicographers' is true. So long as it is not the case that if the statement that states either parathormone regulates the calcium level in the blood or sandbars have (part) slopes is false, then military courts are an arm of the executive branch, 'the statement, etymologists are lexicographers, does not hold' is true. Those that suggest mustelids have well-developed anal scent glands wich produce a potent repellent smell are right. Either either chicken laying mash or dry dog food is excellent feed for raising crickets or some cytokinesis is part of meiosis or some horses live to be fifty, though mares live less long. One may reasonably assume that if either chicken laying mash or dry dog food is excellent feed for raising crickets or some cytokinesis is part of meiosis, then if mustelids have well-developed anal scent glands wich produce a potent repellent smell, then if ideology is part of organizations, then if parathormone regulates the calcium level in the blood, then winged forms have two membranous pairs of wings, with the front pair larger than the hind pair. Given that some horses live to be fifty, though mares live less long, it can be inferred that if mustelids have well-developed anal scent glands wich produce a potent repellent smell, then if ideology is part of organizations, then if parathormone regulates the calcium level in the blood, then winged forms have two membranous pairs of wings, with the front pair larger than the hind pair.
|
Many people rightly believe that winged forms have two membranous pairs of wings, with the front pair larger than the hind pair.
|
Many people rightly believe that winged forms have two membranous pairs of wings, with the front pair larger than the hind pair.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either [1] or [2].).), then [6]. [SC1-2]
Not [6].
Therefore, Either [1] or [2]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (Either [1] or [2].).), then [6].).), then [9].
If (Not (If (Not (Either [1] or [2].).), then [6].).), then (Not [9].).
Therefore, If (Not (Either [1] or [2].).), then [6]..
[SC2-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then (If [1], then [0].). [SC2-2]
If (If [4], then [5].), then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC2-2]
Modus Ponens:
If [10], then (If [3], then (If [1], then [0].).). [SC1-3]
[10]
Therefore, If [3], then (If [1], then [0].)..
[SC1-3]
Disjunction Elimination:
Either (Either [11] or [12].) or [13].
If (Either [11] or [12].), then (If [10], then (If [3], then (If [1], then [0].).).).
If [13], then (If [10], then (If [3], then (If [1], then [0].).).).
Therefore, If [10], then (If [3], then (If [1], then [0].).)..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then [0].).), then (If [7], then [8].).
If (Not (If [2], then [0].).), then (Not (If [7], then [8].).).
Therefore, If [2], then [0]..
|
{0: 'Winged forms have two membranous pairs of wings, with the front pair larger than the hind pair.', 1: 'Parathormone regulates the calcium level in the blood.', 2: 'Sandbars have (part) slopes.', 3: 'Ideology is part of organizations.', 4: 'Dogs like to stick close to their leaders.', 5: 'Articles provide additional details.', 6: 'Military courts are an arm of the executive branch.', 7: 'Beetles eat the most when they are larvae.', 8: 'Some amoebas enter contractile vacuoles.', 9: 'Etymologists are lexicographers.', 10: 'Mustelids have well-developed anal scent glands wich produce a potent repellent smell.', 11: 'Chicken laying mash or dry dog food is excellent feed for raising crickets.', 12: 'Some cytokinesis is part of meiosis.', 13: 'Some horses live to be fifty, though mares live less long.'}
| 7 |
6,089 |
['Either most predators steal prey or if erection is caused during arousal by more blood flowing into the penis than flows out, then microtubules are, as the name implies, very tiny tubes.', 'Given that most predators steal prey, it can be inferred that plants require frequent fertilization.', 'Assuming death is caused by the toxin produced by the bacteria, we know that plants require frequent fertilization.', "If the statement 'if if erection is caused during arousal by more blood flowing into the penis than flows out, then microtubules are, as the name implies, very tiny tubes, then death is caused by the toxin produced by the bacteria' can be considered false, then humidity is the next most common cause of paper jams.", 'Many people rightly believe that massive volcanoes explode all around the Earth.', 'One may reasonably assume that if chinchillas are creatures of habit with strong internal clocks, then if humidity is the next most common cause of paper jams, then manatees are a migrant species.', 'It is true that chinchillas are creatures of habit with strong internal clocks.', 'Given that the claim that if massive volcanoes explode all around the Earth, then the statement that states manatees are a migrant species is false does not reflect reality, it can be inferred that poetic text describes the cycle of day from morning to night.', "The statement 'poetic text describes the cycle of day from morning to night' can be considered false."]
|
Either most predators steal prey or if erection is caused during arousal by more blood flowing into the penis than flows out, then microtubules are, as the name implies, very tiny tubes. Given that most predators steal prey, it can be inferred that plants require frequent fertilization. Assuming death is caused by the toxin produced by the bacteria, we know that plants require frequent fertilization. If the statement 'if if erection is caused during arousal by more blood flowing into the penis than flows out, then microtubules are, as the name implies, very tiny tubes, then death is caused by the toxin produced by the bacteria' can be considered false, then humidity is the next most common cause of paper jams. Many people rightly believe that massive volcanoes explode all around the Earth. One may reasonably assume that if chinchillas are creatures of habit with strong internal clocks, then if humidity is the next most common cause of paper jams, then manatees are a migrant species. It is true that chinchillas are creatures of habit with strong internal clocks. Given that the claim that if massive volcanoes explode all around the Earth, then the statement that states manatees are a migrant species is false does not reflect reality, it can be inferred that poetic text describes the cycle of day from morning to night. The statement 'poetic text describes the cycle of day from morning to night' can be considered false.
|
It is a simple truth that plants require frequent fertilization.
|
The claim that plants require frequent fertilization has no merit.
|
FALSE
|
Disjunction Elimination:
Either [1] or (If [2], then [3].).
If [1], then [0].
If (If [2], then [3].), then [0]. [SC3-1]
Therefore, [0].
[SC3-1]
Hypothetical Syllogism:
If (If [2], then [3].), then [4]. [SC1-2]
If [4], then [0].
Therefore, If (If [2], then [3].), then [0]..
[SC1-2]
Modus Tonens:
If (Not (If (If [2], then [3].), then [4].).), then [5]. [SC1-3]
Not [5]. [SC2-3]
Therefore, If (If [2], then [3].), then [4]..
[SC1-3]
Hypothetical Syllogism:
If (Not (If (If [2], then [3].), then [4].).), then [7].
If [7], then [5]. [SC2-4]
Therefore, If (Not (If (If [2], then [3].), then [4].).), then [5]..
[SC2-4]
Modus Ponens:
If [8], then (If [7], then [5].).
[8]
Therefore, If [7], then [5]..
[SC2-3]
Modus Ponens:
If [6], then (Not [5].). [SC1-4]
[6]
Therefore, Not [5]..
[SC1-4]
Modus Tonens:
If (Not (If [6], then (Not [5].).).), then [9].
Not [9].
Therefore, If [6], then (Not [5].)..
|
{0: 'Plants require frequent fertilization.', 1: 'Most predators steal prey.', 2: 'Erection is caused during arousal by more blood flowing into the penis than flows out.', 3: 'Microtubules are, as the name implies, very tiny tubes.', 4: 'Death is caused by the toxin produced by the bacteria.', 5: 'Manatees are a migrant species.', 6: 'Massive volcanoes explode all around the Earth.', 7: 'Humidity is the next most common cause of paper jams.', 8: 'Chinchillas are creatures of habit with strong internal clocks.', 9: 'Poetic text describes the cycle of day from morning to night.'}
| 7 |
6,609 |
['We know that the claim that diffusion occurs between the capillaries of the two blood supplies is false.', 'Those that suggest some farms destroy habitats are wrong.', 'We know that at least one of two things is true: some animals move seasonally from one location to another, or structure means the shape and arrangement of soil particles into cluster or aggregates.', 'If societies have potential, then if some animals move seasonally from one location to another, then either some farms destroy habitats or if those that suggest either many animals migrate to more southerly regions or point mutations can result from errors in DNA replication or from environmental effects are wrong, then diffusion occurs between the capillaries of the two blood supplies.', 'Should it be the case that gums normally are pink and moist, it follows that if structure means the shape and arrangement of soil particles into cluster or aggregates, then either some farms destroy habitats or if those that suggest either many animals migrate to more southerly regions or point mutations can result from errors in DNA replication or from environmental effects are wrong, then diffusion occurs between the capillaries of the two blood supplies.', 'The idea that gums normally are pink and moist is true.', 'Once we know smaller islands are mainly coral or limestone, we also know that societies have potential.', "Whenever it is true that some droplets fall to ground, others evaporate in air, 'societies have potential' is true.", 'We know that either some yolks are part of eggs or either indicators are chemicals that change colors depending on the pH of the solution or most squirrels receive food.', 'One may reasonably assume that if some yolks are part of eggs, then either smaller islands are mainly coral or limestone or some droplets fall to ground, others evaporate in air.', 'One may reasonably assume that if either indicators are chemicals that change colors depending on the pH of the solution or most squirrels receive food, then either smaller islands are mainly coral or limestone or some droplets fall to ground, others evaporate in air.']
|
We know that the claim that diffusion occurs between the capillaries of the two blood supplies is false. Those that suggest some farms destroy habitats are wrong. We know that at least one of two things is true: some animals move seasonally from one location to another, or structure means the shape and arrangement of soil particles into cluster or aggregates. If societies have potential, then if some animals move seasonally from one location to another, then either some farms destroy habitats or if those that suggest either many animals migrate to more southerly regions or point mutations can result from errors in DNA replication or from environmental effects are wrong, then diffusion occurs between the capillaries of the two blood supplies. Should it be the case that gums normally are pink and moist, it follows that if structure means the shape and arrangement of soil particles into cluster or aggregates, then either some farms destroy habitats or if those that suggest either many animals migrate to more southerly regions or point mutations can result from errors in DNA replication or from environmental effects are wrong, then diffusion occurs between the capillaries of the two blood supplies. The idea that gums normally are pink and moist is true. Once we know smaller islands are mainly coral or limestone, we also know that societies have potential. Whenever it is true that some droplets fall to ground, others evaporate in air, 'societies have potential' is true. We know that either some yolks are part of eggs or either indicators are chemicals that change colors depending on the pH of the solution or most squirrels receive food. One may reasonably assume that if some yolks are part of eggs, then either smaller islands are mainly coral or limestone or some droplets fall to ground, others evaporate in air. One may reasonably assume that if either indicators are chemicals that change colors depending on the pH of the solution or most squirrels receive food, then either smaller islands are mainly coral or limestone or some droplets fall to ground, others evaporate in air.
|
We know that at least one of two things is true: many animals migrate to more southerly regions, or point mutations can result from errors in DNA replication or from environmental effects.
|
At least one of two things is true: most animals seek places, or point mutations can have a significant impact on phenotype, as in the case of sickle-cell disease.
|
Uncertain
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
Not [2].
Therefore, Either [0] or [1]..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If (Not (Either [0] or [1].).), then [2].). [SC1-2]
Not [3].
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Either [3] or (If (Not (Either [0] or [1].).), then [2].).). [SC2-3]
If [5], then (Either [3] or (If (Not (Either [0] or [1].).), then [2].).). [SC3-3]
Therefore, Either [3] or (If (Not (Either [0] or [1].).), then [2].)..
[SC2-3]
Modus Ponens:
If [7], then (If [4], then (Either [3] or (If (Not (Either [0] or [1].).), then [2].).).).
[7] [SC2-4]
Therefore, If [4], then (Either [3] or (If (Not (Either [0] or [1].).), then [2].).)..
[SC2-4]
Disjunction Elimination:
Either [8] or [9]. [SC1-5]
If [8], then [7].
If [9], then [7].
Therefore, [7].
[SC1-5]
Disjunction Elimination:
Either [10] or (Either [11] or [12].).
If [10], then (Either [8] or [9].).
If (Either [11] or [12].), then (Either [8] or [9].).
Therefore, Either [8] or [9]..
[SC3-3]
Modus Ponens:
If [6], then (If [5], then (Either [3] or (If (Not (Either [0] or [1].).), then [2].).).).
[6]
Therefore, If [5], then (Either [3] or (If (Not (Either [0] or [1].).), then [2].).)..
|
{0: 'Many animals migrate to more southerly regions.', 1: 'Point mutations can result from errors in DNA replication or from environmental effects.', 2: 'Diffusion occurs between the capillaries of the two blood supplies.', 3: 'Some farms destroy habitats.', 4: 'Some animals move seasonally from one location to another.', 5: 'Structure means the shape and arrangement of soil particles into cluster or aggregates.', 6: 'Gums normally are pink and moist.', 7: 'Societies have potential.', 8: 'Smaller islands are mainly coral or limestone.', 9: 'Some droplets fall to ground, others evaporate in air.', 10: 'Some yolks are part of eggs.', 11: 'Indicators are chemicals that change colors depending on the pH of the solution.', 12: 'Most squirrels receive food.'}
| 7 |
6,000 |
['When seawater contains excess salts, some of which pass straight through the gut without being absorbed is true, it follows that the statement, if elephants kill people on a constant basis, then forage crops are essential to Northeast agriculture, does not hold.', 'On the condition that the claim that either seawater contains excess salts, some of which pass straight through the gut without being absorbed or mountain lions exists in almost any place offering sufficient prey and adequate cover does not correspond with reality, it is definitely the case that if rheas are gregarious and they generally live in mixed groups of males, females and juveniles, then lossless compression is used for program and dat files.', 'When rain water has salt is true, it follows that if mountain lions exists in almost any place offering sufficient prey and adequate cover, then the statement, if elephants kill people on a constant basis, then forage crops are essential to Northeast agriculture, does not hold.', 'Should it be the case that the claim that either seawater contains excess salts, some of which pass straight through the gut without being absorbed or mountain lions exists in almost any place offering sufficient prey and adequate cover does not correspond with reality, it follows that cowboys have (part) arms.', "So long as if copyrights protect the expression of ideas, then water dries up or is degraded by human activity at an alarming rate, 'rain water has salt' is true.", 'Should it be the case that copyrights protect the expression of ideas, it follows that water dries up or is degraded by human activity at an alarming rate.', 'Given that either animals are adept at concealment or alcohol produces dependence causes concern and chronic liver diseases etc, it can be inferred that if cowboys have (part) arms, then the statement, if rheas are gregarious and they generally live in mixed groups of males, females and juveniles, then lossless compression is used for program and dat files, does not hold.', 'Provided that the claim that either animals are adept at concealment or alcohol produces dependence causes concern and chronic liver diseases etc does not correspond with reality, we know that meiosis involves division.', 'The claim that meiosis involves division is false.']
|
When seawater contains excess salts, some of which pass straight through the gut without being absorbed is true, it follows that the statement, if elephants kill people on a constant basis, then forage crops are essential to Northeast agriculture, does not hold. On the condition that the claim that either seawater contains excess salts, some of which pass straight through the gut without being absorbed or mountain lions exists in almost any place offering sufficient prey and adequate cover does not correspond with reality, it is definitely the case that if rheas are gregarious and they generally live in mixed groups of males, females and juveniles, then lossless compression is used for program and dat files. When rain water has salt is true, it follows that if mountain lions exists in almost any place offering sufficient prey and adequate cover, then the statement, if elephants kill people on a constant basis, then forage crops are essential to Northeast agriculture, does not hold. Should it be the case that the claim that either seawater contains excess salts, some of which pass straight through the gut without being absorbed or mountain lions exists in almost any place offering sufficient prey and adequate cover does not correspond with reality, it follows that cowboys have (part) arms. So long as if copyrights protect the expression of ideas, then water dries up or is degraded by human activity at an alarming rate, 'rain water has salt' is true. Should it be the case that copyrights protect the expression of ideas, it follows that water dries up or is degraded by human activity at an alarming rate. Given that either animals are adept at concealment or alcohol produces dependence causes concern and chronic liver diseases etc, it can be inferred that if cowboys have (part) arms, then the statement, if rheas are gregarious and they generally live in mixed groups of males, females and juveniles, then lossless compression is used for program and dat files, does not hold. Provided that the claim that either animals are adept at concealment or alcohol produces dependence causes concern and chronic liver diseases etc does not correspond with reality, we know that meiosis involves division. The claim that meiosis involves division is false.
|
The statement, if elephants kill people on a constant basis, then forage crops are essential to Northeast agriculture, does not hold.
|
The statement, if elephants kill people on a constant basis, then forage crops are essential to Northeast agriculture, does not hold.
|
TRUE
|
Disjunction Elimination:
Either [2] or [3]. [SC1-1]
If [2], then (Not (If [0], then [1].).).
If [3], then (Not (If [0], then [1].).). [SC3-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [2] or [3].).), then (If [5], then [6].).
If (Not (Either [2] or [3].).), then (Not (If [5], then [6].).). [SC2-2]
Therefore, Either [2] or [3]..
[SC2-2]
Hypothetical Syllogism:
If (Not (Either [2] or [3].).), then [7].
If [7], then (Not (If [5], then [6].).). [SC2-3]
Therefore, If (Not (Either [2] or [3].).), then (Not (If [5], then [6].).)..
[SC2-3]
Modus Ponens:
If (Either [10] or [11].), then (If [7], then (Not (If [5], then [6].).).).
Either [10] or [11]. [SC2-4]
Therefore, If [7], then (Not (If [5], then [6].).)..
[SC2-4]
Modus Tonens:
If (Not (Either [10] or [11].).), then [12].
Not [12].
Therefore, Either [10] or [11]..
[SC3-1]
Modus Ponens:
If [4], then (If [3], then (Not (If [0], then [1].).).).
[4] [SC2-2]
Therefore, If [3], then (Not (If [0], then [1].).)..
[SC2-2]
Modus Ponens:
If (If [8], then [9].), then [4].
If [8], then [9].
Therefore, [4].
|
{0: 'Elephants kill people on a constant basis.', 1: 'Forage crops are essential to Northeast agriculture.', 2: 'Seawater contains excess salts, some of which pass straight through the gut without being absorbed.', 3: 'Mountain lions exists in almost any place offering sufficient prey and adequate cover.', 4: 'Rain water has salt.', 5: 'Rheas are gregarious and they generally live in mixed groups of males, females and juveniles.', 6: 'Lossless compression is used for program and dat files.', 7: 'Cowboys have (part) arms.', 8: 'Copyrights protect the expression of ideas.', 9: 'Water dries up or is degraded by human activity at an alarming rate.', 10: 'Animals are adept at concealment.', 11: 'Alcohol produces dependence causes concern and chronic liver diseases etc.', 12: 'Meiosis involves division.'}
| 7 |
6,392 |
['It is true that acrylic paintings is paintings.', "When either monostotic disease is more common than polyostotic disease or duds are the cowboys' favorite clothes or their best clothes is true, it follows that carbon has (part) atoms.", "There is good reason to believe that either if ceilings are part of rooms, then physical therapy is administered by health care professionals called physical therapists or if fitness can be a relation of genes to other genes, then either either monostotic disease is more common than polyostotic disease or duds are the cowboys' favorite clothes or their best clothes or if acrylic paintings is paintings, then either prenatal yoga is great for pregnancy or ulcers can also produce pain that simulates cardiac ischemia.", 'It is a common misconception that if ceilings are part of rooms, then physical therapy is administered by health care professionals called physical therapists.', 'When the statement that states fitness can be a relation of genes to other genes is false is true, it follows that dance clubs are used for dating.', 'We know that the claim that dance clubs are used for dating is false.', 'Should it be the case that carbon has (part) atoms, it follows that birds are intelligent beings.', 'It is a common misconception that birds are intelligent beings.']
|
It is true that acrylic paintings is paintings. When either monostotic disease is more common than polyostotic disease or duds are the cowboys' favorite clothes or their best clothes is true, it follows that carbon has (part) atoms. There is good reason to believe that either if ceilings are part of rooms, then physical therapy is administered by health care professionals called physical therapists or if fitness can be a relation of genes to other genes, then either either monostotic disease is more common than polyostotic disease or duds are the cowboys' favorite clothes or their best clothes or if acrylic paintings is paintings, then either prenatal yoga is great for pregnancy or ulcers can also produce pain that simulates cardiac ischemia. It is a common misconception that if ceilings are part of rooms, then physical therapy is administered by health care professionals called physical therapists. When the statement that states fitness can be a relation of genes to other genes is false is true, it follows that dance clubs are used for dating. We know that the claim that dance clubs are used for dating is false. Should it be the case that carbon has (part) atoms, it follows that birds are intelligent beings. It is a common misconception that birds are intelligent beings.
|
It is a fact that either prenatal yoga is great for pregnancy or ulcers can also produce pain that simulates cardiac ischemia.
|
It is a fact that either prenatal yoga is great for pregnancy or ulcers can also produce pain that simulates cardiac ischemia.
|
TRUE
|
Modus Ponens:
If [2], then (Either [0] or [1].). [SC1-1]
[2]
Therefore, Either [0] or [1]..
[SC1-1]
Disjunctive Syllogism:
Either (Either [3] or [4].) or (If [2], then (Either [0] or [1].).). [SC1-2]
Not (Either [3] or [4].). [SC2-2]
Therefore, If [2], then (Either [0] or [1].)..
[SC1-2]
Modus Ponens:
If [6], then (Either (Either [3] or [4].) or (If [2], then (Either [0] or [1].).).). [SC1-3]
[6] [SC2-3]
Therefore, Either (Either [3] or [4].) or (If [2], then (Either [0] or [1].).)..
[SC1-3]
Disjunctive Syllogism:
Either (If [7], then [8].) or (If [6], then (Either (Either [3] or [4].) or (If [2], then (Either [0] or [1].).).).).
Not (If [7], then [8].).
Therefore, If [6], then (Either (Either [3] or [4].) or (If [2], then (Either [0] or [1].).).)..
[SC2-3]
Modus Tonens:
If (Not [6].), then [10].
Not [10].
Therefore, [6].
[SC2-2]
Modus Tonens:
If (Either [3] or [4].), then [5].
Not [5]. [SC2-3]
Therefore, Not (Either [3] or [4].)..
[SC2-3]
Modus Tonens:
If [5], then [9].
Not [9].
Therefore, Not [5]..
|
{0: 'Prenatal yoga is great for pregnancy.', 1: 'Ulcers can also produce pain that simulates cardiac ischemia.', 2: 'Acrylic paintings is paintings.', 3: 'Monostotic disease is more common than polyostotic disease.', 4: "Duds are the cowboys' favorite clothes or their best clothes.", 5: 'Carbon has (part) atoms.', 6: 'Fitness can be a relation of genes to other genes.', 7: 'Ceilings are part of rooms.', 8: 'Physical therapy is administered by health care professionals called physical therapists.', 9: 'Birds are intelligent beings.', 10: 'Dance clubs are used for dating.'}
| 7 |
6,476 |
['Assuming the claim that company scrip is a type of money with no value apart from the company is false, we know that if electricity flows through the nerves in our bodies the same way electricity flows through a wire, then adult fish require an unobstructed migration path between the ocean and the stream spawning grounds.', "Given that the statement that states if the claim that company scrip is a type of money with no value apart from the company is false, then the statement that 'if electricity flows through the nerves in our bodies the same way electricity flows through a wire, then adult fish require an unobstructed migration path between the ocean and the stream spawning grounds' is incorrect is false, it can be inferred that the claim that young iguanas are pale green with black-ringed tails does not correspond with reality.", "Given that the statement 'if papayas come in different sizes, then if the statement that states if the claim that company scrip is a type of money with no value apart from the company is false, then the statement that 'if electricity flows through the nerves in our bodies the same way electricity flows through a wire, then adult fish require an unobstructed migration path between the ocean and the stream spawning grounds' is incorrect is false, then young iguanas are pale green with black-ringed tails' can be considered false, it can be inferred that convertible security is a certificate.", 'Once we know all atoms are very small, we also know that papayas come in different sizes.', 'all atoms are very small.', "So long as farms have animals, 'some people mistakenly believe that convertible security is a certificate' is true.", "So long as most liquid water supports life, 'some people mistakenly believe that convertible security is a certificate' is true.", 'Should it be the case that tigers have (part) paws, it follows that either farms have animals or most liquid water supports life.', 'It is fair to say that tigers have (part) paws.']
|
Assuming the claim that company scrip is a type of money with no value apart from the company is false, we know that if electricity flows through the nerves in our bodies the same way electricity flows through a wire, then adult fish require an unobstructed migration path between the ocean and the stream spawning grounds. Given that the statement that states if the claim that company scrip is a type of money with no value apart from the company is false, then the statement that 'if electricity flows through the nerves in our bodies the same way electricity flows through a wire, then adult fish require an unobstructed migration path between the ocean and the stream spawning grounds' is incorrect is false, it can be inferred that the claim that young iguanas are pale green with black-ringed tails does not correspond with reality. Given that the statement 'if papayas come in different sizes, then if the statement that states if the claim that company scrip is a type of money with no value apart from the company is false, then the statement that 'if electricity flows through the nerves in our bodies the same way electricity flows through a wire, then adult fish require an unobstructed migration path between the ocean and the stream spawning grounds' is incorrect is false, then young iguanas are pale green with black-ringed tails' can be considered false, it can be inferred that convertible security is a certificate. Once we know all atoms are very small, we also know that papayas come in different sizes. all atoms are very small. So long as farms have animals, 'some people mistakenly believe that convertible security is a certificate' is true. So long as most liquid water supports life, 'some people mistakenly believe that convertible security is a certificate' is true. Should it be the case that tigers have (part) paws, it follows that either farms have animals or most liquid water supports life. It is fair to say that tigers have (part) paws.
|
The idea that company scrip is a type of money with no value apart from the company is true.
|
Satellites provide images of the sea surface temperatures over the entire ocean.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then (If [1], then [2].).
If (Not [0].), then (Not (If [1], then [2].).). [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then [3]. [SC1-2]
If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then (Not [3].).
Therefore, If (Not [0].), then (Not (If [1], then [2].).)..
[SC1-2]
Modus Ponens:
If [4], then (If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then [3].). [SC1-3]
[4] [SC2-3]
Therefore, If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then [3]..
[SC1-3]
Modus Tonens:
If (Not (If [4], then (If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then [3].).).), then [5].
Not [5]. [SC2-4]
Therefore, If [4], then (If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then [3].)..
[SC2-4]
Disjunction Elimination:
Either [7] or [8]. [SC1-5]
If [7], then (Not [5].).
If [8], then (Not [5].).
Therefore, Not [5]..
[SC1-5]
Modus Ponens:
If [9], then (Either [7] or [8].).
[9]
Therefore, Either [7] or [8]..
[SC2-3]
Modus Ponens:
If [6], then [4].
[6]
Therefore, [4].
|
{0: 'Company scrip is a type of money with no value apart from the company.', 1: 'Electricity flows through the nerves in our bodies the same way electricity flows through a wire.', 2: 'Adult fish require an unobstructed migration path between the ocean and the stream spawning grounds.', 3: 'Young iguanas are pale green with black-ringed tails.', 4: 'Papayas come in different sizes.', 5: 'Convertible security is a certificate.', 6: 'All atoms are very small.', 7: 'Farms have animals.', 8: 'Most liquid water supports life.', 9: 'Tigers have (part) paws.'}
| 7 |
6,799 |
['When emotional abuse can be serious and even life-threatening if left unattended is true, it follows that intellectual capital is an aspect of absolute knowledge.', 'Assuming alveolar environment influences the metabolicand biophysical properties of exogenous surfactants, we know that if shelfs are located in bookstores, then pathologists define catarrh as an inflammation of a mucous membrane.', 'Once we know disinfection uses ozonation and, particularly, chlorination to kill disease-causing microbes, we also know that either trappers use tools or some important pathogen causes gastroenteritis.', 'One may reasonably assume that if if shelfs are located in bookstores, then pathologists define catarrh as an inflammation of a mucous membrane, then paleontologists find lots of plant fossils.', 'On the condition that the statement, if either trappers use tools or some important pathogen causes gastroenteritis, then if if emotional abuse can be serious and even life-threatening if left unattended, then intellectual capital is an aspect of absolute knowledge, then strong ropes make climbing possible and special tools attach ropes to cave walls, does not hold, it is definitely the case that dogwoods are hard to spot with foliage leafing out - at the end of their season.', 'The claim that dogwoods are hard to spot with foliage leafing out - at the end of their season has no merit.', 'Either one or both of these statements are true: most minks eat fish, or either alveolar environment influences the metabolicand biophysical properties of exogenous surfactants or disinfection uses ozonation and, particularly, chlorination to kill disease-causing microbes.', 'The statement, most minks eat fish, does not hold.', 'At least one of two things is true: kelp grows quickly and the plants recover rapidly, or if paleontologists find lots of plant fossils, then if if emotional abuse can be serious and even life-threatening if left unattended, then intellectual capital is an aspect of absolute knowledge, then strong ropes make climbing possible and special tools attach ropes to cave walls.', 'Some people mistakenly believe that kelp grows quickly and the plants recover rapidly.']
|
When emotional abuse can be serious and even life-threatening if left unattended is true, it follows that intellectual capital is an aspect of absolute knowledge. Assuming alveolar environment influences the metabolicand biophysical properties of exogenous surfactants, we know that if shelfs are located in bookstores, then pathologists define catarrh as an inflammation of a mucous membrane. Once we know disinfection uses ozonation and, particularly, chlorination to kill disease-causing microbes, we also know that either trappers use tools or some important pathogen causes gastroenteritis. One may reasonably assume that if if shelfs are located in bookstores, then pathologists define catarrh as an inflammation of a mucous membrane, then paleontologists find lots of plant fossils. On the condition that the statement, if either trappers use tools or some important pathogen causes gastroenteritis, then if if emotional abuse can be serious and even life-threatening if left unattended, then intellectual capital is an aspect of absolute knowledge, then strong ropes make climbing possible and special tools attach ropes to cave walls, does not hold, it is definitely the case that dogwoods are hard to spot with foliage leafing out - at the end of their season. The claim that dogwoods are hard to spot with foliage leafing out - at the end of their season has no merit. Either one or both of these statements are true: most minks eat fish, or either alveolar environment influences the metabolicand biophysical properties of exogenous surfactants or disinfection uses ozonation and, particularly, chlorination to kill disease-causing microbes. The statement, most minks eat fish, does not hold. At least one of two things is true: kelp grows quickly and the plants recover rapidly, or if paleontologists find lots of plant fossils, then if if emotional abuse can be serious and even life-threatening if left unattended, then intellectual capital is an aspect of absolute knowledge, then strong ropes make climbing possible and special tools attach ropes to cave walls. Some people mistakenly believe that kelp grows quickly and the plants recover rapidly.
|
The claim that strong ropes make climbing possible and special tools attach ropes to cave walls holds true.
|
Those that suggest strong ropes make climbing possible and special tools attach ropes to cave walls are wrong.
|
FALSE
|
Modus Ponens:
If (If [1], then [2].), then [0]. [SC1-1]
If [1], then [2].
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (If [3], then [4].) or (Either [5] or [6].). [SC1-2]
If (If [3], then [4].), then (If (If [1], then [2].), then [0].). [SC2-2]
If (Either [5] or [6].), then (If (If [1], then [2].), then [0].). [SC3-2]
Therefore, If (If [1], then [2].), then [0]..
[SC1-2]
Constructive Dilemma:
Either [7] or [8]. [SC1-3]
If [7], then (If [3], then [4].).
If [8], then (Either [5] or [6].).
Therefore, Either (If [3], then [4].) or (Either [5] or [6].)..
[SC1-3]
Disjunctive Syllogism:
Either [11] or (Either [7] or [8].).
Not [11].
Therefore, Either [7] or [8]..
[SC2-2]
Hypothetical Syllogism:
If (If [3], then [4].), then [9].
If [9], then (If (If [1], then [2].), then [0].). [SC2-3]
Therefore, If (If [3], then [4].), then (If (If [1], then [2].), then [0].)..
[SC2-3]
Disjunctive Syllogism:
Either [12] or (If [9], then (If (If [1], then [2].), then [0].).).
Not [12].
Therefore, If [9], then (If (If [1], then [2].), then [0].)..
[SC3-2]
Modus Tonens:
If (Not (If (Either [5] or [6].), then (If (If [1], then [2].), then [0].).).), then [10].
Not [10].
Therefore, If (Either [5] or [6].), then (If (If [1], then [2].), then [0].)..
|
{0: 'Strong ropes make climbing possible and special tools attach ropes to cave walls.', 1: 'Emotional abuse can be serious and even life-threatening if left unattended.', 2: 'Intellectual capital is an aspect of absolute knowledge.', 3: 'Shelfs are located in bookstores.', 4: 'Pathologists define catarrh as an inflammation of a mucous membrane.', 5: 'Trappers use tools.', 6: 'Some important pathogen causes gastroenteritis.', 7: 'Alveolar environment influences the metabolicand biophysical properties of exogenous surfactants.', 8: 'Disinfection uses ozonation and, particularly, chlorination to kill disease-causing microbes.', 9: 'Paleontologists find lots of plant fossils.', 10: 'Dogwoods are hard to spot with foliage leafing out - at the end of their season.', 11: 'Most minks eat fish.', 12: 'Kelp grows quickly and the plants recover rapidly.'}
| 7 |
6,519 |
['It is rational to believe that either abuse can occur even when there is genuine love and affection between the people involved or mycotoxins are toxic chemicals produced by both molds and yeasts.', 'Once we know mycotoxins are toxic chemicals produced by both molds and yeasts, we also know that either vertebrae protect spinal cord or p is a measure of the heat transfer rate across a boundary between two materials.', "Once we know some vehicles have air resistance, we also know that the notion that 'vertebrae protect spinal cord' is untrue.", "So long as abuse can occur even when there is genuine love and affection between the people involved, 'either meal planning are art or snapdragons have (part) corpi' is true.", 'Provided that either meal planning are art or snapdragons have (part) corpi, we know that either vertebrae protect spinal cord or p is a measure of the heat transfer rate across a boundary between two materials.', 'There is good reason to believe that either chimps have the largest geographic range of any ape, living in jungles across central Africa or either gorillas live for years or some vehicles have air resistance.', 'We know that the claim that chimps have the largest geographic range of any ape, living in jungles across central Africa is false.', 'It is not the case that feelings can range from anger, frustration, fear, shame and guilt to numbness.', 'Either one or both of these statements are true: family physicians care for patients of all ages and handle a wide range of medical problems, or plants get most of their water directly from soil surrounding their roots.', 'Assuming family physicians care for patients of all ages and handle a wide range of medical problems, we know that feelings can range from anger, frustration, fear, shame and guilt to numbness.', "When plants get most of their water directly from soil surrounding their roots is true, it follows that if gorillas live for years, then the notion that 'vertebrae protect spinal cord' is untrue."]
|
It is rational to believe that either abuse can occur even when there is genuine love and affection between the people involved or mycotoxins are toxic chemicals produced by both molds and yeasts. Once we know mycotoxins are toxic chemicals produced by both molds and yeasts, we also know that either vertebrae protect spinal cord or p is a measure of the heat transfer rate across a boundary between two materials. Once we know some vehicles have air resistance, we also know that the notion that 'vertebrae protect spinal cord' is untrue. So long as abuse can occur even when there is genuine love and affection between the people involved, 'either meal planning are art or snapdragons have (part) corpi' is true. Provided that either meal planning are art or snapdragons have (part) corpi, we know that either vertebrae protect spinal cord or p is a measure of the heat transfer rate across a boundary between two materials. There is good reason to believe that either chimps have the largest geographic range of any ape, living in jungles across central Africa or either gorillas live for years or some vehicles have air resistance. We know that the claim that chimps have the largest geographic range of any ape, living in jungles across central Africa is false. It is not the case that feelings can range from anger, frustration, fear, shame and guilt to numbness. Either one or both of these statements are true: family physicians care for patients of all ages and handle a wide range of medical problems, or plants get most of their water directly from soil surrounding their roots. Assuming family physicians care for patients of all ages and handle a wide range of medical problems, we know that feelings can range from anger, frustration, fear, shame and guilt to numbness. When plants get most of their water directly from soil surrounding their roots is true, it follows that if gorillas live for years, then the notion that 'vertebrae protect spinal cord' is untrue.
|
The statement 'p is a measure of the heat transfer rate across a boundary between two materials' is true.
|
The statement 'p is a measure of the heat transfer rate across a boundary between two materials' is true.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Either [1] or [0].). [SC2-2]
If [5], then (Either [1] or [0].).
Therefore, Either [1] or [0]..
[SC2-2]
Hypothetical Syllogism:
If [4], then (Either [6] or [7].).
If (Either [6] or [7].), then (Either [1] or [0].).
Therefore, If [4], then (Either [1] or [0].)..
[SC2-1]
Disjunction Elimination:
Either [2] or [3]. [SC1-2]
If [2], then (Not [1].). [SC2-2]
If [3], then (Not [1].).
Therefore, Not [1]..
[SC1-2]
Disjunctive Syllogism:
Either [8] or (Either [2] or [3].).
Not [8].
Therefore, Either [2] or [3]..
[SC2-2]
Disjunctive Syllogism:
Either [9] or (If [2], then (Not [1].).). [SC1-3]
Not [9].
Therefore, If [2], then (Not [1].)..
[SC1-3]
Constructive Dilemma:
Either [10] or [11].
If [10], then [9].
If [11], then (If [2], then (Not [1].).).
Therefore, Either [9] or (If [2], then (Not [1].).)..
|
{0: 'P is a measure of the heat transfer rate across a boundary between two materials.', 1: 'Vertebrae protect spinal cord.', 2: 'Gorillas live for years.', 3: 'Some vehicles have air resistance.', 4: 'Abuse can occur even when there is genuine love and affection between the people involved.', 5: 'Mycotoxins are toxic chemicals produced by both molds and yeasts.', 6: 'Meal planning are art.', 7: 'Snapdragons have (part) corpi.', 8: 'Chimps have the largest geographic range of any ape, living in jungles across central Africa.', 9: 'Feelings can range from anger, frustration, fear, shame and guilt to numbness.', 10: 'Family physicians care for patients of all ages and handle a wide range of medical problems.', 11: 'Plants get most of their water directly from soil surrounding their roots.'}
| 7 |
6,107 |
['It is the case that muscles of respiration are the diaphragm and intercostal muscles of the rib cage.', 'If life is what makes inorganic material organic, then heart rate varies between people because of fitness, age and genetics.', "The notion that 'a thwart is a bracing' is untrue.", "Once we know either some biologists work with crocodiles or many parents give information, we also know that the statement 'heart rate varies between people because of fitness, age and genetics' can be considered false.", 'It is a fact that either some biologists work with crocodiles or many parents give information.', "So long as the claim that if the statement 'if muscles of respiration are the diaphragm and intercostal muscles of the rib cage, then if the notion that 'some plants have specific pH preferences' is untrue, then life is what makes inorganic material organic' can be considered false, then a thwart is a bracing is false, 'if pesticide exposure has major impact, then mating systems affect greatly the degree of allele persistence, especially in small populations' is true.", "Given that the claim that if the statement 'if muscles of respiration are the diaphragm and intercostal muscles of the rib cage, then if the notion that 'some plants have specific pH preferences' is untrue, then life is what makes inorganic material organic' can be considered false, then a thwart is a bracing is false, it can be inferred that predatory thrips are tiny, slender, black insects that can be locally important mite predators.", "So long as predatory thrips are tiny, slender, black insects that can be locally important mite predators, 'the claim that if pesticide exposure has major impact, then mating systems affect greatly the degree of allele persistence, especially in small populations is false' is true."]
|
It is the case that muscles of respiration are the diaphragm and intercostal muscles of the rib cage. If life is what makes inorganic material organic, then heart rate varies between people because of fitness, age and genetics. The notion that 'a thwart is a bracing' is untrue. Once we know either some biologists work with crocodiles or many parents give information, we also know that the statement 'heart rate varies between people because of fitness, age and genetics' can be considered false. It is a fact that either some biologists work with crocodiles or many parents give information. So long as the claim that if the statement 'if muscles of respiration are the diaphragm and intercostal muscles of the rib cage, then if the notion that 'some plants have specific pH preferences' is untrue, then life is what makes inorganic material organic' can be considered false, then a thwart is a bracing is false, 'if pesticide exposure has major impact, then mating systems affect greatly the degree of allele persistence, especially in small populations' is true. Given that the claim that if the statement 'if muscles of respiration are the diaphragm and intercostal muscles of the rib cage, then if the notion that 'some plants have specific pH preferences' is untrue, then life is what makes inorganic material organic' can be considered false, then a thwart is a bracing is false, it can be inferred that predatory thrips are tiny, slender, black insects that can be locally important mite predators. So long as predatory thrips are tiny, slender, black insects that can be locally important mite predators, 'the claim that if pesticide exposure has major impact, then mating systems affect greatly the degree of allele persistence, especially in small populations is false' is true.
|
It is the case that some plants have specific pH preferences.
|
It is a common misconception that some plants have specific pH preferences.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (If (Not [0].), then [1].). [SC1-2]
[3]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Tonens:
If (Not (If [3], then (If (Not [0].), then [1].).).), then [6]. [SC1-3]
Not [6].
Therefore, If [3], then (If (Not [0].), then [1].)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If (Not (If [3], then (If (Not [0].), then [1].).).), then [6].).), then (If [7], then [8].).
If (Not (If (Not (If [3], then (If (Not [0].), then [1].).).), then [6].).), then (Not (If [7], then [8].).). [SC2-4]
Therefore, If (Not (If [3], then (If (Not [0].), then [1].).).), then [6]..
[SC2-4]
Hypothetical Syllogism:
If (Not (If (Not (If [3], then (If (Not [0].), then [1].).).), then [6].).), then [9].
If [9], then (Not (If [7], then [8].).).
Therefore, If (Not (If (Not (If [3], then (If (Not [0].), then [1].).).), then [6].).), then (Not (If [7], then [8].).)..
[SC2-1]
Modus Tonens:
If [1], then [2].
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Modus Ponens:
If (Either [4] or [5].), then (Not [2].).
Either [4] or [5].
Therefore, Not [2]..
|
{0: 'Some plants have specific pH preferences.', 1: 'Life is what makes inorganic material organic.', 2: 'Heart rate varies between people because of fitness, age and genetics.', 3: 'Muscles of respiration are the diaphragm and intercostal muscles of the rib cage.', 4: 'Some biologists work with crocodiles.', 5: 'Many parents give information.', 6: 'A thwart is a bracing.', 7: 'Pesticide exposure has major impact.', 8: 'Mating systems affect greatly the degree of allele persistence, especially in small populations.', 9: 'Predatory thrips are tiny, slender, black insects that can be locally important mite predators.'}
| 7 |
6,708 |
['Should it be the case that older people play a vital role in our society, it follows that if adoption is a method of joining a family just as birth is, then some alveoluses have walls.', 'Either one or both of these statements are true: a mudder is a horse, or the statement that states some alveoluses have walls is false.', 'If most underwater photographers display coloration, then either older people play a vital role in our society or feet are the main mode of transport.', 'It is rational to agree that most underwater photographers display coloration.', 'When feet are the main mode of transport is true, it follows that acid deposition can have many harmful ecological effects in both aquatic and terrestrial systems.', 'Once we know acid deposition can have many harmful ecological effects in both aquatic and terrestrial systems, we also know that if adoption is a method of joining a family just as birth is, then some alveoluses have walls.', 'Given that a mudder is a horse, it can be inferred that radiant heat is heat that comes from a source such as the sun, a fire, furnace or a heat lamp.', 'There is good reason to believe that either sites support few individuals or child is the father to man.', "Whenever it is true that sites support few individuals, 'if a mudder is a horse, then the claim that radiant heat is heat that comes from a source such as the sun, a fire, furnace or a heat lamp does not reflect reality' is true.", "So long as child is the father to man, 'if a mudder is a horse, then the claim that radiant heat is heat that comes from a source such as the sun, a fire, furnace or a heat lamp does not reflect reality' is true."]
|
Should it be the case that older people play a vital role in our society, it follows that if adoption is a method of joining a family just as birth is, then some alveoluses have walls. Either one or both of these statements are true: a mudder is a horse, or the statement that states some alveoluses have walls is false. If most underwater photographers display coloration, then either older people play a vital role in our society or feet are the main mode of transport. It is rational to agree that most underwater photographers display coloration. When feet are the main mode of transport is true, it follows that acid deposition can have many harmful ecological effects in both aquatic and terrestrial systems. Once we know acid deposition can have many harmful ecological effects in both aquatic and terrestrial systems, we also know that if adoption is a method of joining a family just as birth is, then some alveoluses have walls. Given that a mudder is a horse, it can be inferred that radiant heat is heat that comes from a source such as the sun, a fire, furnace or a heat lamp. There is good reason to believe that either sites support few individuals or child is the father to man. Whenever it is true that sites support few individuals, 'if a mudder is a horse, then the claim that radiant heat is heat that comes from a source such as the sun, a fire, furnace or a heat lamp does not reflect reality' is true. So long as child is the father to man, 'if a mudder is a horse, then the claim that radiant heat is heat that comes from a source such as the sun, a fire, furnace or a heat lamp does not reflect reality' is true.
|
The claim that adoption is a method of joining a family just as birth is is false.
|
The statement 'adoption is a legal process' can be considered false.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [2] or [3]. [SC1-2]
If [2], then (If [0], then [1].).
If [3], then (If [0], then [1].). [SC3-2]
Therefore, If [0], then [1]..
[SC1-2]
Modus Ponens:
If [6], then (Either [2] or [3].).
[6]
Therefore, Either [2] or [3]..
[SC3-2]
Hypothetical Syllogism:
If [3], then [5].
If [5], then (If [0], then [1].).
Therefore, If [3], then (If [0], then [1].)..
[SC2-1]
Disjunctive Syllogism:
Either [4] or (Not [1].).
Not [4]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Reductio Ad Absurdum:
If [4], then [7].
If [4], then (Not [7].). [SC2-3]
Therefore, Not [4]..
[SC2-3]
Disjunction Elimination:
Either [8] or [9].
If [8], then (If [4], then (Not [7].).).
If [9], then (If [4], then (Not [7].).).
Therefore, If [4], then (Not [7].)..
|
{0: 'Adoption is a method of joining a family just as birth is.', 1: 'Some alveoluses have walls.', 2: 'Older people play a vital role in our society.', 3: 'Feet are the main mode of transport.', 4: 'A mudder is a horse.', 5: 'Acid deposition can have many harmful ecological effects in both aquatic and terrestrial systems.', 6: 'Most underwater photographers display coloration.', 7: 'Radiant heat is heat that comes from a source such as the sun, a fire, furnace or a heat lamp.', 8: 'Sites support few individuals.', 9: 'Child is the father to man.'}
| 7 |
6,634 |
["On the condition that the notion that 'vocalization is also of great use to the ring-tailed lemur' is untrue, it is definitely the case that pressure sodium vapor light has lesser effects.", "If most people inhabit countries, then if the notion that 'vocalization is also of great use to the ring-tailed lemur' is untrue, then the statement 'animals return to homes' can be considered false.", "The statement 'most people inhabit countries' is true.", "Should it be the case that those that suggest if pressure sodium vapor light has lesser effects, then animals return to homes are wrong, it follows that the notion that 'either biblical references mention barley's dietary use in long-ago cultures or kidney stones come in virtually any color,though most are yellow to brown' is untrue.", "Assuming the claim that if those that suggest if pressure sodium vapor light has lesser effects, then animals return to homes are wrong, then either biblical references mention barley's dietary use in long-ago cultures or kidney stones come in virtually any color,though most are yellow to brown has no merit, we know that behavior reveals states.", 'At least one of two things is true: crocodilians use a variety of calls, smells and water behavior to communicate with each other, or anxiety is characterized by excessive worry about unrealistic or exaggerated life circumstances.', "Once we know anxiety is characterized by excessive worry about unrealistic or exaggerated life circumstances, we also know that if the claim that if those that suggest if pressure sodium vapor light has lesser effects, then animals return to homes are wrong, then either biblical references mention barley's dietary use in long-ago cultures or kidney stones come in virtually any color,though most are yellow to brown has no merit, then those that suggest behavior reveals states are wrong.", 'Assuming crocodilians use a variety of calls, smells and water behavior to communicate with each other, we know that infants can eat well and grow properly when parents feed on demand.', "So long as infants can eat well and grow properly when parents feed on demand, 'if the claim that if those that suggest if pressure sodium vapor light has lesser effects, then animals return to homes are wrong, then either biblical references mention barley's dietary use in long-ago cultures or kidney stones come in virtually any color,though most are yellow to brown has no merit, then those that suggest behavior reveals states are wrong' is true."]
|
On the condition that the notion that 'vocalization is also of great use to the ring-tailed lemur' is untrue, it is definitely the case that pressure sodium vapor light has lesser effects. If most people inhabit countries, then if the notion that 'vocalization is also of great use to the ring-tailed lemur' is untrue, then the statement 'animals return to homes' can be considered false. The statement 'most people inhabit countries' is true. Should it be the case that those that suggest if pressure sodium vapor light has lesser effects, then animals return to homes are wrong, it follows that the notion that 'either biblical references mention barley's dietary use in long-ago cultures or kidney stones come in virtually any color,though most are yellow to brown' is untrue. Assuming the claim that if those that suggest if pressure sodium vapor light has lesser effects, then animals return to homes are wrong, then either biblical references mention barley's dietary use in long-ago cultures or kidney stones come in virtually any color,though most are yellow to brown has no merit, we know that behavior reveals states. At least one of two things is true: crocodilians use a variety of calls, smells and water behavior to communicate with each other, or anxiety is characterized by excessive worry about unrealistic or exaggerated life circumstances. Once we know anxiety is characterized by excessive worry about unrealistic or exaggerated life circumstances, we also know that if the claim that if those that suggest if pressure sodium vapor light has lesser effects, then animals return to homes are wrong, then either biblical references mention barley's dietary use in long-ago cultures or kidney stones come in virtually any color,though most are yellow to brown has no merit, then those that suggest behavior reveals states are wrong. Assuming crocodilians use a variety of calls, smells and water behavior to communicate with each other, we know that infants can eat well and grow properly when parents feed on demand. So long as infants can eat well and grow properly when parents feed on demand, 'if the claim that if those that suggest if pressure sodium vapor light has lesser effects, then animals return to homes are wrong, then either biblical references mention barley's dietary use in long-ago cultures or kidney stones come in virtually any color,though most are yellow to brown has no merit, then those that suggest behavior reveals states are wrong' is true.
|
It is fair to say that vocalization is also of great use to the ring-tailed lemur.
|
It is fair to say that vocalization is also of great use to the ring-tailed lemur.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [3].
If [3], then [1]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [3], then [1].).), then (Either [4] or [5].). [SC1-3]
If (Not (If [3], then [1].).), then (Not (Either [4] or [5].).).
Therefore, If [3], then [1]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If (Not (If [3], then [1].).), then (Either [4] or [5].).).), then [6].
If (Not (If (Not (If [3], then [1].).), then (Either [4] or [5].).).), then (Not [6].). [SC2-4]
Therefore, If (Not (If [3], then [1].).), then (Either [4] or [5].)..
[SC2-4]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If (Not (If (Not (If [3], then [1].).), then (Either [4] or [5].).).), then (Not [6].).). [SC2-5]
If [8], then (If (Not (If (Not (If [3], then [1].).), then (Either [4] or [5].).).), then (Not [6].).).
Therefore, If (Not (If (Not (If [3], then [1].).), then (Either [4] or [5].).).), then (Not [6].)..
[SC2-5]
Hypothetical Syllogism:
If [7], then [9].
If [9], then (If (Not (If (Not (If [3], then [1].).), then (Either [4] or [5].).).), then (Not [6].).).
Therefore, If [7], then (If (Not (If (Not (If [3], then [1].).), then (Either [4] or [5].).).), then (Not [6].).)..
[SC2-1]
Modus Ponens:
If [2], then (If (Not [0].), then (Not [1].).).
[2]
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Vocalization is also of great use to the ring-tailed lemur.', 1: 'Animals return to homes.', 2: 'Most people inhabit countries.', 3: 'Pressure sodium vapor light has lesser effects.', 4: "Biblical references mention barley's dietary use in long-ago cultures.", 5: 'Kidney stones come in virtually any color,though most are yellow to brown.', 6: 'Behavior reveals states.', 7: 'Crocodilians use a variety of calls, smells and water behavior to communicate with each other.', 8: 'Anxiety is characterized by excessive worry about unrealistic or exaggerated life circumstances.', 9: 'Infants can eat well and grow properly when parents feed on demand.'}
| 7 |
6,223 |
["Whenever it is true that the claim that if it is a common misconception that a megalomania is a mental condition, then oil provides a route for heat to escape is false, 'either bankruptcy is a remedy that is governed almost exclusively by federal law or law is itself the expression of a state of order and rhythm eternally established in the universe' is true.", 'Given that oil provides a route for heat to escape, it can be inferred that piano tuners increase and decrease the tension of piano strings to tune pianos to the proper pitch.', "Given that oil provides a route for heat to escape, it can be inferred that the notion that 'piano tuners increase and decrease the tension of piano strings to tune pianos to the proper pitch' is untrue.", 'If it is not true that if finite populations can behave very differently from infinite populations, then the claim that either bankruptcy is a remedy that is governed almost exclusively by federal law or law is itself the expression of a state of order and rhythm eternally established in the universe does not correspond with reality, then rocks are produced in a variety of ways and have been cycled in some area many times.', 'Provided that it is not true that if finite populations can behave very differently from infinite populations, then the claim that either bankruptcy is a remedy that is governed almost exclusively by federal law or law is itself the expression of a state of order and rhythm eternally established in the universe does not correspond with reality, we know that we know that the claim that rocks are produced in a variety of ways and have been cycled in some area many times is false.', 'Given that it is a common misconception that finite populations can behave very differently from infinite populations, it can be inferred that salamanders can live in water as well as on land.', 'One may reasonably assume that if anions are hydrogen atoms, which carry extra electrons, then the statement, salamanders can live in water as well as on land, does not hold.', 'Many people rightly believe that anions are hydrogen atoms, which carry extra electrons.']
|
Whenever it is true that the claim that if it is a common misconception that a megalomania is a mental condition, then oil provides a route for heat to escape is false, 'either bankruptcy is a remedy that is governed almost exclusively by federal law or law is itself the expression of a state of order and rhythm eternally established in the universe' is true. Given that oil provides a route for heat to escape, it can be inferred that piano tuners increase and decrease the tension of piano strings to tune pianos to the proper pitch. Given that oil provides a route for heat to escape, it can be inferred that the notion that 'piano tuners increase and decrease the tension of piano strings to tune pianos to the proper pitch' is untrue. If it is not true that if finite populations can behave very differently from infinite populations, then the claim that either bankruptcy is a remedy that is governed almost exclusively by federal law or law is itself the expression of a state of order and rhythm eternally established in the universe does not correspond with reality, then rocks are produced in a variety of ways and have been cycled in some area many times. Provided that it is not true that if finite populations can behave very differently from infinite populations, then the claim that either bankruptcy is a remedy that is governed almost exclusively by federal law or law is itself the expression of a state of order and rhythm eternally established in the universe does not correspond with reality, we know that we know that the claim that rocks are produced in a variety of ways and have been cycled in some area many times is false. Given that it is a common misconception that finite populations can behave very differently from infinite populations, it can be inferred that salamanders can live in water as well as on land. One may reasonably assume that if anions are hydrogen atoms, which carry extra electrons, then the statement, salamanders can live in water as well as on land, does not hold. Many people rightly believe that anions are hydrogen atoms, which carry extra electrons.
|
The claim that a megalomania is a mental condition holds true.
|
The claim that a megalomania is a mental condition does not correspond with reality.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Not [0].), then [1].).), then (Either [3] or [4].).
Not (Either [3] or [4].). [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Modus Ponens:
If [5], then (Not (Either [3] or [4].).). [SC1-3]
[5] [SC2-3]
Therefore, Not (Either [3] or [4].)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If [5], then (Not (Either [3] or [4].).).).), then [6].
If (Not (If [5], then (Not (Either [3] or [4].).).).), then (Not [6].).
Therefore, If [5], then (Not (Either [3] or [4].).)..
[SC2-3]
Modus Tonens:
If (Not [5].), then [7].
Not [7]. [SC2-4]
Therefore, [5].
[SC2-4]
Modus Ponens:
If [8], then (Not [7].).
[8]
Therefore, Not [7]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2].
If [1], then (Not [2].).
Therefore, Not [1]..
|
{0: 'A megalomania is a mental condition.', 1: 'Oil provides a route for heat to escape.', 2: 'Piano tuners increase and decrease the tension of piano strings to tune pianos to the proper pitch.', 3: 'Bankruptcy is a remedy that is governed almost exclusively by federal law.', 4: 'Law is itself the expression of a state of order and rhythm eternally established in the universe.', 5: 'Finite populations can behave very differently from infinite populations.', 6: 'Rocks are produced in a variety of ways and have been cycled in some area many times.', 7: 'Salamanders can live in water as well as on land.', 8: 'Anions are hydrogen atoms, which carry extra electrons.'}
| 7 |
6,327 |
['The claim that some deficiencies lead to deficiency anemia holds true.', 'It is rational to believe that either either spicules are highly varied, and to some extent, are distinct for each species of sponge or moray eels possess a menacing appearance, with their mouths constantly agape or ringworm is a superficial skin infection, also known as tinea.', 'Either one or both of these statements are true: air can enter the body through the nostrils and the mouth, or isometric exercises release tension and help alleviate neck spasms.', 'Given that air can enter the body through the nostrils and the mouth, it can be inferred that if either spicules are highly varied, and to some extent, are distinct for each species of sponge or moray eels possess a menacing appearance, with their mouths constantly agape, then if some deficiencies lead to deficiency anemia, then new muscles are formed by muscle stem cells.', 'There is good reason to believe that either if molecular biology is the field of genetic engineering, then equinox isa entity or surface layer is rich in oxygen because of photosynthesis and contact with the atmosphere.', 'Once we know if molecular biology is the field of genetic engineering, then equinox isa entity, we also know that if isometric exercises release tension and help alleviate neck spasms, then if either spicules are highly varied, and to some extent, are distinct for each species of sponge or moray eels possess a menacing appearance, with their mouths constantly agape, then if some deficiencies lead to deficiency anemia, then new muscles are formed by muscle stem cells.', 'On the condition that surface layer is rich in oxygen because of photosynthesis and contact with the atmosphere, it is definitely the case that if isometric exercises release tension and help alleviate neck spasms, then if either spicules are highly varied, and to some extent, are distinct for each species of sponge or moray eels possess a menacing appearance, with their mouths constantly agape, then if some deficiencies lead to deficiency anemia, then new muscles are formed by muscle stem cells.', 'We know that at least one of two things is true: wild yak prefer to live in herds of tens or even hundreds of animals, or if the claim that if ringworm is a superficial skin infection, also known as tinea, then if some deficiencies lead to deficiency anemia, then new muscles are formed by muscle stem cells has no merit, then migratory behaviour has components.', "The notion that 'wild yak prefer to live in herds of tens or even hundreds of animals' is untrue.", 'One may reasonably assume that if if starlings are a dark chunky, muscular bird, then banks are in the business of renting money, then it is a common misconception that migratory behaviour has components.', 'On the condition that starlings are a dark chunky, muscular bird, it is definitely the case that banks are in the business of renting money.']
|
The claim that some deficiencies lead to deficiency anemia holds true. It is rational to believe that either either spicules are highly varied, and to some extent, are distinct for each species of sponge or moray eels possess a menacing appearance, with their mouths constantly agape or ringworm is a superficial skin infection, also known as tinea. Either one or both of these statements are true: air can enter the body through the nostrils and the mouth, or isometric exercises release tension and help alleviate neck spasms. Given that air can enter the body through the nostrils and the mouth, it can be inferred that if either spicules are highly varied, and to some extent, are distinct for each species of sponge or moray eels possess a menacing appearance, with their mouths constantly agape, then if some deficiencies lead to deficiency anemia, then new muscles are formed by muscle stem cells. There is good reason to believe that either if molecular biology is the field of genetic engineering, then equinox isa entity or surface layer is rich in oxygen because of photosynthesis and contact with the atmosphere. Once we know if molecular biology is the field of genetic engineering, then equinox isa entity, we also know that if isometric exercises release tension and help alleviate neck spasms, then if either spicules are highly varied, and to some extent, are distinct for each species of sponge or moray eels possess a menacing appearance, with their mouths constantly agape, then if some deficiencies lead to deficiency anemia, then new muscles are formed by muscle stem cells. On the condition that surface layer is rich in oxygen because of photosynthesis and contact with the atmosphere, it is definitely the case that if isometric exercises release tension and help alleviate neck spasms, then if either spicules are highly varied, and to some extent, are distinct for each species of sponge or moray eels possess a menacing appearance, with their mouths constantly agape, then if some deficiencies lead to deficiency anemia, then new muscles are formed by muscle stem cells. We know that at least one of two things is true: wild yak prefer to live in herds of tens or even hundreds of animals, or if the claim that if ringworm is a superficial skin infection, also known as tinea, then if some deficiencies lead to deficiency anemia, then new muscles are formed by muscle stem cells has no merit, then migratory behaviour has components. The notion that 'wild yak prefer to live in herds of tens or even hundreds of animals' is untrue. One may reasonably assume that if if starlings are a dark chunky, muscular bird, then banks are in the business of renting money, then it is a common misconception that migratory behaviour has components. On the condition that starlings are a dark chunky, muscular bird, it is definitely the case that banks are in the business of renting money.
|
The statement 'new muscles are formed by muscle stem cells' is true.
|
The statement 'new muscles are formed by muscle stem cells' is true.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [2] or [3].) or [4].
If (Either [2] or [3].), then (If [1], then [0].). [SC2-2]
If [4], then (If [1], then [0].). [SC3-2]
Therefore, If [1], then [0]..
[SC2-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Either [2] or [3].), then (If [1], then [0].).).
If [6], then (If (Either [2] or [3].), then (If [1], then [0].).). [SC3-3]
Therefore, If (Either [2] or [3].), then (If [1], then [0].)..
[SC3-3]
Disjunction Elimination:
Either (If [11], then [12].) or [13].
If (If [11], then [12].), then (If [6], then (If (Either [2] or [3].), then (If [1], then [0].).).).
If [13], then (If [6], then (If (Either [2] or [3].), then (If [1], then [0].).).).
Therefore, If [6], then (If (Either [2] or [3].), then (If [1], then [0].).)..
[SC3-2]
Modus Tonens:
If (Not (If [4], then (If [1], then [0].).).), then [7]. [SC1-3]
Not [7]. [SC2-3]
Therefore, If [4], then (If [1], then [0].)..
[SC1-3]
Disjunctive Syllogism:
Either [8] or (If (Not (If [4], then (If [1], then [0].).).), then [7].).
Not [8].
Therefore, If (Not (If [4], then (If [1], then [0].).).), then [7]..
[SC2-3]
Modus Ponens:
If (If [9], then [10].), then (Not [7].).
If [9], then [10].
Therefore, Not [7]..
|
{0: 'New muscles are formed by muscle stem cells.', 1: 'Some deficiencies lead to deficiency anemia.', 2: 'Spicules are highly varied, and to some extent, are distinct for each species of sponge.', 3: 'Moray eels possess a menacing appearance, with their mouths constantly agape.', 4: 'Ringworm is a superficial skin infection, also known as tinea.', 5: 'Air can enter the body through the nostrils and the mouth.', 6: 'Isometric exercises release tension and help alleviate neck spasms.', 7: 'Migratory behaviour has components.', 8: 'Wild yak prefer to live in herds of tens or even hundreds of animals.', 9: 'Starlings are a dark chunky, muscular bird.', 10: 'Banks are in the business of renting money.', 11: 'Molecular biology is the field of genetic engineering.', 12: 'Equinox isa entity.', 13: 'Surface layer is rich in oxygen because of photosynthesis and contact with the atmosphere.'}
| 7 |
6,102 |
['On the condition that direct sunlight adds heat to the body by radiation, it is definitely the case that organisms grow on limestone, shaping the spire shapes.', 'Once we know lucifer means light-bearer , we also know that either direct sunlight adds heat to the body by radiation or lung cancer is one of the major health threats facing American women today.', 'At least one of two things is true: athletes include rhythmic gymnasts, or if dark pans absorb more heat than light ones and cook cakes faster, then flowers have stems.', 'Once we know either coral reefs are very fragile colonies that can be damaged by human trespassing or glycolysis is a determined sequence of ten enzyme -catalyzed reactions, we also know that either risk is considered to be part of investing or lucifer means light-bearer .', 'It is rational to believe that either coral reefs are very fragile colonies that can be damaged by human trespassing or glycolysis is a determined sequence of ten enzyme -catalyzed reactions.', "At least one of two things is true: if some women hate squirrels, then nutrient pollution appears to have a significant impact on the crab's habitat, or most cockleburs are classified as weeds.", "Assuming if some women hate squirrels, then nutrient pollution appears to have a significant impact on the crab's habitat, we know that if risk is considered to be part of investing, then either direct sunlight adds heat to the body by radiation or lung cancer is one of the major health threats facing American women today.", 'If most cockleburs are classified as weeds, then if risk is considered to be part of investing, then either direct sunlight adds heat to the body by radiation or lung cancer is one of the major health threats facing American women today.', 'Should it be the case that molds are the decomposers of the food chain, and that is also their ecological niche, it follows that if athletes include rhythmic gymnasts, then if lung cancer is one of the major health threats facing American women today, then organisms grow on limestone, shaping the spire shapes.', 'It is the case that molds are the decomposers of the food chain, and that is also their ecological niche.', 'Given that if dark pans absorb more heat than light ones and cook cakes faster, then flowers have stems, it can be inferred that either every culture has a history of using medicinal plants to cure their ailments or short life is the price of being a magnetar.', 'One may reasonably assume that if either every culture has a history of using medicinal plants to cure their ailments or short life is the price of being a magnetar, then if lung cancer is one of the major health threats facing American women today, then organisms grow on limestone, shaping the spire shapes.']
|
On the condition that direct sunlight adds heat to the body by radiation, it is definitely the case that organisms grow on limestone, shaping the spire shapes. Once we know lucifer means light-bearer , we also know that either direct sunlight adds heat to the body by radiation or lung cancer is one of the major health threats facing American women today. At least one of two things is true: athletes include rhythmic gymnasts, or if dark pans absorb more heat than light ones and cook cakes faster, then flowers have stems. Once we know either coral reefs are very fragile colonies that can be damaged by human trespassing or glycolysis is a determined sequence of ten enzyme -catalyzed reactions, we also know that either risk is considered to be part of investing or lucifer means light-bearer . It is rational to believe that either coral reefs are very fragile colonies that can be damaged by human trespassing or glycolysis is a determined sequence of ten enzyme -catalyzed reactions. At least one of two things is true: if some women hate squirrels, then nutrient pollution appears to have a significant impact on the crab's habitat, or most cockleburs are classified as weeds. Assuming if some women hate squirrels, then nutrient pollution appears to have a significant impact on the crab's habitat, we know that if risk is considered to be part of investing, then either direct sunlight adds heat to the body by radiation or lung cancer is one of the major health threats facing American women today. If most cockleburs are classified as weeds, then if risk is considered to be part of investing, then either direct sunlight adds heat to the body by radiation or lung cancer is one of the major health threats facing American women today. Should it be the case that molds are the decomposers of the food chain, and that is also their ecological niche, it follows that if athletes include rhythmic gymnasts, then if lung cancer is one of the major health threats facing American women today, then organisms grow on limestone, shaping the spire shapes. It is the case that molds are the decomposers of the food chain, and that is also their ecological niche. Given that if dark pans absorb more heat than light ones and cook cakes faster, then flowers have stems, it can be inferred that either every culture has a history of using medicinal plants to cure their ailments or short life is the price of being a magnetar. One may reasonably assume that if either every culture has a history of using medicinal plants to cure their ailments or short life is the price of being a magnetar, then if lung cancer is one of the major health threats facing American women today, then organisms grow on limestone, shaping the spire shapes.
|
organisms grow on limestone, shaping the spire shapes.
|
The claim that organisms grow on limestone, shaping the spire shapes has no merit.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [6] or [7]. [SC1-2]
If [6], then (Either [1] or [2].). [SC2-2]
If [7], then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC1-2]
Modus Ponens:
If (Either [8] or [9].), then (Either [6] or [7].).
Either [8] or [9].
Therefore, Either [6] or [7]..
[SC2-2]
Disjunction Elimination:
Either (If [10], then [11].) or [12].
If (If [10], then [11].), then (If [6], then (Either [1] or [2].).).
If [12], then (If [6], then (Either [1] or [2].).).
Therefore, If [6], then (Either [1] or [2].)..
[SC3-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then (If [2], then [0].). [SC2-2]
If (If [4], then [5].), then (If [2], then [0].). [SC3-2]
Therefore, If [2], then [0]..
[SC2-2]
Modus Ponens:
If [13], then (If [3], then (If [2], then [0].).).
[13]
Therefore, If [3], then (If [2], then [0].)..
[SC3-2]
Hypothetical Syllogism:
If (If [4], then [5].), then (Either [14] or [15].).
If (Either [14] or [15].), then (If [2], then [0].).
Therefore, If (If [4], then [5].), then (If [2], then [0].)..
|
{0: 'Organisms grow on limestone, shaping the spire shapes.', 1: 'Direct sunlight adds heat to the body by radiation.', 2: 'Lung cancer is one of the major health threats facing American women today.', 3: 'Athletes include rhythmic gymnasts.', 4: 'Dark pans absorb more heat than light ones and cook cakes faster.', 5: 'Flowers have stems.', 6: 'Risk is considered to be part of investing.', 7: 'Lucifer means light-bearer .', 8: 'Coral reefs are very fragile colonies that can be damaged by human trespassing.', 9: 'Glycolysis is a determined sequence of ten enzyme -catalyzed reactions.', 10: 'Some women hate squirrels.', 11: "Nutrient pollution appears to have a significant impact on the crab's habitat.", 12: 'Most cockleburs are classified as weeds.', 13: 'Molds are the decomposers of the food chain, and that is also their ecological niche.', 14: 'Every culture has a history of using medicinal plants to cure their ailments.', 15: 'Short life is the price of being a magnetar.'}
| 7 |
6,704 |
['Assuming crakes have (part) sterna, we know that the claim that canned good is located in pantries is false.', "So long as either most female flowers contain stigma or birds are the desert's alarm clock, 'the claim that canned good is located in pantries is false' is true.", 'When wind dispersal allows for movement over long distances is true, it follows that good compost contains an enormous number of food resources for beneficial organisms.', "When good compost contains an enormous number of food resources for beneficial organisms is true, it follows that either crakes have (part) sterna or either most female flowers contain stigma or birds are the desert's alarm clock.", 'We know that either insurance agents help individuals and businesses protect their financial assets or life is the characteristic state of organisms.', 'Should it be the case that life is the characteristic state of organisms, it follows that wind dispersal allows for movement over long distances.', 'There is good reason to believe that either spark power is voltage times the current times a correction factor or if some people mistakenly believe that if insurance agents help individuals and businesses protect their financial assets, then wind dispersal allows for movement over long distances, then either infected ticks transmit the rickettsiae to rabbits, squirrels, deer, bears, dogs, and humans or physiological function is based on substance.', 'We know that the claim that spark power is voltage times the current times a correction factor is false.', 'We know that at least one of two things is true: most astronomers use optical telescopes, or if some people mistakenly believe that if insurance agents help individuals and businesses protect their financial assets, then wind dispersal allows for movement over long distances, then some people mistakenly believe that either infected ticks transmit the rickettsiae to rabbits, squirrels, deer, bears, dogs, and humans or physiological function is based on substance.', 'It is not true that most astronomers use optical telescopes.']
|
Assuming crakes have (part) sterna, we know that the claim that canned good is located in pantries is false. So long as either most female flowers contain stigma or birds are the desert's alarm clock, 'the claim that canned good is located in pantries is false' is true. When wind dispersal allows for movement over long distances is true, it follows that good compost contains an enormous number of food resources for beneficial organisms. When good compost contains an enormous number of food resources for beneficial organisms is true, it follows that either crakes have (part) sterna or either most female flowers contain stigma or birds are the desert's alarm clock. We know that either insurance agents help individuals and businesses protect their financial assets or life is the characteristic state of organisms. Should it be the case that life is the characteristic state of organisms, it follows that wind dispersal allows for movement over long distances. There is good reason to believe that either spark power is voltage times the current times a correction factor or if some people mistakenly believe that if insurance agents help individuals and businesses protect their financial assets, then wind dispersal allows for movement over long distances, then either infected ticks transmit the rickettsiae to rabbits, squirrels, deer, bears, dogs, and humans or physiological function is based on substance. We know that the claim that spark power is voltage times the current times a correction factor is false. We know that at least one of two things is true: most astronomers use optical telescopes, or if some people mistakenly believe that if insurance agents help individuals and businesses protect their financial assets, then wind dispersal allows for movement over long distances, then some people mistakenly believe that either infected ticks transmit the rickettsiae to rabbits, squirrels, deer, bears, dogs, and humans or physiological function is based on substance. It is not true that most astronomers use optical telescopes.
|
The claim that canned good is located in pantries is false.
|
Many people rightly believe that canned good is located in pantries.
|
FALSE
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].). [SC1-1]
If [1], then (Not [0].).
If (Either [2] or [3].), then (Not [0].).
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [4], then (Either [1] or (Either [2] or [3].).). [SC1-2]
[4] [SC2-2]
Therefore, Either [1] or (Either [2] or [3].)..
[SC1-2]
Hypothetical Syllogism:
If [4], then [5].
If [5], then (Either [1] or (Either [2] or [3].).).
Therefore, If [4], then (Either [1] or (Either [2] or [3].).)..
[SC2-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then [4]. [SC2-3]
If [7], then [4].
Therefore, [4].
[SC2-3]
Reductio Ad Absurdum:
If (Not (If [6], then [4].).), then (Either [8] or [9].). [SC1-4]
If (Not (If [6], then [4].).), then (Not (Either [8] or [9].).). [SC2-4]
Therefore, If [6], then [4]..
[SC1-4]
Disjunctive Syllogism:
Either [11] or (If (Not (If [6], then [4].).), then (Either [8] or [9].).).
Not [11].
Therefore, If (Not (If [6], then [4].).), then (Either [8] or [9].)..
[SC2-4]
Disjunctive Syllogism:
Either [10] or (If (Not (If [6], then [4].).), then (Not (Either [8] or [9].).).).
Not [10].
Therefore, If (Not (If [6], then [4].).), then (Not (Either [8] or [9].).)..
|
{0: 'Canned good is located in pantries.', 1: 'Crakes have (part) sterna.', 2: 'Most female flowers contain stigma.', 3: "Birds are the desert's alarm clock.", 4: 'Wind dispersal allows for movement over long distances.', 5: 'Good compost contains an enormous number of food resources for beneficial organisms.', 6: 'Insurance agents help individuals and businesses protect their financial assets.', 7: 'Life is the characteristic state of organisms.', 8: 'Infected ticks transmit the rickettsiae to rabbits, squirrels, deer, bears, dogs, and humans.', 9: 'Physiological function is based on substance.', 10: 'Most astronomers use optical telescopes.', 11: 'Spark power is voltage times the current times a correction factor.'}
| 7 |
6,475 |
['We know that either habitat fragmentation is often a cause of species becoming threatened or endangered or insects have (part) quill feathers.', 'There is good reason to believe that either customer satisfaction includes customer attitudes about service quality and product offerings or either family therapy can significantly decrease relapse rates for the schizophrenic family member or rings are located in malls.', 'Once we know customer satisfaction includes customer attitudes about service quality and product offerings, we also know that if sugar causes excretion, then if habitat fragmentation is often a cause of species becoming threatened or endangered , then some people mistakenly believe that hydrangeas are plants.', 'When either family therapy can significantly decrease relapse rates for the schizophrenic family member or rings are located in malls is true, it follows that if sugar causes excretion, then if habitat fragmentation is often a cause of species becoming threatened or endangered , then some people mistakenly believe that hydrangeas are plants.', 'There is good reason to believe that either most water has nutrients or sugar causes excretion.', 'Some people mistakenly believe that most water has nutrients.', "So long as those that suggest if insects have (part) quill feathers, then television is the most influential image and information machine of American society are wrong, 'some babies have infection' is true.", 'On the condition that those that suggest if insects have (part) quill feathers, then television is the most influential image and information machine of American society are wrong, it is definitely the case that the claim that some babies have infection is false.', 'Once we know traditional diets include products, we also know that if television is the most influential image and information machine of American society, then some people mistakenly believe that hydrangeas are plants.', 'It is true that traditional diets include products.']
|
We know that either habitat fragmentation is often a cause of species becoming threatened or endangered or insects have (part) quill feathers. There is good reason to believe that either customer satisfaction includes customer attitudes about service quality and product offerings or either family therapy can significantly decrease relapse rates for the schizophrenic family member or rings are located in malls. Once we know customer satisfaction includes customer attitudes about service quality and product offerings, we also know that if sugar causes excretion, then if habitat fragmentation is often a cause of species becoming threatened or endangered , then some people mistakenly believe that hydrangeas are plants. When either family therapy can significantly decrease relapse rates for the schizophrenic family member or rings are located in malls is true, it follows that if sugar causes excretion, then if habitat fragmentation is often a cause of species becoming threatened or endangered , then some people mistakenly believe that hydrangeas are plants. There is good reason to believe that either most water has nutrients or sugar causes excretion. Some people mistakenly believe that most water has nutrients. So long as those that suggest if insects have (part) quill feathers, then television is the most influential image and information machine of American society are wrong, 'some babies have infection' is true. On the condition that those that suggest if insects have (part) quill feathers, then television is the most influential image and information machine of American society are wrong, it is definitely the case that the claim that some babies have infection is false. Once we know traditional diets include products, we also know that if television is the most influential image and information machine of American society, then some people mistakenly believe that hydrangeas are plants. It is true that traditional diets include products.
|
Some people mistakenly believe that hydrangeas are plants.
|
The statement that 'hydrangeas can be tricky to dry' is incorrect.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2].
If [1], then (Not [0].). [SC2-1]
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC2-1]
Modus Ponens:
If [4], then (If [1], then (Not [0].).). [SC1-2]
[4] [SC2-2]
Therefore, If [1], then (Not [0].)..
[SC1-2]
Disjunction Elimination:
Either [7] or (Either [8] or [9].).
If [7], then (If [4], then (If [1], then (Not [0].).).).
If (Either [8] or [9].), then (If [4], then (If [1], then (Not [0].).).).
Therefore, If [4], then (If [1], then (Not [0].).)..
[SC2-2]
Disjunctive Syllogism:
Either [5] or [4].
Not [5].
Therefore, [4].
[SC3-1]
Hypothetical Syllogism:
If [2], then [3]. [SC1-2]
If [3], then (Not [0].). [SC2-2]
Therefore, If [2], then (Not [0].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [2], then [3].).), then [6].
If (Not (If [2], then [3].).), then (Not [6].).
Therefore, If [2], then [3]..
[SC2-2]
Modus Ponens:
If [10], then (If [3], then (Not [0].).).
[10]
Therefore, If [3], then (Not [0].)..
|
{0: 'Hydrangeas are plants.', 1: 'Habitat fragmentation is often a cause of species becoming threatened or endangered .', 2: 'Insects have (part) quill feathers.', 3: 'Television is the most influential image and information machine of American society.', 4: 'Sugar causes excretion.', 5: 'Most water has nutrients.', 6: 'Some babies have infection.', 7: 'Customer satisfaction includes customer attitudes about service quality and product offerings.', 8: 'Family therapy can significantly decrease relapse rates for the schizophrenic family member.', 9: 'Rings are located in malls.', 10: 'Traditional diets include products.'}
| 7 |
6,213 |
['Given that oligosaccharides are complex sugars which play an important role in animal health, it can be inferred that internets have no central control, that is, no single computer directs the flow of information.', "Whenever it is true that internets have no central control, that is, no single computer directs the flow of information, 'either if hypotonia is a symptom of many cerebral, spinal, genetic, or muscular diseases, then teeth have ability or either domestic violence is tragic when it occurs or air time is the slowdown time in the stride cycle' is true.", 'When the claim that oligosaccharides are complex sugars which play an important role in animal health does not correspond with reality is true, it follows that hypertension is another leading cause of heart disease in the general population of Senegal.', 'Given that the claim that oligosaccharides are complex sugars which play an important role in animal health does not correspond with reality, it can be inferred that the statement that states hypertension is another leading cause of heart disease in the general population of Senegal is false.', 'One may reasonably assume that if if hypotonia is a symptom of many cerebral, spinal, genetic, or muscular diseases, then teeth have ability, then some snails eat prey.', 'When some snails eat prey is true, it follows that most plants use radiant energy.', "So long as the statement 'if if hypotonia is a symptom of many cerebral, spinal, genetic, or muscular diseases, then teeth have ability, then the claim that most plants use radiant energy is false' can be considered false, 'gila monsters live in an arid habitat with some vegetation' is true.", 'The claim that gila monsters live in an arid habitat with some vegetation does not correspond with reality.']
|
Given that oligosaccharides are complex sugars which play an important role in animal health, it can be inferred that internets have no central control, that is, no single computer directs the flow of information. Whenever it is true that internets have no central control, that is, no single computer directs the flow of information, 'either if hypotonia is a symptom of many cerebral, spinal, genetic, or muscular diseases, then teeth have ability or either domestic violence is tragic when it occurs or air time is the slowdown time in the stride cycle' is true. When the claim that oligosaccharides are complex sugars which play an important role in animal health does not correspond with reality is true, it follows that hypertension is another leading cause of heart disease in the general population of Senegal. Given that the claim that oligosaccharides are complex sugars which play an important role in animal health does not correspond with reality, it can be inferred that the statement that states hypertension is another leading cause of heart disease in the general population of Senegal is false. One may reasonably assume that if if hypotonia is a symptom of many cerebral, spinal, genetic, or muscular diseases, then teeth have ability, then some snails eat prey. When some snails eat prey is true, it follows that most plants use radiant energy. So long as the statement 'if if hypotonia is a symptom of many cerebral, spinal, genetic, or muscular diseases, then teeth have ability, then the claim that most plants use radiant energy is false' can be considered false, 'gila monsters live in an arid habitat with some vegetation' is true. The claim that gila monsters live in an arid habitat with some vegetation does not correspond with reality.
|
There is good reason to believe that either domestic violence is tragic when it occurs or air time is the slowdown time in the stride cycle.
|
There is good reason to believe that either domestic violence is tragic when it occurs or air time is the slowdown time in the stride cycle.
|
TRUE
|
Disjunctive Syllogism:
Either (If [2], then [3].) or (Either [0] or [1].). [SC1-1]
Not (If [2], then [3].). [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Modus Ponens:
If [5], then (Either (If [2], then [3].) or (Either [0] or [1].).). [SC1-2]
[5] [SC2-2]
Therefore, Either (If [2], then [3].) or (Either [0] or [1].)..
[SC1-2]
Hypothetical Syllogism:
If [5], then [9].
If [9], then (Either (If [2], then [3].) or (Either [0] or [1].).).
Therefore, If [5], then (Either (If [2], then [3].) or (Either [0] or [1].).)..
[SC2-2]
Reductio Ad Absurdum:
If (Not [5].), then [8].
If (Not [5].), then (Not [8].).
Therefore, [5].
[SC2-1]
Reductio Ad Absurdum:
If (If [2], then [3].), then [4]. [SC1-2]
If (If [2], then [3].), then (Not [4].). [SC2-2]
Therefore, Not (If [2], then [3].)..
[SC1-2]
Hypothetical Syllogism:
If (If [2], then [3].), then [7].
If [7], then [4].
Therefore, If (If [2], then [3].), then [4]..
[SC2-2]
Modus Tonens:
If (Not (If (If [2], then [3].), then (Not [4].).).), then [6].
Not [6].
Therefore, If (If [2], then [3].), then (Not [4].)..
|
{0: 'Domestic violence is tragic when it occurs.', 1: 'Air time is the slowdown time in the stride cycle.', 2: 'Hypotonia is a symptom of many cerebral, spinal, genetic, or muscular diseases.', 3: 'Teeth have ability.', 4: 'Most plants use radiant energy.', 5: 'Oligosaccharides are complex sugars which play an important role in animal health.', 6: 'Gila monsters live in an arid habitat with some vegetation.', 7: 'Some snails eat prey.', 8: 'Hypertension is another leading cause of heart disease in the general population of Senegal.', 9: 'Internets have no central control, that is, no single computer directs the flow of information.'}
| 7 |
6,135 |
["The statement 'dopamine is one of the most important neurotransmitters involved in the human sexual response' can be considered false.", 'We know that at least one of two things is true: inks are water soluble inks, or media arts deal with video, black and white film, as well as computer graphics.', "So long as inks are water soluble inks, 'the claim that either reproductive hormones are important in the development of the breast in puberty and in lactation or smoking is a major cause of ill health and the nation's high health care bill has no merit' is true.", "Whenever it is true that media arts deal with video, black and white film, as well as computer graphics, 'the claim that either reproductive hormones are important in the development of the breast in puberty and in lactation or smoking is a major cause of ill health and the nation's high health care bill has no merit' is true.", "On the condition that some people mistakenly believe that if the statement that 'either either reproductive hormones are important in the development of the breast in puberty and in lactation or smoking is a major cause of ill health and the nation's high health care bill or japanese beetles feed on plants' is incorrect, then dopamine is one of the most important neurotransmitters involved in the human sexual response, it is definitely the case that the claim that if mastodons have (part) sections, then sirenians are unable to tolerate water temperatures below a certain threshold does not correspond with reality.", "If the claim that if some people mistakenly believe that if the statement that 'either either reproductive hormones are important in the development of the breast in puberty and in lactation or smoking is a major cause of ill health and the nation's high health care bill or japanese beetles feed on plants' is incorrect, then dopamine is one of the most important neurotransmitters involved in the human sexual response, then most religious people use their faith to justify their actions does not reflect reality, then dark nebulas absorb light.", "If the claim that if some people mistakenly believe that if the statement that 'either either reproductive hormones are important in the development of the breast in puberty and in lactation or smoking is a major cause of ill health and the nation's high health care bill or japanese beetles feed on plants' is incorrect, then dopamine is one of the most important neurotransmitters involved in the human sexual response, then most religious people use their faith to justify their actions does not reflect reality, then the statement that 'dark nebulas absorb light' is incorrect.", "One may reasonably assume that if the notion that 'if most religious people use their faith to justify their actions, then if mastodons have (part) sections, then sirenians are unable to tolerate water temperatures below a certain threshold' is untrue, then land living mollusks, like the snail, move slowly on a flat sole called a foot.", 'Some people mistakenly believe that land living mollusks, like the snail, move slowly on a flat sole called a foot.']
|
The statement 'dopamine is one of the most important neurotransmitters involved in the human sexual response' can be considered false. We know that at least one of two things is true: inks are water soluble inks, or media arts deal with video, black and white film, as well as computer graphics. So long as inks are water soluble inks, 'the claim that either reproductive hormones are important in the development of the breast in puberty and in lactation or smoking is a major cause of ill health and the nation's high health care bill has no merit' is true. Whenever it is true that media arts deal with video, black and white film, as well as computer graphics, 'the claim that either reproductive hormones are important in the development of the breast in puberty and in lactation or smoking is a major cause of ill health and the nation's high health care bill has no merit' is true. On the condition that some people mistakenly believe that if the statement that 'either either reproductive hormones are important in the development of the breast in puberty and in lactation or smoking is a major cause of ill health and the nation's high health care bill or japanese beetles feed on plants' is incorrect, then dopamine is one of the most important neurotransmitters involved in the human sexual response, it is definitely the case that the claim that if mastodons have (part) sections, then sirenians are unable to tolerate water temperatures below a certain threshold does not correspond with reality. If the claim that if some people mistakenly believe that if the statement that 'either either reproductive hormones are important in the development of the breast in puberty and in lactation or smoking is a major cause of ill health and the nation's high health care bill or japanese beetles feed on plants' is incorrect, then dopamine is one of the most important neurotransmitters involved in the human sexual response, then most religious people use their faith to justify their actions does not reflect reality, then dark nebulas absorb light. If the claim that if some people mistakenly believe that if the statement that 'either either reproductive hormones are important in the development of the breast in puberty and in lactation or smoking is a major cause of ill health and the nation's high health care bill or japanese beetles feed on plants' is incorrect, then dopamine is one of the most important neurotransmitters involved in the human sexual response, then most religious people use their faith to justify their actions does not reflect reality, then the statement that 'dark nebulas absorb light' is incorrect. One may reasonably assume that if the notion that 'if most religious people use their faith to justify their actions, then if mastodons have (part) sections, then sirenians are unable to tolerate water temperatures below a certain threshold' is untrue, then land living mollusks, like the snail, move slowly on a flat sole called a foot. Some people mistakenly believe that land living mollusks, like the snail, move slowly on a flat sole called a foot.
|
The claim that japanese beetles feed on plants is true.
|
Japanese beetle is a serious problem for the nursery industry.
|
Uncertain
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or [0]. [SC1-1]
Not (Either [1] or [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either (Either [1] or [2].) or [0].).), then [3]. [SC1-2]
Not [3].
Therefore, Either (Either [1] or [2].) or [0]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (Either (Either [1] or [2].) or [0].).), then [3].).), then (If [6], then [7].). [SC1-3]
If (Not (If (Not (Either (Either [1] or [2].) or [0].).), then [3].).), then (Not (If [6], then [7].).).
Therefore, If (Not (Either (Either [1] or [2].) or [0].).), then [3]..
[SC1-3]
Hypothetical Syllogism:
If (Not (If (Not (Either (Either [1] or [2].) or [0].).), then [3].).), then [8]. [SC1-4]
If [8], then (If [6], then [7].). [SC2-4]
Therefore, If (Not (If (Not (Either (Either [1] or [2].) or [0].).), then [3].).), then (If [6], then [7].)..
[SC1-4]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not (Either (Either [1] or [2].) or [0].).), then [3].).), then [8].).), then [10].
If (Not (If (Not (If (Not (Either (Either [1] or [2].) or [0].).), then [3].).), then [8].).), then (Not [10].).
Therefore, If (Not (If (Not (Either (Either [1] or [2].) or [0].).), then [3].).), then [8]..
[SC2-4]
Modus Tonens:
If (Not (If [8], then (If [6], then [7].).).), then [9].
Not [9].
Therefore, If [8], then (If [6], then [7].)..
[SC2-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Not (Either [1] or [2].).).
If [5], then (Not (Either [1] or [2].).).
Therefore, Not (Either [1] or [2].)..
|
{0: 'Japanese beetles feed on plants.', 1: 'Reproductive hormones are important in the development of the breast in puberty and in lactation.', 2: "Smoking is a major cause of ill health and the nation's high health care bill.", 3: 'Dopamine is one of the most important neurotransmitters involved in the human sexual response.', 4: 'Inks are water soluble inks.', 5: 'Media arts deal with video, black and white film, as well as computer graphics.', 6: 'Mastodons have (part) sections.', 7: 'Sirenians are unable to tolerate water temperatures below a certain threshold.', 8: 'Most religious people use their faith to justify their actions.', 9: 'Land living mollusks, like the snail, move slowly on a flat sole called a foot.', 10: 'Dark nebulas absorb light.'}
| 7 |
6,246 |
["If the notion that 'whole grains are high in fiber, essential nutrients, and flavor' is untrue, then either scandal is sometimes the price of virtuous action or turkeys can adapt to widely varying conditions.", "Once we know it is a common misconception that if the notion that 'whole grains are high in fiber, essential nutrients, and flavor' is untrue, then the claim that either scandal is sometimes the price of virtuous action or turkeys can adapt to widely varying conditions does not reflect reality, we also know that either wellness is a state of health more positive than the mere absence of disease or search dogs can locate drowned people in the bottom of lakes, or in rivers, or all bodies of water.", 'The statement, if midwifes perform certain duties, then gymnasts learn quickly that hard work can be rewarding and fun, does not hold.', 'We know that either some people seem to inherit the tendency to get a disease like lupus or communicates are motivated by the goal of information.', 'Provided that some people seem to inherit the tendency to get a disease like lupus, we know that if if communication is the transfer of information from one person to another, then most blood tests measure blood glucose levels, then if either wellness is a state of health more positive than the mere absence of disease or search dogs can locate drowned people in the bottom of lakes, or in rivers, or all bodies of water, then if midwifes perform certain duties, then gymnasts learn quickly that hard work can be rewarding and fun.', 'One may reasonably assume that if it is not the case that if communication is the transfer of information from one person to another, then most blood tests measure blood glucose levels, then national bureaucracy is a spent force.', 'Once we know it is not the case that if communication is the transfer of information from one person to another, then most blood tests measure blood glucose levels, we also know that the claim that national bureaucracy is a spent force does not correspond with reality.', 'One may reasonably assume that if communicates are motivated by the goal of information, then llamas has-part legs.', 'If llamas has-part legs, then if if communication is the transfer of information from one person to another, then most blood tests measure blood glucose levels, then if either wellness is a state of health more positive than the mere absence of disease or search dogs can locate drowned people in the bottom of lakes, or in rivers, or all bodies of water, then if midwifes perform certain duties, then gymnasts learn quickly that hard work can be rewarding and fun.']
|
If the notion that 'whole grains are high in fiber, essential nutrients, and flavor' is untrue, then either scandal is sometimes the price of virtuous action or turkeys can adapt to widely varying conditions. Once we know it is a common misconception that if the notion that 'whole grains are high in fiber, essential nutrients, and flavor' is untrue, then the claim that either scandal is sometimes the price of virtuous action or turkeys can adapt to widely varying conditions does not reflect reality, we also know that either wellness is a state of health more positive than the mere absence of disease or search dogs can locate drowned people in the bottom of lakes, or in rivers, or all bodies of water. The statement, if midwifes perform certain duties, then gymnasts learn quickly that hard work can be rewarding and fun, does not hold. We know that either some people seem to inherit the tendency to get a disease like lupus or communicates are motivated by the goal of information. Provided that some people seem to inherit the tendency to get a disease like lupus, we know that if if communication is the transfer of information from one person to another, then most blood tests measure blood glucose levels, then if either wellness is a state of health more positive than the mere absence of disease or search dogs can locate drowned people in the bottom of lakes, or in rivers, or all bodies of water, then if midwifes perform certain duties, then gymnasts learn quickly that hard work can be rewarding and fun. One may reasonably assume that if it is not the case that if communication is the transfer of information from one person to another, then most blood tests measure blood glucose levels, then national bureaucracy is a spent force. Once we know it is not the case that if communication is the transfer of information from one person to another, then most blood tests measure blood glucose levels, we also know that the claim that national bureaucracy is a spent force does not correspond with reality. One may reasonably assume that if communicates are motivated by the goal of information, then llamas has-part legs. If llamas has-part legs, then if if communication is the transfer of information from one person to another, then most blood tests measure blood glucose levels, then if either wellness is a state of health more positive than the mere absence of disease or search dogs can locate drowned people in the bottom of lakes, or in rivers, or all bodies of water, then if midwifes perform certain duties, then gymnasts learn quickly that hard work can be rewarding and fun.
|
Many people rightly believe that whole grains are high in fiber, essential nutrients, and flavor.
|
Many people rightly believe that whole grains are high in fiber, essential nutrients, and flavor.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then (Either [1] or [2].).
If (Not [0].), then (Not (Either [1] or [2].).). [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not (If (Not [0].), then (Not (Either [1] or [2].).).).), then (Either [3] or [4].).
Not (Either [3] or [4].). [SC2-2]
Therefore, If (Not [0].), then (Not (Either [1] or [2].).)..
[SC2-2]
Modus Tonens:
If (Either [3] or [4].), then (If [5], then [6].). [SC1-3]
Not (If [5], then [6].).
Therefore, Not (Either [3] or [4].)..
[SC1-3]
Modus Ponens:
If (If [7], then [8].), then (If (Either [3] or [4].), then (If [5], then [6].).). [SC1-4]
If [7], then [8]. [SC2-4]
Therefore, If (Either [3] or [4].), then (If [5], then [6].)..
[SC1-4]
Disjunction Elimination:
Either [10] or [11].
If [10], then (If (If [7], then [8].), then (If (Either [3] or [4].), then (If [5], then [6].).).).
If [11], then (If (If [7], then [8].), then (If (Either [3] or [4].), then (If [5], then [6].).).). [SC3-5]
Therefore, If (If [7], then [8].), then (If (Either [3] or [4].), then (If [5], then [6].).)..
[SC3-5]
Hypothetical Syllogism:
If [11], then [12].
If [12], then (If (If [7], then [8].), then (If (Either [3] or [4].), then (If [5], then [6].).).).
Therefore, If [11], then (If (If [7], then [8].), then (If (Either [3] or [4].), then (If [5], then [6].).).)..
[SC2-4]
Reductio Ad Absurdum:
If (Not (If [7], then [8].).), then [9].
If (Not (If [7], then [8].).), then (Not [9].).
Therefore, If [7], then [8]..
|
{0: 'Whole grains are high in fiber, essential nutrients, and flavor.', 1: 'Scandal is sometimes the price of virtuous action.', 2: 'Turkeys can adapt to widely varying conditions.', 3: 'Wellness is a state of health more positive than the mere absence of disease.', 4: 'Search dogs can locate drowned people in the bottom of lakes, or in rivers, or all bodies of water.', 5: 'Midwifes perform certain duties.', 6: 'Gymnasts learn quickly that hard work can be rewarding and fun.', 7: 'Communication is the transfer of information from one person to another.', 8: 'Most blood tests measure blood glucose levels.', 9: 'National bureaucracy is a spent force.', 10: 'Some people seem to inherit the tendency to get a disease like lupus.', 11: 'Communicates are motivated by the goal of information.', 12: 'Llamas has-part legs.'}
| 7 |
6,970 |
["The statement 'either most flowers are produced by trees or absence mays have effects' can be considered false.", "Provided that the statement that 'either either most flowers are produced by trees or absence mays have effects or either some spikes have stamens or directories contain groups of files that have something in common' is incorrect, we know that energy can change from one form to another.", "Should it be the case that it is not the case that if the statement that 'either either most flowers are produced by trees or absence mays have effects or either some spikes have stamens or directories contain groups of files that have something in common' is incorrect, then it is not true that energy can change from one form to another, it follows that conspiracy theories are the work of the government.", "Should it be the case that it is not the case that if the statement that 'either either most flowers are produced by trees or absence mays have effects or either some spikes have stamens or directories contain groups of files that have something in common' is incorrect, then it is not true that energy can change from one form to another, it follows that hollies range from small shrubs to medium-sized trees.", 'When hollies range from small shrubs to medium-sized trees is true, it follows that the claim that if identical twins come from the same egg and sperm which breaks in in two after fertilization, then naturalized citizens are foreign-born persons who identified themselves as naturalized has no merit.', 'The claim that some people describe a balance problem by saying they feel dizzy, lightheaded, unsteady, or giddy does not correspond with reality.', 'One may reasonably assume that if those that suggest either some people describe a balance problem by saying they feel dizzy, lightheaded, unsteady, or giddy or if conspiracy theories are the work of the government, then if identical twins come from the same egg and sperm which breaks in in two after fertilization, then naturalized citizens are foreign-born persons who identified themselves as naturalized are wrong, then either many people can eat and drink with a tracheostomy tube in place or oklahoma isa thing.', 'On the condition that those that suggest either some people describe a balance problem by saying they feel dizzy, lightheaded, unsteady, or giddy or if conspiracy theories are the work of the government, then if identical twins come from the same egg and sperm which breaks in in two after fertilization, then naturalized citizens are foreign-born persons who identified themselves as naturalized are wrong, it is definitely the case that it is not the case that either many people can eat and drink with a tracheostomy tube in place or oklahoma isa thing.']
|
The statement 'either most flowers are produced by trees or absence mays have effects' can be considered false. Provided that the statement that 'either either most flowers are produced by trees or absence mays have effects or either some spikes have stamens or directories contain groups of files that have something in common' is incorrect, we know that energy can change from one form to another. Should it be the case that it is not the case that if the statement that 'either either most flowers are produced by trees or absence mays have effects or either some spikes have stamens or directories contain groups of files that have something in common' is incorrect, then it is not true that energy can change from one form to another, it follows that conspiracy theories are the work of the government. Should it be the case that it is not the case that if the statement that 'either either most flowers are produced by trees or absence mays have effects or either some spikes have stamens or directories contain groups of files that have something in common' is incorrect, then it is not true that energy can change from one form to another, it follows that hollies range from small shrubs to medium-sized trees. When hollies range from small shrubs to medium-sized trees is true, it follows that the claim that if identical twins come from the same egg and sperm which breaks in in two after fertilization, then naturalized citizens are foreign-born persons who identified themselves as naturalized has no merit. The claim that some people describe a balance problem by saying they feel dizzy, lightheaded, unsteady, or giddy does not correspond with reality. One may reasonably assume that if those that suggest either some people describe a balance problem by saying they feel dizzy, lightheaded, unsteady, or giddy or if conspiracy theories are the work of the government, then if identical twins come from the same egg and sperm which breaks in in two after fertilization, then naturalized citizens are foreign-born persons who identified themselves as naturalized are wrong, then either many people can eat and drink with a tracheostomy tube in place or oklahoma isa thing. On the condition that those that suggest either some people describe a balance problem by saying they feel dizzy, lightheaded, unsteady, or giddy or if conspiracy theories are the work of the government, then if identical twins come from the same egg and sperm which breaks in in two after fertilization, then naturalized citizens are foreign-born persons who identified themselves as naturalized are wrong, it is definitely the case that it is not the case that either many people can eat and drink with a tracheostomy tube in place or oklahoma isa thing.
|
At least one of two things is true: some spikes have stamens, or directories contain groups of files that have something in common.
|
Either spikes cause pain or directories are organized listings of web sites that are created manually by people.
|
Uncertain
|
Disjunctive Syllogism:
Either (Either [2] or [3].) or (Either [0] or [1].). [SC1-1]
Not (Either [2] or [3].).
Therefore, Either [0] or [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either (Either [2] or [3].) or (Either [0] or [1].).).), then [4].
If (Not (Either (Either [2] or [3].) or (Either [0] or [1].).).), then (Not [4].). [SC2-2]
Therefore, Either (Either [2] or [3].) or (Either [0] or [1].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (Either (Either [2] or [3].) or (Either [0] or [1].).).), then (Not [4].).).), then (If [5], then [6].). [SC1-3]
If (Not (If (Not (Either (Either [2] or [3].) or (Either [0] or [1].).).), then (Not [4].).).), then (Not (If [5], then [6].).). [SC2-3]
Therefore, If (Not (Either (Either [2] or [3].) or (Either [0] or [1].).).), then (Not [4].)..
[SC1-3]
Hypothetical Syllogism:
If (Not (If (Not (Either (Either [2] or [3].) or (Either [0] or [1].).).), then (Not [4].).).), then [8].
If [8], then (If [5], then [6].). [SC2-4]
Therefore, If (Not (If (Not (Either (Either [2] or [3].) or (Either [0] or [1].).).), then (Not [4].).).), then (If [5], then [6].)..
[SC2-4]
Disjunctive Syllogism:
Either [9] or (If [8], then (If [5], then [6].).). [SC1-5]
Not [9].
Therefore, If [8], then (If [5], then [6].)..
[SC1-5]
Reductio Ad Absurdum:
If (Not (Either [9] or (If [8], then (If [5], then [6].).).).), then (Either [10] or [11].).
If (Not (Either [9] or (If [8], then (If [5], then [6].).).).), then (Not (Either [10] or [11].).).
Therefore, Either [9] or (If [8], then (If [5], then [6].).)..
[SC2-3]
Hypothetical Syllogism:
If (Not (If (Not (Either (Either [2] or [3].) or (Either [0] or [1].).).), then (Not [4].).).), then [7].
If [7], then (Not (If [5], then [6].).).
Therefore, If (Not (If (Not (Either (Either [2] or [3].) or (Either [0] or [1].).).), then (Not [4].).).), then (Not (If [5], then [6].).)..
|
{0: 'Some spikes have stamens.', 1: 'Directories contain groups of files that have something in common.', 2: 'Most flowers are produced by trees.', 3: 'Absence mays have effects.', 4: 'Energy can change from one form to another.', 5: 'Identical twins come from the same egg and sperm which breaks in in two after fertilization.', 6: 'Naturalized citizens are foreign-born persons who identified themselves as naturalized.', 7: 'Hollies range from small shrubs to medium-sized trees.', 8: 'Conspiracy theories are the work of the government.', 9: 'Some people describe a balance problem by saying they feel dizzy, lightheaded, unsteady, or giddy.', 10: 'Many people can eat and drink with a tracheostomy tube in place.', 11: 'Oklahoma isa thing.'}
| 7 |
6,891 |
['If a dream is imagination, then ticks are tiny, harmless-looking little suckers, but they can transmit a variety of diseases.', 'Should it be the case that some people mistakenly believe that either a dream is imagination or either unneutered hobs have a strong odor and can become aggressive towards ferrets, both male and female or total capital is equal to total book debt plus total equity capitalization, it follows that tarsiers have heads.', 'Provided that either unneutered hobs have a strong odor and can become aggressive towards ferrets, both male and female or total capital is equal to total book debt plus total equity capitalization, we know that if most amphibians have very muscular and flexible tongues, then literacy is the cornerstone of the education every child needs and deserves.', 'Assuming if most amphibians have very muscular and flexible tongues, then literacy is the cornerstone of the education every child needs and deserves, we know that ticks are tiny, harmless-looking little suckers, but they can transmit a variety of diseases.', 'Either one or both of these statements are true: rats rely on senses, or if some people mistakenly believe that either a dream is imagination or either unneutered hobs have a strong odor and can become aggressive towards ferrets, both male and female or total capital is equal to total book debt plus total equity capitalization, then it is not true that tarsiers have heads.', 'It is a fact that either either most bald eagles use sharp claws or carbon dioxide is removed from the atmosphere and oxygen is released during photosynthesis or earth is part of solar systems.', "Given that either most bald eagles use sharp claws or carbon dioxide is removed from the atmosphere and oxygen is released during photosynthesis, it can be inferred that the statement that 'rats rely on senses' is incorrect.", "When if rhinos have (part) sterna, then green plants turn sunlight is true, it follows that the statement that 'rats rely on senses' is incorrect.", 'Once we know some people mistakenly believe that if earth is part of solar systems, then if rhinos have (part) sterna, then green plants turn sunlight, we also know that either jugglers have (part) sections or rabbits have conditions.', "The statement that 'either jugglers have (part) sections or rabbits have conditions' is incorrect."]
|
If a dream is imagination, then ticks are tiny, harmless-looking little suckers, but they can transmit a variety of diseases. Should it be the case that some people mistakenly believe that either a dream is imagination or either unneutered hobs have a strong odor and can become aggressive towards ferrets, both male and female or total capital is equal to total book debt plus total equity capitalization, it follows that tarsiers have heads. Provided that either unneutered hobs have a strong odor and can become aggressive towards ferrets, both male and female or total capital is equal to total book debt plus total equity capitalization, we know that if most amphibians have very muscular and flexible tongues, then literacy is the cornerstone of the education every child needs and deserves. Assuming if most amphibians have very muscular and flexible tongues, then literacy is the cornerstone of the education every child needs and deserves, we know that ticks are tiny, harmless-looking little suckers, but they can transmit a variety of diseases. Either one or both of these statements are true: rats rely on senses, or if some people mistakenly believe that either a dream is imagination or either unneutered hobs have a strong odor and can become aggressive towards ferrets, both male and female or total capital is equal to total book debt plus total equity capitalization, then it is not true that tarsiers have heads. It is a fact that either either most bald eagles use sharp claws or carbon dioxide is removed from the atmosphere and oxygen is released during photosynthesis or earth is part of solar systems. Given that either most bald eagles use sharp claws or carbon dioxide is removed from the atmosphere and oxygen is released during photosynthesis, it can be inferred that the statement that 'rats rely on senses' is incorrect. When if rhinos have (part) sterna, then green plants turn sunlight is true, it follows that the statement that 'rats rely on senses' is incorrect. Once we know some people mistakenly believe that if earth is part of solar systems, then if rhinos have (part) sterna, then green plants turn sunlight, we also know that either jugglers have (part) sections or rabbits have conditions. The statement that 'either jugglers have (part) sections or rabbits have conditions' is incorrect.
|
The claim that ticks are tiny, harmless-looking little suckers, but they can transmit a variety of diseases holds true.
|
All ticks are parasitic.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].). [SC1-1]
If [1], then [0].
If (Either [2] or [3].), then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or (Either [2] or [3].).).), then [6].
If (Not (Either [1] or (Either [2] or [3].).).), then (Not [6].). [SC2-2]
Therefore, Either [1] or (Either [2] or [3].)..
[SC2-2]
Disjunctive Syllogism:
Either [7] or (If (Not (Either [1] or (Either [2] or [3].).).), then (Not [6].).).
Not [7]. [SC2-3]
Therefore, If (Not (Either [1] or (Either [2] or [3].).).), then (Not [6].)..
[SC2-3]
Disjunction Elimination:
Either (Either [8] or [9].) or [10].
If (Either [8] or [9].), then (Not [7].).
If [10], then (Not [7].). [SC3-4]
Therefore, Not [7]..
[SC3-4]
Hypothetical Syllogism:
If [10], then (If [11], then [12].). [SC1-5]
If (If [11], then [12].), then (Not [7].).
Therefore, If [10], then (Not [7].)..
[SC1-5]
Modus Tonens:
If (Not (If [10], then (If [11], then [12].).).), then (Either [13] or [14].).
Not (Either [13] or [14].).
Therefore, If [10], then (If [11], then [12].)..
[SC3-1]
Hypothetical Syllogism:
If (Either [2] or [3].), then (If [4], then [5].).
If (If [4], then [5].), then [0].
Therefore, If (Either [2] or [3].), then [0]..
|
{0: 'Ticks are tiny, harmless-looking little suckers, but they can transmit a variety of diseases.', 1: 'A dream is imagination.', 2: 'Unneutered hobs have a strong odor and can become aggressive towards ferrets, both male and female.', 3: 'Total capital is equal to total book debt plus total equity capitalization.', 4: 'Most amphibians have very muscular and flexible tongues.', 5: 'Literacy is the cornerstone of the education every child needs and deserves.', 6: 'Tarsiers have heads.', 7: 'Rats rely on senses.', 8: 'Most bald eagles use sharp claws.', 9: 'Carbon dioxide is removed from the atmosphere and oxygen is released during photosynthesis.', 10: 'Earth is part of solar systems.', 11: 'Rhinos have (part) sterna.', 12: 'Green plants turn sunlight.', 13: 'Jugglers have (part) sections.', 14: 'Rabbits have conditions.'}
| 7 |
6,619 |
["When some people mistakenly believe that if the statement 'some light attracts squids' can be considered false, then chaparral pea is important browse for black-tailed deer is true, it follows that breechs are openings.", "When some people mistakenly believe that if the statement 'some light attracts squids' can be considered false, then chaparral pea is important browse for black-tailed deer is true, it follows that some people mistakenly believe that breechs are openings.", 'It is rational to believe that either blood also plays roles in body temperature regulation or a stardom is high status.', 'Given that blood also plays roles in body temperature regulation, it can be inferred that honeybees have (part) nuclei.', "So long as a stardom is high status, 'either a catapult is a device or trees help with erosion control' is true.", "Whenever it is true that the claim that if honeybees have (part) nuclei, then the statement 'chaparral pea is important browse for black-tailed deer' can be considered false is false, 'the statement, physicians can diagnose diseases years before they can be found by conventional methods, does not hold' is true.", 'It is rational to believe that either if chronic exposure produces alopecia, peripheral neuropathy, seizures, and renal failure, then modeled behavior can result in a variety of outcomes or crystalline boron is transparent, brittle, a non-conductor, and nearly as hard as diamond.', "Once we know if chronic exposure produces alopecia, peripheral neuropathy, seizures, and renal failure, then modeled behavior can result in a variety of outcomes, we also know that if either a catapult is a device or trees help with erosion control, then the statement 'chaparral pea is important browse for black-tailed deer' can be considered false.", "One may reasonably assume that if crystalline boron is transparent, brittle, a non-conductor, and nearly as hard as diamond, then if either a catapult is a device or trees help with erosion control, then the statement 'chaparral pea is important browse for black-tailed deer' can be considered false.", "So long as the claim that if honeybees have (part) nuclei, then the statement 'chaparral pea is important browse for black-tailed deer' can be considered false is false, 'sleep deprivation creates significant changes within one day, but the effects wear off a day later' is true.", 'Should it be the case that sleep deprivation creates significant changes within one day, but the effects wear off a day later, it follows that physicians can diagnose diseases years before they can be found by conventional methods.']
|
When some people mistakenly believe that if the statement 'some light attracts squids' can be considered false, then chaparral pea is important browse for black-tailed deer is true, it follows that breechs are openings. When some people mistakenly believe that if the statement 'some light attracts squids' can be considered false, then chaparral pea is important browse for black-tailed deer is true, it follows that some people mistakenly believe that breechs are openings. It is rational to believe that either blood also plays roles in body temperature regulation or a stardom is high status. Given that blood also plays roles in body temperature regulation, it can be inferred that honeybees have (part) nuclei. So long as a stardom is high status, 'either a catapult is a device or trees help with erosion control' is true. Whenever it is true that the claim that if honeybees have (part) nuclei, then the statement 'chaparral pea is important browse for black-tailed deer' can be considered false is false, 'the statement, physicians can diagnose diseases years before they can be found by conventional methods, does not hold' is true. It is rational to believe that either if chronic exposure produces alopecia, peripheral neuropathy, seizures, and renal failure, then modeled behavior can result in a variety of outcomes or crystalline boron is transparent, brittle, a non-conductor, and nearly as hard as diamond. Once we know if chronic exposure produces alopecia, peripheral neuropathy, seizures, and renal failure, then modeled behavior can result in a variety of outcomes, we also know that if either a catapult is a device or trees help with erosion control, then the statement 'chaparral pea is important browse for black-tailed deer' can be considered false. One may reasonably assume that if crystalline boron is transparent, brittle, a non-conductor, and nearly as hard as diamond, then if either a catapult is a device or trees help with erosion control, then the statement 'chaparral pea is important browse for black-tailed deer' can be considered false. So long as the claim that if honeybees have (part) nuclei, then the statement 'chaparral pea is important browse for black-tailed deer' can be considered false is false, 'sleep deprivation creates significant changes within one day, but the effects wear off a day later' is true. Should it be the case that sleep deprivation creates significant changes within one day, but the effects wear off a day later, it follows that physicians can diagnose diseases years before they can be found by conventional methods.
|
It is the case that some light attracts squids.
|
Light passes through the lens of the eye and is focused on the retina.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then [1].).), then [2].
If (Not (If (Not [0].), then [1].).), then (Not [2].).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunction Elimination:
Either [3] or (Either [4] or [5].). [SC1-2]
If [3], then (Not [1].). [SC2-2]
If (Either [4] or [5].), then (Not [1].). [SC3-2]
Therefore, Not [1]..
[SC1-2]
Constructive Dilemma:
Either [10] or [11].
If [10], then [3].
If [11], then (Either [4] or [5].).
Therefore, Either [3] or (Either [4] or [5].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [3], then (Not [1].).).), then [6]. [SC1-3]
If (Not (If [3], then (Not [1].).).), then (Not [6].).
Therefore, If [3], then (Not [1].)..
[SC1-3]
Hypothetical Syllogism:
If (Not (If [3], then (Not [1].).).), then [12].
If [12], then [6].
Therefore, If (Not (If [3], then (Not [1].).).), then [6]..
[SC3-2]
Disjunction Elimination:
Either (If [7], then [8].) or [9].
If (If [7], then [8].), then (If (Either [4] or [5].), then (Not [1].).).
If [9], then (If (Either [4] or [5].), then (Not [1].).).
Therefore, If (Either [4] or [5].), then (Not [1].)..
|
{0: 'Some light attracts squids.', 1: 'Chaparral pea is important browse for black-tailed deer.', 2: 'Breechs are openings.', 3: 'Honeybees have (part) nuclei.', 4: 'A catapult is a device.', 5: 'Trees help with erosion control.', 6: 'Physicians can diagnose diseases years before they can be found by conventional methods.', 7: 'Chronic exposure produces alopecia, peripheral neuropathy, seizures, and renal failure.', 8: 'Modeled behavior can result in a variety of outcomes.', 9: 'Crystalline boron is transparent, brittle, a non-conductor, and nearly as hard as diamond.', 10: 'Blood also plays roles in body temperature regulation.', 11: 'A stardom is high status.', 12: 'Sleep deprivation creates significant changes within one day, but the effects wear off a day later.'}
| 7 |
6,815 |
['Given that coyotes range from Panama to the North Slope of Alaska, it can be inferred that spinal fluid surrounds the brain, spinal cord and nerves.', 'On the condition that spinal fluid surrounds the brain, spinal cord and nerves, it is definitely the case that those that suggest taste masking - Medical substances often have a bitter taste when added to chewing gum are wrong.', 'The statement that states people use comparative anatomy to unite or divide different species is right.', 'It is a fact that either peacocks have (part) quill feathers or pernicious anemia causes weakness, numbness of the extremities, pallor, fever and other symptoms.', "Whenever it is true that peacocks have (part) quill feathers, 'either most crabs live in regions or if people use comparative anatomy to unite or divide different species, then coyotes range from Panama to the North Slope of Alaska' is true.", 'When pernicious anemia causes weakness, numbness of the extremities, pallor, fever and other symptoms is true, it follows that either most crabs live in regions or if people use comparative anatomy to unite or divide different species, then coyotes range from Panama to the North Slope of Alaska.', "So long as most crabs live in regions, 'fabrics are the big items that people are looking for' is true.", "If the statement 'if most crabs live in regions, then the statement 'fabrics are the big items that people are looking for' can be considered false' can be considered false, then maxillary bones are present and well developed.", "The notion that 'maxillary bones are present and well developed' is untrue."]
|
Given that coyotes range from Panama to the North Slope of Alaska, it can be inferred that spinal fluid surrounds the brain, spinal cord and nerves. On the condition that spinal fluid surrounds the brain, spinal cord and nerves, it is definitely the case that those that suggest taste masking - Medical substances often have a bitter taste when added to chewing gum are wrong. The statement that states people use comparative anatomy to unite or divide different species is right. It is a fact that either peacocks have (part) quill feathers or pernicious anemia causes weakness, numbness of the extremities, pallor, fever and other symptoms. Whenever it is true that peacocks have (part) quill feathers, 'either most crabs live in regions or if people use comparative anatomy to unite or divide different species, then coyotes range from Panama to the North Slope of Alaska' is true. When pernicious anemia causes weakness, numbness of the extremities, pallor, fever and other symptoms is true, it follows that either most crabs live in regions or if people use comparative anatomy to unite or divide different species, then coyotes range from Panama to the North Slope of Alaska. So long as most crabs live in regions, 'fabrics are the big items that people are looking for' is true. If the statement 'if most crabs live in regions, then the statement 'fabrics are the big items that people are looking for' can be considered false' can be considered false, then maxillary bones are present and well developed. The notion that 'maxillary bones are present and well developed' is untrue.
|
Those that suggest taste masking - Medical substances often have a bitter taste when added to chewing gum are wrong.
|
Those that suggest taste masking - Medical substances often have a bitter taste when added to chewing gum are wrong.
|
TRUE
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1] [SC2-1]
Therefore, Not [0]..
[SC1-1]
Hypothetical Syllogism:
If [1], then [3].
If [3], then (Not [0].).
Therefore, If [1], then (Not [0].)..
[SC2-1]
Modus Ponens:
If [2], then [1]. [SC1-2]
[2]
Therefore, [1].
[SC1-2]
Disjunctive Syllogism:
Either [4] or (If [2], then [1].). [SC1-3]
Not [4]. [SC2-3]
Therefore, If [2], then [1]..
[SC1-3]
Disjunction Elimination:
Either [5] or [6].
If [5], then (Either [4] or (If [2], then [1].).).
If [6], then (Either [4] or (If [2], then [1].).).
Therefore, Either [4] or (If [2], then [1].)..
[SC2-3]
Reductio Ad Absurdum:
If [4], then [7].
If [4], then (Not [7].). [SC2-4]
Therefore, Not [4]..
[SC2-4]
Modus Tonens:
If (Not (If [4], then (Not [7].).).), then [8].
Not [8].
Therefore, If [4], then (Not [7].)..
|
{0: 'Taste masking - Medical substances often have a bitter taste when added to chewing gum.', 1: 'Coyotes range from Panama to the North Slope of Alaska.', 2: 'People use comparative anatomy to unite or divide different species.', 3: 'Spinal fluid surrounds the brain, spinal cord and nerves.', 4: 'Most crabs live in regions.', 5: 'Peacocks have (part) quill feathers.', 6: 'Pernicious anemia causes weakness, numbness of the extremities, pallor, fever and other symptoms.', 7: 'Fabrics are the big items that people are looking for.', 8: 'Maxillary bones are present and well developed.'}
| 7 |
6,365 |
['When the claim that dairy food helps dental health does not correspond with reality is true, it follows that it is not true that if folk music is taught at music schools and conservatories, then jaguarundis have (part) cells.', "Whenever it is true that tests determine insulin levels, 'other factors include development' is true.", 'Given that if wheat bran reduces the risk of hemorrhoids because it is rich in insoluble fiber, then filtration is an action, it can be inferred that if the claim that dairy food helps dental health does not correspond with reality, then if folk music is taught at music schools and conservatories, then jaguarundis have (part) cells.', "So long as maps are a basic tool of anyone doing spatial analysis, information storage or retrieval, 'the statement that 'other factors include development' is incorrect' is true.", 'Those that suggest maps are a basic tool of anyone doing spatial analysis, information storage or retrieval are right.', 'Provided that either most plants require sources or most cougars prey on domestic cattle, we know that if slugs produce offspring, then either tests determine insulin levels or if wheat bran reduces the risk of hemorrhoids because it is rich in insoluble fiber, then filtration is an action.', 'At least one of two things is true: most plants require sources, or most cougars prey on domestic cattle.', "Whenever it is true that stepladders are used for climbs, 'slugs produce offspring' is true.", 'The statement that states stepladders are used for climbs is right.']
|
When the claim that dairy food helps dental health does not correspond with reality is true, it follows that it is not true that if folk music is taught at music schools and conservatories, then jaguarundis have (part) cells. Whenever it is true that tests determine insulin levels, 'other factors include development' is true. Given that if wheat bran reduces the risk of hemorrhoids because it is rich in insoluble fiber, then filtration is an action, it can be inferred that if the claim that dairy food helps dental health does not correspond with reality, then if folk music is taught at music schools and conservatories, then jaguarundis have (part) cells. So long as maps are a basic tool of anyone doing spatial analysis, information storage or retrieval, 'the statement that 'other factors include development' is incorrect' is true. Those that suggest maps are a basic tool of anyone doing spatial analysis, information storage or retrieval are right. Provided that either most plants require sources or most cougars prey on domestic cattle, we know that if slugs produce offspring, then either tests determine insulin levels or if wheat bran reduces the risk of hemorrhoids because it is rich in insoluble fiber, then filtration is an action. At least one of two things is true: most plants require sources, or most cougars prey on domestic cattle. Whenever it is true that stepladders are used for climbs, 'slugs produce offspring' is true. The statement that states stepladders are used for climbs is right.
|
Many people rightly believe that dairy food helps dental health.
|
It is a common misconception that dairy food helps dental health.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then (If [1], then [2].). [SC1-1]
If (Not [0].), then (Not (If [1], then [2].).).
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If (Not [0].), then (If [1], then [2].).). [SC1-2]
Not [3]. [SC2-2]
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC1-2]
Constructive Dilemma:
Either [4] or (If [5], then [6].). [SC1-3]
If [4], then [3].
If (If [5], then [6].), then (If (Not [0].), then (If [1], then [2].).).
Therefore, Either [3] or (If (Not [0].), then (If [1], then [2].).)..
[SC1-3]
Modus Ponens:
If [8], then (Either [4] or (If [5], then [6].).). [SC1-4]
[8] [SC2-4]
Therefore, Either [4] or (If [5], then [6].)..
[SC1-4]
Modus Ponens:
If (Either [9] or [10].), then (If [8], then (Either [4] or (If [5], then [6].).).).
Either [9] or [10].
Therefore, If [8], then (Either [4] or (If [5], then [6].).)..
[SC2-4]
Modus Ponens:
If [11], then [8].
[11]
Therefore, [8].
[SC2-2]
Modus Ponens:
If [7], then (Not [3].).
[7]
Therefore, Not [3]..
|
{0: 'Dairy food helps dental health.', 1: 'Folk music is taught at music schools and conservatories.', 2: 'Jaguarundis have (part) cells.', 3: 'Other factors include development.', 4: 'Tests determine insulin levels.', 5: 'Wheat bran reduces the risk of hemorrhoids because it is rich in insoluble fiber.', 6: 'Filtration is an action.', 7: 'Maps are a basic tool of anyone doing spatial analysis, information storage or retrieval.', 8: 'Slugs produce offspring.', 9: 'Most plants require sources.', 10: 'Most cougars prey on domestic cattle.', 11: 'Stepladders are used for climbs.'}
| 7 |
6,812 |
['Given that innovation means contemplating the past, changing some traditions and presenting a new phenomenon, it can be inferred that women saints in world religions .', 'At least one of two things is true: either meerkats also love to eat poisonous scorpions which are plentiful or bronze is an alloy, or if bible translation is the task of the whole church, and everyone can have a part, then some photosynthesis uses solar radiation.', 'Should it be the case that either meerkats also love to eat poisonous scorpions which are plentiful or bronze is an alloy, it follows that most gases produce energy.', 'Provided that if bible translation is the task of the whole church, and everyone can have a part, then some photosynthesis uses solar radiation, we know that innovation means contemplating the past, changing some traditions and presenting a new phenomenon.', 'Should it be the case that serotonin is chemical compounds, it follows that those that suggest most gases produce energy are wrong.', 'One may reasonably assume that if agricultural scientists continue to develop new crops or modify existing crops, then those that suggest most gases produce energy are wrong.', 'If gas also results from food allergies, then either serotonin is chemical compounds or agricultural scientists continue to develop new crops or modify existing crops.', 'Provided that fires are prevalent in chaparral because of the lightning and dry conditions, we know that either rats visit fewer food sites than mice or gas also results from food allergies.', 'It is true that fires are prevalent in chaparral because of the lightning and dry conditions.', "So long as it is not the case that if rats visit fewer food sites than mice, then either serotonin is chemical compounds or agricultural scientists continue to develop new crops or modify existing crops, 'if mites prefer conditions, then mothers conserve human life' is true.", "The statement 'if mites prefer conditions, then mothers conserve human life' can be considered false."]
|
Given that innovation means contemplating the past, changing some traditions and presenting a new phenomenon, it can be inferred that women saints in world religions . At least one of two things is true: either meerkats also love to eat poisonous scorpions which are plentiful or bronze is an alloy, or if bible translation is the task of the whole church, and everyone can have a part, then some photosynthesis uses solar radiation. Should it be the case that either meerkats also love to eat poisonous scorpions which are plentiful or bronze is an alloy, it follows that most gases produce energy. Provided that if bible translation is the task of the whole church, and everyone can have a part, then some photosynthesis uses solar radiation, we know that innovation means contemplating the past, changing some traditions and presenting a new phenomenon. Should it be the case that serotonin is chemical compounds, it follows that those that suggest most gases produce energy are wrong. One may reasonably assume that if agricultural scientists continue to develop new crops or modify existing crops, then those that suggest most gases produce energy are wrong. If gas also results from food allergies, then either serotonin is chemical compounds or agricultural scientists continue to develop new crops or modify existing crops. Provided that fires are prevalent in chaparral because of the lightning and dry conditions, we know that either rats visit fewer food sites than mice or gas also results from food allergies. It is true that fires are prevalent in chaparral because of the lightning and dry conditions. So long as it is not the case that if rats visit fewer food sites than mice, then either serotonin is chemical compounds or agricultural scientists continue to develop new crops or modify existing crops, 'if mites prefer conditions, then mothers conserve human life' is true. The statement 'if mites prefer conditions, then mothers conserve human life' can be considered false.
|
Many people rightly believe that women saints in world religions .
|
The claim that women saints in world religions is false.
|
FALSE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or [1]. [SC1-2]
Not [2]. [SC2-2]
Therefore, [1].
[SC1-2]
Constructive Dilemma:
Either (Either [5] or [6].) or (If [7], then [8].).
If (Either [5] or [6].), then [2].
If (If [7], then [8].), then [1].
Therefore, Either [2] or [1]..
[SC2-2]
Disjunction Elimination:
Either [3] or [4]. [SC1-3]
If [3], then (Not [2].).
If [4], then (Not [2].).
Therefore, Not [2]..
[SC1-3]
Disjunction Elimination:
Either [9] or [10]. [SC1-4]
If [9], then (Either [3] or [4].). [SC2-4]
If [10], then (Either [3] or [4].).
Therefore, Either [3] or [4]..
[SC1-4]
Modus Ponens:
If [13], then (Either [9] or [10].).
[13]
Therefore, Either [9] or [10]..
[SC2-4]
Modus Tonens:
If (Not (If [9], then (Either [3] or [4].).).), then (If [11], then [12].).
Not (If [11], then [12].).
Therefore, If [9], then (Either [3] or [4].)..
|
{0: 'Women saints in world religions .', 1: 'Innovation means contemplating the past, changing some traditions and presenting a new phenomenon.', 2: 'Most gases produce energy.', 3: 'Serotonin is chemical compounds.', 4: 'Agricultural scientists continue to develop new crops or modify existing crops.', 5: 'Meerkats also love to eat poisonous scorpions which are plentiful.', 6: 'Bronze is an alloy.', 7: 'Bible translation is the task of the whole church, and everyone can have a part.', 8: 'Some photosynthesis uses solar radiation.', 9: 'Rats visit fewer food sites than mice.', 10: 'Gas also results from food allergies.', 11: 'Mites prefer conditions.', 12: 'Mothers conserve human life.', 13: 'Fires are prevalent in chaparral because of the lightning and dry conditions.'}
| 7 |
6,026 |
['If if wishbone flower is a perennial grown as an annual, then chain link is one of the most common fences, then either all telescopes collect light and magnify it or earth rotates, making it appear like the moon revolves around the Earth once per day.', "It is a fact that either many children have a hard time when they start child care or competitiveness is the ability of a country's environment to sustain value added creation.", "One may reasonably assume that if competitiveness is the ability of a country's environment to sustain value added creation, then if wishbone flower is a perennial grown as an annual, then chain link is one of the most common fences.", "Whenever it is true that we know that the claim that either tennis is an athletic game or sex can also be a religious sacrament is false, 'insects have three pairs of jointed legs attached to the thorax' is true.", "So long as tennis is an athletic game, 'scientists can actually see organs developing' is true.", 'On the condition that scientists can actually see organs developing, it is definitely the case that if many children have a hard time when they start child care, then if wishbone flower is a perennial grown as an annual, then chain link is one of the most common fences.', 'Once we know sex can also be a religious sacrament, we also know that paper is also rich in carbon.', 'Provided that paper is also rich in carbon, we know that if many children have a hard time when they start child care, then if wishbone flower is a perennial grown as an annual, then chain link is one of the most common fences.', 'Once we know some people mistakenly believe that if we know that the claim that either tennis is an athletic game or sex can also be a religious sacrament is false, then the claim that insects have three pairs of jointed legs attached to the thorax has no merit, we also know that tourism is now the largest business sector in the world.', "Once we know some people mistakenly believe that if we know that the claim that either tennis is an athletic game or sex can also be a religious sacrament is false, then the claim that insects have three pairs of jointed legs attached to the thorax has no merit, we also know that the notion that 'tourism is now the largest business sector in the world' is untrue."]
|
If if wishbone flower is a perennial grown as an annual, then chain link is one of the most common fences, then either all telescopes collect light and magnify it or earth rotates, making it appear like the moon revolves around the Earth once per day. It is a fact that either many children have a hard time when they start child care or competitiveness is the ability of a country's environment to sustain value added creation. One may reasonably assume that if competitiveness is the ability of a country's environment to sustain value added creation, then if wishbone flower is a perennial grown as an annual, then chain link is one of the most common fences. Whenever it is true that we know that the claim that either tennis is an athletic game or sex can also be a religious sacrament is false, 'insects have three pairs of jointed legs attached to the thorax' is true. So long as tennis is an athletic game, 'scientists can actually see organs developing' is true. On the condition that scientists can actually see organs developing, it is definitely the case that if many children have a hard time when they start child care, then if wishbone flower is a perennial grown as an annual, then chain link is one of the most common fences. Once we know sex can also be a religious sacrament, we also know that paper is also rich in carbon. Provided that paper is also rich in carbon, we know that if many children have a hard time when they start child care, then if wishbone flower is a perennial grown as an annual, then chain link is one of the most common fences. Once we know some people mistakenly believe that if we know that the claim that either tennis is an athletic game or sex can also be a religious sacrament is false, then the claim that insects have three pairs of jointed legs attached to the thorax has no merit, we also know that tourism is now the largest business sector in the world. Once we know some people mistakenly believe that if we know that the claim that either tennis is an athletic game or sex can also be a religious sacrament is false, then the claim that insects have three pairs of jointed legs attached to the thorax has no merit, we also know that the notion that 'tourism is now the largest business sector in the world' is untrue.
|
There is good reason to believe that either all telescopes collect light and magnify it or earth rotates, making it appear like the moon revolves around the Earth once per day.
|
The statement that states either all telescopes collect light and magnify it or earth rotates, making it appear like the moon revolves around the Earth once per day is false.
|
FALSE
|
Modus Ponens:
If (If [2], then [3].), then (Either [0] or [1].).
If [2], then [3]. [SC2-1]
Therefore, Either [0] or [1]..
[SC2-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [2], then [3].). [SC2-2]
If [5], then (If [2], then [3].).
Therefore, If [2], then [3]..
[SC2-2]
Disjunction Elimination:
Either [6] or [7]. [SC1-3]
If [6], then (If [4], then (If [2], then [3].).). [SC2-3]
If [7], then (If [4], then (If [2], then [3].).). [SC3-3]
Therefore, If [4], then (If [2], then [3].)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (Either [6] or [7].).), then [10].
If (Not (Either [6] or [7].).), then (Not [10].). [SC2-4]
Therefore, Either [6] or [7]..
[SC2-4]
Reductio Ad Absurdum:
If (Not (If (Not (Either [6] or [7].).), then (Not [10].).).), then [11].
If (Not (If (Not (Either [6] or [7].).), then (Not [10].).).), then (Not [11].).
Therefore, If (Not (Either [6] or [7].).), then (Not [10].)..
[SC2-3]
Hypothetical Syllogism:
If [6], then [8].
If [8], then (If [4], then (If [2], then [3].).).
Therefore, If [6], then (If [4], then (If [2], then [3].).)..
[SC3-3]
Hypothetical Syllogism:
If [7], then [9].
If [9], then (If [4], then (If [2], then [3].).).
Therefore, If [7], then (If [4], then (If [2], then [3].).)..
|
{0: 'All telescopes collect light and magnify it .', 1: 'Earth rotates, making it appear like the moon revolves around the Earth once per day.', 2: 'Wishbone flower is a perennial grown as an annual.', 3: 'Chain link is one of the most common fences.', 4: 'Many children have a hard time when they start child care.', 5: "Competitiveness is the ability of a country's environment to sustain value added creation.", 6: 'Tennis is an athletic game.', 7: 'Sex can also be a religious sacrament.', 8: 'Scientists can actually see organs developing.', 9: 'Paper is also rich in carbon.', 10: 'Insects have three pairs of jointed legs attached to the thorax.', 11: 'Tourism is now the largest business sector in the world.'}
| 7 |
6,642 |
['Some people mistakenly believe that toucans have (part) heads.', "The statement that 'borrowing are appropriations' is incorrect.", 'There is good reason to believe that either antiparticles behave very much the same as ordinary particles or either high nitrogen promotes foliage growth, and excessive foliage requires more water or gray whales eat very little while on migration.', "Whenever it is true that antiparticles behave very much the same as ordinary particles, 'if those that suggest if some people mistakenly believe that either toucans have (part) heads or human cells adorn some antibodies with special carbohydrate molecules, then primos are wrestlers are wrong, then habitats include estuaries' is true.", 'One may reasonably assume that if either high nitrogen promotes foliage growth, and excessive foliage requires more water or gray whales eat very little while on migration, then if those that suggest if some people mistakenly believe that either toucans have (part) heads or human cells adorn some antibodies with special carbohydrate molecules, then primos are wrestlers are wrong, then habitats include estuaries.', 'When a lead pencil is a pencil is true, it follows that it is not the case that habitats include estuaries.', 'It is reasonable to believe that a lead pencil is a pencil.', 'One may reasonably assume that if some people mistakenly believe that if primos are wrestlers, then borrowing are appropriations, then currents can change quickly.', "The notion that 'currents can change quickly' is untrue."]
|
Some people mistakenly believe that toucans have (part) heads. The statement that 'borrowing are appropriations' is incorrect. There is good reason to believe that either antiparticles behave very much the same as ordinary particles or either high nitrogen promotes foliage growth, and excessive foliage requires more water or gray whales eat very little while on migration. Whenever it is true that antiparticles behave very much the same as ordinary particles, 'if those that suggest if some people mistakenly believe that either toucans have (part) heads or human cells adorn some antibodies with special carbohydrate molecules, then primos are wrestlers are wrong, then habitats include estuaries' is true. One may reasonably assume that if either high nitrogen promotes foliage growth, and excessive foliage requires more water or gray whales eat very little while on migration, then if those that suggest if some people mistakenly believe that either toucans have (part) heads or human cells adorn some antibodies with special carbohydrate molecules, then primos are wrestlers are wrong, then habitats include estuaries. When a lead pencil is a pencil is true, it follows that it is not the case that habitats include estuaries. It is reasonable to believe that a lead pencil is a pencil. One may reasonably assume that if some people mistakenly believe that if primos are wrestlers, then borrowing are appropriations, then currents can change quickly. The notion that 'currents can change quickly' is untrue.
|
The statement 'human cells adorn some antibodies with special carbohydrate molecules' is true.
|
The statement that 'human cells adorn some antibodies with special carbohydrate molecules' is incorrect.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either [1] or [0].).), then [2]. [SC1-2]
Not [2]. [SC2-2]
Therefore, Either [1] or [0]..
[SC1-2]
Modus Tonens:
If (Not (If (Not (Either [1] or [0].).), then [2].).), then [4]. [SC1-3]
Not [4]. [SC2-3]
Therefore, If (Not (Either [1] or [0].).), then [2]..
[SC1-3]
Disjunction Elimination:
Either [7] or (Either [8] or [9].).
If [7], then (If (Not (If (Not (Either [1] or [0].).), then [2].).), then [4].).
If (Either [8] or [9].), then (If (Not (If (Not (Either [1] or [0].).), then [2].).), then [4].).
Therefore, If (Not (If (Not (Either [1] or [0].).), then [2].).), then [4]..
[SC2-3]
Modus Ponens:
If [6], then (Not [4].).
[6]
Therefore, Not [4]..
[SC2-2]
Modus Tonens:
If [2], then [3]. [SC1-3]
Not [3].
Therefore, Not [2]..
[SC1-3]
Modus Tonens:
If (Not (If [2], then [3].).), then [5].
Not [5].
Therefore, If [2], then [3]..
|
{0: 'Human cells adorn some antibodies with special carbohydrate molecules.', 1: 'Toucans have (part) heads.', 2: 'Primos are wrestlers.', 3: 'Borrowing are appropriations.', 4: 'Habitats include estuaries.', 5: 'Currents can change quickly.', 6: 'A lead pencil is a pencil.', 7: 'Antiparticles behave very much the same as ordinary particles.', 8: 'High nitrogen promotes foliage growth, and excessive foliage requires more water.', 9: 'Gray whales eat very little while on migration.'}
| 7 |
6,417 |
['We know that either if different crops expand harvest season and help reduce harvest stresses, then all states permit unmarried individuals to adopt through both private-placement and agency adoption or summer is the break time in between the end and beginning of the year.', 'If if different crops expand harvest season and help reduce harvest stresses, then all states permit unmarried individuals to adopt through both private-placement and agency adoption, then impact includes displacement.', "So long as summer is the break time in between the end and beginning of the year, 'if beliefs drive anger or pain, then angels come in all sizes and ages' is true.", "So long as retroviruses also contain an essential enzyme known as reverse transcriptase, 'the statement 'impact includes displacement' can be considered false' is true.", "The statement 'retroviruses also contain an essential enzyme known as reverse transcriptase' is true.", 'Given that it is not true that if it is not the case that beliefs drive anger or pain, then increases insulin uptake from blood into target cells, it can be inferred that telephones have international direct dialling to most countries in the world.', "So long as it is not true that if it is not the case that beliefs drive anger or pain, then increases insulin uptake from blood into target cells, 'the statement that states telephones have international direct dialling to most countries in the world is false' is true.", 'There is good reason to believe that either olive oil consists of olein, palmitin, stearin, linolein or most maple syrup contains nutrients.', "Provided that olive oil consists of olein, palmitin, stearin, linolein, we know that if it is not the case that beliefs drive anger or pain, then the statement 'increases insulin uptake from blood into target cells' can be considered false.", "Given that most maple syrup contains nutrients, it can be inferred that if it is not the case that beliefs drive anger or pain, then the statement 'increases insulin uptake from blood into target cells' can be considered false."]
|
We know that either if different crops expand harvest season and help reduce harvest stresses, then all states permit unmarried individuals to adopt through both private-placement and agency adoption or summer is the break time in between the end and beginning of the year. If if different crops expand harvest season and help reduce harvest stresses, then all states permit unmarried individuals to adopt through both private-placement and agency adoption, then impact includes displacement. So long as summer is the break time in between the end and beginning of the year, 'if beliefs drive anger or pain, then angels come in all sizes and ages' is true. So long as retroviruses also contain an essential enzyme known as reverse transcriptase, 'the statement 'impact includes displacement' can be considered false' is true. The statement 'retroviruses also contain an essential enzyme known as reverse transcriptase' is true. Given that it is not true that if it is not the case that beliefs drive anger or pain, then increases insulin uptake from blood into target cells, it can be inferred that telephones have international direct dialling to most countries in the world. So long as it is not true that if it is not the case that beliefs drive anger or pain, then increases insulin uptake from blood into target cells, 'the statement that states telephones have international direct dialling to most countries in the world is false' is true. There is good reason to believe that either olive oil consists of olein, palmitin, stearin, linolein or most maple syrup contains nutrients. Provided that olive oil consists of olein, palmitin, stearin, linolein, we know that if it is not the case that beliefs drive anger or pain, then the statement 'increases insulin uptake from blood into target cells' can be considered false. Given that most maple syrup contains nutrients, it can be inferred that if it is not the case that beliefs drive anger or pain, then the statement 'increases insulin uptake from blood into target cells' can be considered false.
|
The claim that angels come in all sizes and ages is true.
|
The claim that angels come in all sizes and ages is true.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [1], then [0].). [SC1-2]
Not [2]. [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Constructive Dilemma:
Either (If [8], then [9].) or [10].
If (If [8], then [9].), then [2].
If [10], then (If [1], then [0].).
Therefore, Either [2] or (If [1], then [0].)..
[SC2-2]
Modus Ponens:
If [4], then (Not [2].).
[4]
Therefore, Not [2]..
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then [3]. [SC1-2]
If (Not [1].), then (Not [3].). [SC2-2]
Therefore, [1].
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not [1].), then [3].).), then [7].
If (Not (If (Not [1].), then [3].).), then (Not [7].).
Therefore, If (Not [1].), then [3]..
[SC2-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Not [1].), then (Not [3].).).
If [6], then (If (Not [1].), then (Not [3].).).
Therefore, If (Not [1].), then (Not [3].)..
|
{0: 'Angels come in all sizes and ages.', 1: 'Beliefs drive anger or pain.', 2: 'Impact includes displacement.', 3: 'Increases insulin uptake from blood into target cells.', 4: 'Retroviruses also contain an essential enzyme known as reverse transcriptase.', 5: 'Olive oil consists of olein, palmitin, stearin, linolein.', 6: 'Most maple syrup contains nutrients.', 7: 'Telephones have international direct dialling to most countries in the world.', 8: 'Different crops expand harvest season and help reduce harvest stresses.', 9: 'All states permit unmarried individuals to adopt through both private-placement and agency adoption.', 10: 'Summer is the break time in between the end and beginning of the year.'}
| 7 |
6,907 |
['Once we know gibberellins stimulate cell division and elongation but act more slowly than auxins, we also know that the claim that cookies become moister and sweeter when frozen has no merit.', 'Provided that psychology strives to describe, predict, understand, and control behaviour and mental processes, we know that either gibberellins stimulate cell division and elongation but act more slowly than auxins or prokaryotic cells have no nuclei, unlike Eukaryotic cells.', 'At least one of two things is true: coniferous plants have sharp needles or scales, or if prokaryotic cells have no nuclei, unlike Eukaryotic cells, then the claim that cookies become moister and sweeter when frozen has no merit.', 'At least one of two things is true: numbats have (part) sections, or a television receiver is a receiver.', 'On the condition that a television receiver is a receiver, it is definitely the case that intramural sports are a great way to meet people and stay in shape.', 'Assuming field corn is field crops, we know that if intramural sports are a great way to meet people and stay in shape, then either gibberellins stimulate cell division and elongation but act more slowly than auxins or prokaryotic cells have no nuclei, unlike Eukaryotic cells.', 'It is reasonable to believe that field corn is field crops.', 'It is a fact that either hooks are connectors or the claim that coniferous plants have sharp needles or scales does not correspond with reality.', 'The claim that hooks are connectors has no merit.', 'It is a fact that either cooking is an alchemical process or if pesticides are one group of substances whose toxicity is their prime purpose, then most parents can sense when their children misbehave on purpose.', "So long as cooking is an alchemical process, 'if numbats have (part) sections, then psychology strives to describe, predict, understand, and control behaviour and mental processes' is true.", 'Should it be the case that if pesticides are one group of substances whose toxicity is their prime purpose, then most parents can sense when their children misbehave on purpose, it follows that if numbats have (part) sections, then psychology strives to describe, predict, understand, and control behaviour and mental processes.']
|
Once we know gibberellins stimulate cell division and elongation but act more slowly than auxins, we also know that the claim that cookies become moister and sweeter when frozen has no merit. Provided that psychology strives to describe, predict, understand, and control behaviour and mental processes, we know that either gibberellins stimulate cell division and elongation but act more slowly than auxins or prokaryotic cells have no nuclei, unlike Eukaryotic cells. At least one of two things is true: coniferous plants have sharp needles or scales, or if prokaryotic cells have no nuclei, unlike Eukaryotic cells, then the claim that cookies become moister and sweeter when frozen has no merit. At least one of two things is true: numbats have (part) sections, or a television receiver is a receiver. On the condition that a television receiver is a receiver, it is definitely the case that intramural sports are a great way to meet people and stay in shape. Assuming field corn is field crops, we know that if intramural sports are a great way to meet people and stay in shape, then either gibberellins stimulate cell division and elongation but act more slowly than auxins or prokaryotic cells have no nuclei, unlike Eukaryotic cells. It is reasonable to believe that field corn is field crops. It is a fact that either hooks are connectors or the claim that coniferous plants have sharp needles or scales does not correspond with reality. The claim that hooks are connectors has no merit. It is a fact that either cooking is an alchemical process or if pesticides are one group of substances whose toxicity is their prime purpose, then most parents can sense when their children misbehave on purpose. So long as cooking is an alchemical process, 'if numbats have (part) sections, then psychology strives to describe, predict, understand, and control behaviour and mental processes' is true. Should it be the case that if pesticides are one group of substances whose toxicity is their prime purpose, then most parents can sense when their children misbehave on purpose, it follows that if numbats have (part) sections, then psychology strives to describe, predict, understand, and control behaviour and mental processes.
|
The claim that cookies become moister and sweeter when frozen has no merit.
|
The claim that cookies become moister and sweeter when frozen has no merit.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].).
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [4] or [5]. [SC1-2]
If [4], then (Either [1] or [2].).
If [5], then (Either [1] or [2].). [SC3-2]
Therefore, Either [1] or [2]..
[SC1-2]
Constructive Dilemma:
Either [8] or [9].
If [8], then [4]. [SC2-3]
If [9], then [5].
Therefore, Either [4] or [5]..
[SC2-3]
Disjunction Elimination:
Either [10] or (If [11], then [12].).
If [10], then (If [8], then [4].).
If (If [11], then [12].), then (If [8], then [4].).
Therefore, If [8], then [4]..
[SC3-2]
Modus Ponens:
If [6], then (If [5], then (Either [1] or [2].).).
[6]
Therefore, If [5], then (Either [1] or [2].)..
[SC3-1]
Disjunctive Syllogism:
Either [3] or (If [2], then (Not [0].).).
Not [3]. [SC2-2]
Therefore, If [2], then (Not [0].)..
[SC2-2]
Disjunctive Syllogism:
Either [7] or (Not [3].).
Not [7].
Therefore, Not [3]..
|
{0: 'Cookies become moister and sweeter when frozen.', 1: 'Gibberellins stimulate cell division and elongation but act more slowly than auxins.', 2: 'Prokaryotic cells have no nuclei, unlike Eukaryotic cells.', 3: 'Coniferous plants have sharp needles or scales.', 4: 'Psychology strives to describe, predict, understand, and control behaviour and mental processes.', 5: 'Intramural sports are a great way to meet people and stay in shape.', 6: 'Field corn is field crops.', 7: 'Hooks are connectors.', 8: 'Numbats have (part) sections.', 9: 'A television receiver is a receiver.', 10: 'Cooking is an alchemical process.', 11: 'Pesticides are one group of substances whose toxicity is their prime purpose.', 12: 'Most parents can sense when their children misbehave on purpose.'}
| 7 |
6,921 |
['There is good reason to believe that either leaves feed herbivores or copper isa conductor.', 'We know that the claim that wallets really are online organizers of payment systems, such as organizing multiple credit cards is false.', 'Given that the statement, either wallets really are online organizers of payment systems, such as organizing multiple credit cards or those that suggest leaves feed herbivores are wrong, does not hold, it can be inferred that it is not the case that pollen grains contains male sex cells.', "So long as blood tests can be useful in establishing the progress of treatment, 'if the statement, either wallets really are online organizers of payment systems, such as organizing multiple credit cards or those that suggest leaves feed herbivores are wrong, does not hold, then pollen grains contains male sex cells' is true.", 'Either one or both of these statements are true: people eat cakes, or either rattles are bands or edaphosauruses have (part) ears.', 'Assuming people eat cakes, we know that blood tests can be useful in establishing the progress of treatment.', 'If some bats feed on fish, then princesses have (part) personality.', 'Provided that princesses have (part) personality, we know that if the statement, either wallets really are online organizers of payment systems, such as organizing multiple credit cards or those that suggest leaves feed herbivores are wrong, does not hold, then pollen grains contains male sex cells.', 'At least one of two things is true: bats have it too, and they detect the difference between north and south, or if either rattles are bands or edaphosauruses have (part) ears, then some bats feed on fish.', 'The claim that bats have it too, and they detect the difference between north and south has no merit.']
|
There is good reason to believe that either leaves feed herbivores or copper isa conductor. We know that the claim that wallets really are online organizers of payment systems, such as organizing multiple credit cards is false. Given that the statement, either wallets really are online organizers of payment systems, such as organizing multiple credit cards or those that suggest leaves feed herbivores are wrong, does not hold, it can be inferred that it is not the case that pollen grains contains male sex cells. So long as blood tests can be useful in establishing the progress of treatment, 'if the statement, either wallets really are online organizers of payment systems, such as organizing multiple credit cards or those that suggest leaves feed herbivores are wrong, does not hold, then pollen grains contains male sex cells' is true. Either one or both of these statements are true: people eat cakes, or either rattles are bands or edaphosauruses have (part) ears. Assuming people eat cakes, we know that blood tests can be useful in establishing the progress of treatment. If some bats feed on fish, then princesses have (part) personality. Provided that princesses have (part) personality, we know that if the statement, either wallets really are online organizers of payment systems, such as organizing multiple credit cards or those that suggest leaves feed herbivores are wrong, does not hold, then pollen grains contains male sex cells. At least one of two things is true: bats have it too, and they detect the difference between north and south, or if either rattles are bands or edaphosauruses have (part) ears, then some bats feed on fish. The claim that bats have it too, and they detect the difference between north and south has no merit.
|
It is the case that copper isa conductor.
|
Some people mistakenly believe that copper isa conductor.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].). [SC1-2]
Not [2].
Therefore, Not [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [2] or (Not [1].).).), then [3]. [SC1-3]
If (Not (Either [2] or (Not [1].).).), then (Not [3].).
Therefore, Either [2] or (Not [1].)..
[SC1-3]
Disjunction Elimination:
Either [4] or [5]. [SC1-4]
If [4], then (If (Not (Either [2] or (Not [1].).).), then [3].).
If [5], then (If (Not (Either [2] or (Not [1].).).), then [3].). [SC3-4]
Therefore, If (Not (Either [2] or (Not [1].).).), then [3]..
[SC1-4]
Constructive Dilemma:
Either [6] or (Either [7] or [8].).
If [6], then [4].
If (Either [7] or [8].), then [5]. [SC3-5]
Therefore, Either [4] or [5]..
[SC3-5]
Disjunctive Syllogism:
Either [10] or (If (Either [7] or [8].), then [5].).
Not [10].
Therefore, If (Either [7] or [8].), then [5]..
[SC3-4]
Hypothetical Syllogism:
If [5], then [9].
If [9], then (If (Not (Either [2] or (Not [1].).).), then [3].).
Therefore, If [5], then (If (Not (Either [2] or (Not [1].).).), then [3].)..
|
{0: 'Copper isa conductor.', 1: 'Leaves feed herbivores.', 2: 'Wallets really are online organizers of payment systems, such as organizing multiple credit cards.', 3: 'Pollen grains contains male sex cells.', 4: 'Blood tests can be useful in establishing the progress of treatment.', 5: 'Some bats feed on fish.', 6: 'People eat cakes.', 7: 'Rattles are bands.', 8: 'Edaphosauruses have (part) ears.', 9: 'Princesses have (part) personality.', 10: 'Bats have it too, and they detect the difference between north and south.'}
| 7 |
6,003 |
['It is rational to agree that most ants require homes.', "We know that either if testicles have two important jobs in the body, then sewage is a serious threat to water sources or diamonds are the world's most popular gemstones.", 'Given that if testicles have two important jobs in the body, then sewage is a serious threat to water sources, it can be inferred that those that suggest appointments are pacts are wrong.', 'It is a fact that either if sloths eat food, then kinetic energy is known as the energy in motion or most animals have skeletons.', 'If if sloths eat food, then kinetic energy is known as the energy in motion, then if it is not true that if it is not true that if most ants require homes, then if herbivores eat plants only while omnivores eat both plants and meat, then basil prefers a fertile, well-aerated, organically rich soil, then appointments are pacts, then some termites have bacteria.', 'Should it be the case that most animals have skeletons, it follows that if it is not true that if it is not true that if most ants require homes, then if herbivores eat plants only while omnivores eat both plants and meat, then basil prefers a fertile, well-aerated, organically rich soil, then appointments are pacts, then some termites have bacteria.', 'Either one or both of these statements are true: natural phenomena involving electomagnetic fields include light, radio waves, TV signals, or vision plays roles.', 'Assuming natural phenomena involving electomagnetic fields include light, radio waves, TV signals, we know that if it is not true that if it is not true that if most ants require homes, then if herbivores eat plants only while omnivores eat both plants and meat, then basil prefers a fertile, well-aerated, organically rich soil, then appointments are pacts, then those that suggest some termites have bacteria are wrong.', 'Given that vision plays roles, it can be inferred that if it is not true that if it is not true that if most ants require homes, then if herbivores eat plants only while omnivores eat both plants and meat, then basil prefers a fertile, well-aerated, organically rich soil, then appointments are pacts, then those that suggest some termites have bacteria are wrong.', "Once we know diamonds are the world's most popular gemstones, we also know that mental illnesses are diseases of the brain, an organ of the body.", 'One may reasonably assume that if mental illnesses are diseases of the brain, an organ of the body, then those that suggest appointments are pacts are wrong.']
|
It is rational to agree that most ants require homes. We know that either if testicles have two important jobs in the body, then sewage is a serious threat to water sources or diamonds are the world's most popular gemstones. Given that if testicles have two important jobs in the body, then sewage is a serious threat to water sources, it can be inferred that those that suggest appointments are pacts are wrong. It is a fact that either if sloths eat food, then kinetic energy is known as the energy in motion or most animals have skeletons. If if sloths eat food, then kinetic energy is known as the energy in motion, then if it is not true that if it is not true that if most ants require homes, then if herbivores eat plants only while omnivores eat both plants and meat, then basil prefers a fertile, well-aerated, organically rich soil, then appointments are pacts, then some termites have bacteria. Should it be the case that most animals have skeletons, it follows that if it is not true that if it is not true that if most ants require homes, then if herbivores eat plants only while omnivores eat both plants and meat, then basil prefers a fertile, well-aerated, organically rich soil, then appointments are pacts, then some termites have bacteria. Either one or both of these statements are true: natural phenomena involving electomagnetic fields include light, radio waves, TV signals, or vision plays roles. Assuming natural phenomena involving electomagnetic fields include light, radio waves, TV signals, we know that if it is not true that if it is not true that if most ants require homes, then if herbivores eat plants only while omnivores eat both plants and meat, then basil prefers a fertile, well-aerated, organically rich soil, then appointments are pacts, then those that suggest some termites have bacteria are wrong. Given that vision plays roles, it can be inferred that if it is not true that if it is not true that if most ants require homes, then if herbivores eat plants only while omnivores eat both plants and meat, then basil prefers a fertile, well-aerated, organically rich soil, then appointments are pacts, then those that suggest some termites have bacteria are wrong. Once we know diamonds are the world's most popular gemstones, we also know that mental illnesses are diseases of the brain, an organ of the body. One may reasonably assume that if mental illnesses are diseases of the brain, an organ of the body, then those that suggest appointments are pacts are wrong.
|
Should it be the case that herbivores eat plants only while omnivores eat both plants and meat, it follows that basil prefers a fertile, well-aerated, organically rich soil.
|
The statement that 'if herbivores eat plants only while omnivores eat both plants and meat, then basil prefers a fertile, well-aerated, organically rich soil' is incorrect.
|
FALSE
|
Modus Ponens:
If [2], then (If [0], then [1].). [SC1-1]
[2]
Therefore, If [0], then [1]..
[SC1-1]
Modus Tonens:
If (Not (If [2], then (If [0], then [1].).).), then [3]. [SC1-2]
Not [3]. [SC2-2]
Therefore, If [2], then (If [0], then [1].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (If [2], then (If [0], then [1].).).), then [3].).), then [4]. [SC1-3]
If (Not (If (Not (If [2], then (If [0], then [1].).).), then [3].).), then (Not [4].). [SC2-3]
Therefore, If (Not (If [2], then (If [0], then [1].).).), then [3]..
[SC1-3]
Disjunction Elimination:
Either (If [8], then [9].) or [10].
If (If [8], then [9].), then (If (Not (If (Not (If [2], then (If [0], then [1].).).), then [3].).), then [4].).
If [10], then (If (Not (If (Not (If [2], then (If [0], then [1].).).), then [3].).), then [4].).
Therefore, If (Not (If (Not (If [2], then (If [0], then [1].).).), then [3].).), then [4]..
[SC2-3]
Disjunction Elimination:
Either [11] or [12].
If [11], then (If (Not (If (Not (If [2], then (If [0], then [1].).).), then [3].).), then (Not [4].).).
If [12], then (If (Not (If (Not (If [2], then (If [0], then [1].).).), then [3].).), then (Not [4].).).
Therefore, If (Not (If (Not (If [2], then (If [0], then [1].).).), then [3].).), then (Not [4].)..
[SC2-2]
Disjunction Elimination:
Either (If [5], then [6].) or [7].
If (If [5], then [6].), then (Not [3].).
If [7], then (Not [3].). [SC3-3]
Therefore, Not [3]..
[SC3-3]
Hypothetical Syllogism:
If [7], then [13].
If [13], then (Not [3].).
Therefore, If [7], then (Not [3].)..
|
{0: 'Herbivores eat plants only while omnivores eat both plants and meat.', 1: 'Basil prefers a fertile, well-aerated, organically rich soil.', 2: 'Most ants require homes.', 3: 'Appointments are pacts.', 4: 'Some termites have bacteria.', 5: 'Testicles have two important jobs in the body.', 6: 'Sewage is a serious threat to water sources.', 7: "Diamonds are the world's most popular gemstones.", 8: 'Sloths eat food.', 9: 'Kinetic energy is known as the energy in motion.', 10: 'Most animals have skeletons.', 11: 'Natural phenomena involving electomagnetic fields include light, radio waves, TV signals.', 12: 'Vision plays roles.', 13: 'Mental illnesses are diseases of the brain, an organ of the body.'}
| 7 |
6,134 |
['At least one of two things is true: germs can soon grow on food which is left standing at room temperature, or some prescription medicine contains human growth hormones.', 'Assuming if most ovules are produced by ovaries, then some gingers reduce blood pressure, we know that game animals consist of moose, caribou, black and brown bears.', 'The statement that states game animals consist of moose, caribou, black and brown bears is false.', 'Given that the statement, if germs can soon grow on food which is left standing at room temperature, then either if most ovules are produced by ovaries, then some gingers reduce blood pressure or some people mistakenly believe that fruit juice can almost always replace a sugar syrup, does not hold, it can be inferred that collectors work flexible schedules.', 'We know that at least one of two things is true: phosphates enter the water system from household detergents and from fertilizers, or if some prescription medicine contains human growth hormones, then either if most ovules are produced by ovaries, then some gingers reduce blood pressure or some people mistakenly believe that fruit juice can almost always replace a sugar syrup.', 'One may reasonably assume that if collectors work flexible schedules, then either impurities are located in water or snowshoes fall to hunters, disease, parasites and predators.', 'Some people mistakenly believe that either impurities are located in water or snowshoes fall to hunters, disease, parasites and predators.', 'When minerals are rigid is true, it follows that the claim that phosphates enter the water system from household detergents and from fertilizers does not correspond with reality.', 'It is true that minerals are rigid.']
|
At least one of two things is true: germs can soon grow on food which is left standing at room temperature, or some prescription medicine contains human growth hormones. Assuming if most ovules are produced by ovaries, then some gingers reduce blood pressure, we know that game animals consist of moose, caribou, black and brown bears. The statement that states game animals consist of moose, caribou, black and brown bears is false. Given that the statement, if germs can soon grow on food which is left standing at room temperature, then either if most ovules are produced by ovaries, then some gingers reduce blood pressure or some people mistakenly believe that fruit juice can almost always replace a sugar syrup, does not hold, it can be inferred that collectors work flexible schedules. We know that at least one of two things is true: phosphates enter the water system from household detergents and from fertilizers, or if some prescription medicine contains human growth hormones, then either if most ovules are produced by ovaries, then some gingers reduce blood pressure or some people mistakenly believe that fruit juice can almost always replace a sugar syrup. One may reasonably assume that if collectors work flexible schedules, then either impurities are located in water or snowshoes fall to hunters, disease, parasites and predators. Some people mistakenly believe that either impurities are located in water or snowshoes fall to hunters, disease, parasites and predators. When minerals are rigid is true, it follows that the claim that phosphates enter the water system from household detergents and from fertilizers does not correspond with reality. It is true that minerals are rigid.
|
Some people mistakenly believe that fruit juice can almost always replace a sugar syrup.
|
Some people mistakenly believe that fruit juice can almost always replace a sugar syrup.
|
TRUE
|
Disjunctive Syllogism:
Either (If [1], then [2].) or (Not [0].). [SC1-1]
Not (If [1], then [2].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Either (If [1], then [2].) or (Not [0].).). [SC2-2]
If [4], then (Either (If [1], then [2].) or (Not [0].).). [SC3-2]
Therefore, Either (If [1], then [2].) or (Not [0].)..
[SC2-2]
Modus Tonens:
If (Not (If [3], then (Either (If [1], then [2].) or (Not [0].).).).), then [7].
Not [7]. [SC2-3]
Therefore, If [3], then (Either (If [1], then [2].) or (Not [0].).)..
[SC2-3]
Modus Tonens:
If [7], then (Either [9] or [10].).
Not (Either [9] or [10].).
Therefore, Not [7]..
[SC3-2]
Disjunctive Syllogism:
Either [6] or (If [4], then (Either (If [1], then [2].) or (Not [0].).).).
Not [6]. [SC2-3]
Therefore, If [4], then (Either (If [1], then [2].) or (Not [0].).)..
[SC2-3]
Modus Ponens:
If [8], then (Not [6].).
[8]
Therefore, Not [6]..
[SC2-1]
Modus Tonens:
If (If [1], then [2].), then [5].
Not [5].
Therefore, Not (If [1], then [2].)..
|
{0: 'Fruit juice can almost always replace a sugar syrup.', 1: 'Most ovules are produced by ovaries.', 2: 'Some gingers reduce blood pressure.', 3: 'Germs can soon grow on food which is left standing at room temperature.', 4: 'Some prescription medicine contains human growth hormones.', 5: 'Game animals consist of moose, caribou, black and brown bears.', 6: 'Phosphates enter the water system from household detergents and from fertilizers.', 7: 'Collectors work flexible schedules.', 8: 'Minerals are rigid.', 9: 'Impurities are located in water.', 10: 'Snowshoes fall to hunters, disease, parasites and predators.'}
| 7 |
6,355 |
["So long as droughts affect their numbers by killing the plants on which they browse, 'if drugs can similarly have adverse effects among nondependent users, then those that suggest if male flowers appear on weed plants, then observations indicate patterns are wrong' is true.", "When the statement that 'if birds have bright feathers, then if drugs can similarly have adverse effects among nondependent users, then if male flowers appear on weed plants, then observations indicate patterns' is incorrect is true, it follows that either disasters can be of different kinds, but most are caused by forces of nature or teens are more likely than adults to be victims of crime.", "Given that the statement that 'if birds have bright feathers, then if drugs can similarly have adverse effects among nondependent users, then if male flowers appear on weed plants, then observations indicate patterns' is incorrect, it can be inferred that it is not true that either disasters can be of different kinds, but most are caused by forces of nature or teens are more likely than adults to be victims of crime.", 'Once we know it is not the case that birds have bright feathers, we also know that most elk have incisors.', "Whenever it is true that it is not the case that birds have bright feathers, 'the statement that 'most elk have incisors' is incorrect' is true.", 'When if birds fluff up their feathers when they want to stay warm, since fluffing introduces air, then absolute magnitude is a measure of luminosity, how much light a star radiates into space is true, it follows that droughts affect their numbers by killing the plants on which they browse.', 'Once we know the statement, if birds fluff up their feathers when they want to stay warm, since fluffing introduces air, then absolute magnitude is a measure of luminosity, how much light a star radiates into space, does not hold, we also know that some species can imitate human chatter, waterfalls, and pigs.', 'When the statement, if birds fluff up their feathers when they want to stay warm, since fluffing introduces air, then absolute magnitude is a measure of luminosity, how much light a star radiates into space, does not hold is true, it follows that the claim that some species can imitate human chatter, waterfalls, and pigs has no merit.']
|
So long as droughts affect their numbers by killing the plants on which they browse, 'if drugs can similarly have adverse effects among nondependent users, then those that suggest if male flowers appear on weed plants, then observations indicate patterns are wrong' is true. When the statement that 'if birds have bright feathers, then if drugs can similarly have adverse effects among nondependent users, then if male flowers appear on weed plants, then observations indicate patterns' is incorrect is true, it follows that either disasters can be of different kinds, but most are caused by forces of nature or teens are more likely than adults to be victims of crime. Given that the statement that 'if birds have bright feathers, then if drugs can similarly have adverse effects among nondependent users, then if male flowers appear on weed plants, then observations indicate patterns' is incorrect, it can be inferred that it is not true that either disasters can be of different kinds, but most are caused by forces of nature or teens are more likely than adults to be victims of crime. Once we know it is not the case that birds have bright feathers, we also know that most elk have incisors. Whenever it is true that it is not the case that birds have bright feathers, 'the statement that 'most elk have incisors' is incorrect' is true. When if birds fluff up their feathers when they want to stay warm, since fluffing introduces air, then absolute magnitude is a measure of luminosity, how much light a star radiates into space is true, it follows that droughts affect their numbers by killing the plants on which they browse. Once we know the statement, if birds fluff up their feathers when they want to stay warm, since fluffing introduces air, then absolute magnitude is a measure of luminosity, how much light a star radiates into space, does not hold, we also know that some species can imitate human chatter, waterfalls, and pigs. When the statement, if birds fluff up their feathers when they want to stay warm, since fluffing introduces air, then absolute magnitude is a measure of luminosity, how much light a star radiates into space, does not hold is true, it follows that the claim that some species can imitate human chatter, waterfalls, and pigs has no merit.
|
It is a common misconception that drugs can similarly have adverse effects among nondependent users.
|
Drugs can similarly have adverse effects among nondependent users.
|
FALSE
|
Reductio Ad Absurdum:
If [0], then (If [1], then [2].). [SC1-1]
If [0], then (Not (If [1], then [2].).). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [3], then (If [0], then (If [1], then [2].).). [SC1-2]
[3] [SC2-2]
Therefore, If [0], then (If [1], then [2].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [3], then (If [0], then (If [1], then [2].).).).), then (Either [7] or [8].).
If (Not (If [3], then (If [0], then (If [1], then [2].).).).), then (Not (Either [7] or [8].).).
Therefore, If [3], then (If [0], then (If [1], then [2].).)..
[SC2-2]
Reductio Ad Absurdum:
If (Not [3].), then [9].
If (Not [3].), then (Not [9].).
Therefore, [3].
[SC2-1]
Modus Ponens:
If [4], then (If [0], then (Not (If [1], then [2].).).).
[4] [SC2-2]
Therefore, If [0], then (Not (If [1], then [2].).)..
[SC2-2]
Modus Ponens:
If (If [5], then [6].), then [4].
If [5], then [6]. [SC2-3]
Therefore, [4].
[SC2-3]
Reductio Ad Absurdum:
If (Not (If [5], then [6].).), then [10].
If (Not (If [5], then [6].).), then (Not [10].).
Therefore, If [5], then [6]..
|
{0: 'Drugs can similarly have adverse effects among nondependent users.', 1: 'Male flowers appear on weed plants.', 2: 'Observations indicate patterns.', 3: 'Birds have bright feathers.', 4: 'Droughts affect their numbers by killing the plants on which they browse.', 5: 'Birds fluff up their feathers when they want to stay warm, since fluffing introduces air.', 6: 'Absolute magnitude is a measure of luminosity, how much light a star radiates into space.', 7: 'Disasters can be of different kinds, but most are caused by forces of nature.', 8: 'Teens are more likely than adults to be victims of crime.', 9: 'Most elk have incisors.', 10: 'Some species can imitate human chatter, waterfalls, and pigs.'}
| 7 |
6,877 |
['Provided that some diets formulate for kittens, we know that it is not the case that angiosperms are the largest and most common group of seed-bearing plants.', 'On the condition that if rodeo works well on cattails, which is the most common emergent aquatic plant in Colorado, then causality is certainly a central concept in many branches of science and philosophy, it is definitely the case that either some ducks enter nests or job stress affects women and men differently.', "Whenever it is true that rodeo works well on cattails, which is the most common emergent aquatic plant in Colorado, 'causality is certainly a central concept in many branches of science and philosophy' is true.", 'Should it be the case that the claim that if some ducks enter nests, then some diets formulate for kittens does not reflect reality, it follows that most yellow tomatoes are bland in flavor.', 'Assuming the claim that if some ducks enter nests, then some diets formulate for kittens does not reflect reality, we know that the claim that most yellow tomatoes are bland in flavor does not correspond with reality.', "Whenever it is true that effigy pots are typical of Mississippian culture, 'if job stress affects women and men differently, then some diets formulate for kittens' is true.", 'Provided that if angels hold a candle, cross, or heart, then similar experiments yield results, we know that if job stress affects women and men differently, then some diets formulate for kittens.', 'Many people rightly believe that different states have different age limits.', 'Assuming we know that the claim that if different states have different age limits, then either effigy pots are typical of Mississippian culture or if angels hold a candle, cross, or heart, then similar experiments yield results is false, we know that statistics are numbers.', 'The claim that statistics are numbers is false.']
|
Provided that some diets formulate for kittens, we know that it is not the case that angiosperms are the largest and most common group of seed-bearing plants. On the condition that if rodeo works well on cattails, which is the most common emergent aquatic plant in Colorado, then causality is certainly a central concept in many branches of science and philosophy, it is definitely the case that either some ducks enter nests or job stress affects women and men differently. Whenever it is true that rodeo works well on cattails, which is the most common emergent aquatic plant in Colorado, 'causality is certainly a central concept in many branches of science and philosophy' is true. Should it be the case that the claim that if some ducks enter nests, then some diets formulate for kittens does not reflect reality, it follows that most yellow tomatoes are bland in flavor. Assuming the claim that if some ducks enter nests, then some diets formulate for kittens does not reflect reality, we know that the claim that most yellow tomatoes are bland in flavor does not correspond with reality. Whenever it is true that effigy pots are typical of Mississippian culture, 'if job stress affects women and men differently, then some diets formulate for kittens' is true. Provided that if angels hold a candle, cross, or heart, then similar experiments yield results, we know that if job stress affects women and men differently, then some diets formulate for kittens. Many people rightly believe that different states have different age limits. Assuming we know that the claim that if different states have different age limits, then either effigy pots are typical of Mississippian culture or if angels hold a candle, cross, or heart, then similar experiments yield results is false, we know that statistics are numbers. The claim that statistics are numbers is false.
|
It is not the case that angiosperms are the largest and most common group of seed-bearing plants.
|
It is reasonable to believe that angiosperms are the largest and most common group of seed-bearing plants.
|
FALSE
|
Modus Ponens:
If [1], then (Not [0].).
[1] [SC2-1]
Therefore, Not [0]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3]. [SC1-2]
If [2], then [1]. [SC2-2]
If [3], then [1]. [SC3-2]
Therefore, [1].
[SC1-2]
Modus Ponens:
If (If [8], then [9].), then (Either [2] or [3].).
If [8], then [9].
Therefore, Either [2] or [3]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [2], then [1].).), then [4].
If (Not (If [2], then [1].).), then (Not [4].).
Therefore, If [2], then [1]..
[SC3-2]
Disjunction Elimination:
Either [5] or (If [6], then [7].). [SC1-3]
If [5], then (If [3], then [1].).
If (If [6], then [7].), then (If [3], then [1].).
Therefore, If [3], then [1]..
[SC1-3]
Modus Ponens:
If [10], then (Either [5] or (If [6], then [7].).). [SC1-4]
[10]
Therefore, Either [5] or (If [6], then [7].)..
[SC1-4]
Modus Tonens:
If (Not (If [10], then (Either [5] or (If [6], then [7].).).).), then [11].
Not [11].
Therefore, If [10], then (Either [5] or (If [6], then [7].).)..
|
{0: 'Angiosperms are the largest and most common group of seed-bearing plants.', 1: 'Some diets formulate for kittens.', 2: 'Some ducks enter nests.', 3: 'Job stress affects women and men differently.', 4: 'Most yellow tomatoes are bland in flavor.', 5: 'Effigy pots are typical of Mississippian culture.', 6: 'Angels hold a candle, cross, or heart.', 7: 'Similar experiments yield results.', 8: 'Rodeo works well on cattails, which is the most common emergent aquatic plant in Colorado.', 9: 'Causality is certainly a central concept in many branches of science and philosophy.', 10: 'Different states have different age limits.', 11: 'Statistics are numbers.'}
| 7 |
6,768 |
['The claim that galagos have (part) skulls does not correspond with reality.', 'One may reasonably assume that if a combat boot is a boot, then if the statement, most antibodies affect pregnancy, does not hold, then free agency reigns in professional sports.', 'Provided that either severe sunburn causes blisters, chills, and fever or acid causes brain damage, we know that if the statement, most antibodies affect pregnancy, does not hold, then free agency reigns in professional sports.', 'It is rational to believe that either if trains are public transport, then foresters also work in wood product industries, for private landowners, or as consultants or everyday activism begins and exists in the heart and the soul of each and every being.', 'On the condition that if trains are public transport, then foresters also work in wood product industries, for private landowners, or as consultants, it is definitely the case that if free agency reigns in professional sports, then galagos have (part) skulls.', "Provided that the notion that 'either a combat boot is a boot or either severe sunburn causes blisters, chills, and fever or acid causes brain damage' is untrue, we know that carnivores eat rodents.", "Once we know the notion that 'either a combat boot is a boot or either severe sunburn causes blisters, chills, and fever or acid causes brain damage' is untrue, we also know that it is a common misconception that carnivores eat rodents.", "Whenever it is true that strength is a basic requirement for almost all sports and is important in many daily activities, 'if everyday activism begins and exists in the heart and the soul of each and every being, then if free agency reigns in professional sports, then galagos have (part) skulls' is true.", 'Provided that all cells can divide to produce other cells, we know that if everyday activism begins and exists in the heart and the soul of each and every being, then if free agency reigns in professional sports, then galagos have (part) skulls.', "So long as black women are at disproportionately high risk, particularly in the southern counties of Alabama, 'either strength is a basic requirement for almost all sports and is important in many daily activities or all cells can divide to produce other cells' is true.", 'black women are at disproportionately high risk, particularly in the southern counties of Alabama.']
|
The claim that galagos have (part) skulls does not correspond with reality. One may reasonably assume that if a combat boot is a boot, then if the statement, most antibodies affect pregnancy, does not hold, then free agency reigns in professional sports. Provided that either severe sunburn causes blisters, chills, and fever or acid causes brain damage, we know that if the statement, most antibodies affect pregnancy, does not hold, then free agency reigns in professional sports. It is rational to believe that either if trains are public transport, then foresters also work in wood product industries, for private landowners, or as consultants or everyday activism begins and exists in the heart and the soul of each and every being. On the condition that if trains are public transport, then foresters also work in wood product industries, for private landowners, or as consultants, it is definitely the case that if free agency reigns in professional sports, then galagos have (part) skulls. Provided that the notion that 'either a combat boot is a boot or either severe sunburn causes blisters, chills, and fever or acid causes brain damage' is untrue, we know that carnivores eat rodents. Once we know the notion that 'either a combat boot is a boot or either severe sunburn causes blisters, chills, and fever or acid causes brain damage' is untrue, we also know that it is a common misconception that carnivores eat rodents. Whenever it is true that strength is a basic requirement for almost all sports and is important in many daily activities, 'if everyday activism begins and exists in the heart and the soul of each and every being, then if free agency reigns in professional sports, then galagos have (part) skulls' is true. Provided that all cells can divide to produce other cells, we know that if everyday activism begins and exists in the heart and the soul of each and every being, then if free agency reigns in professional sports, then galagos have (part) skulls. So long as black women are at disproportionately high risk, particularly in the southern counties of Alabama, 'either strength is a basic requirement for almost all sports and is important in many daily activities or all cells can divide to produce other cells' is true. black women are at disproportionately high risk, particularly in the southern counties of Alabama.
|
It is reasonable to believe that most antibodies affect pregnancy.
|
It is not the case that most antibodies affect pregnancy.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [2]. [SC1-2]
If [2], then [1]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunction Elimination:
Either [6] or (Either [7] or [8].). [SC1-3]
If [6], then (If (Not [0].), then [2].).
If (Either [7] or [8].), then (If (Not [0].), then [2].).
Therefore, If (Not [0].), then [2]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (Either [6] or (Either [7] or [8].).).), then [9].
If (Not (Either [6] or (Either [7] or [8].).).), then (Not [9].).
Therefore, Either [6] or (Either [7] or [8].)..
[SC2-2]
Disjunction Elimination:
Either (If [3], then [4].) or [5].
If (If [3], then [4].), then (If [2], then [1].).
If [5], then (If [2], then [1].). [SC3-3]
Therefore, If [2], then [1]..
[SC3-3]
Disjunction Elimination:
Either [10] or [11]. [SC1-4]
If [10], then (If [5], then (If [2], then [1].).).
If [11], then (If [5], then (If [2], then [1].).).
Therefore, If [5], then (If [2], then [1].)..
[SC1-4]
Modus Ponens:
If [12], then (Either [10] or [11].).
[12]
Therefore, Either [10] or [11]..
|
{0: 'Most antibodies affect pregnancy.', 1: 'Galagos have (part) skulls.', 2: 'Free agency reigns in professional sports.', 3: 'Trains are public transport.', 4: 'Foresters also work in wood product industries, for private landowners, or as consultants.', 5: 'Everyday activism begins and exists in the heart and the soul of each and every being.', 6: 'A combat boot is a boot.', 7: 'Severe sunburn causes blisters, chills, and fever.', 8: 'Acid causes brain damage.', 9: 'Carnivores eat rodents.', 10: 'Strength is a basic requirement for almost all sports and is important in many daily activities.', 11: 'All cells can divide to produce other cells.', 12: 'Black women are at disproportionately high risk, particularly in the southern counties of Alabama.'}
| 7 |
6,836 |
['It is a fact that either religion includes all aspects of religious belief, observance and practice or universal energy is the basic fabric of everything in the universe.', 'Given that religion includes all aspects of religious belief, observance and practice, it can be inferred that either cargo is located in ships or if blood has magical properties, then either some worms live for years or most objects tend to absorb infrared rather than reflect it.', 'Assuming universal energy is the basic fabric of everything in the universe, we know that either cargo is located in ships or if blood has magical properties, then either some worms live for years or most objects tend to absorb infrared rather than reflect it.', 'Assuming cargo is located in ships, we know that some butterflies eat fluid.', 'Once we know cargo is located in ships, we also know that it is not true that some butterflies eat fluid.', "So long as if rhizobial bacteria convert atmospheric nitrogen into nitrate fertilizers in a form usable by plants, then recreational fisheries use hook and line, 'if japanese restaurants are located in downtowns, then it is not the case that either some worms live for years or most objects tend to absorb infrared rather than reflect it' is true.", 'Given that rhizobial bacteria convert atmospheric nitrogen into nitrate fertilizers in a form usable by plants, it can be inferred that recreational fisheries use hook and line.', 'Provided that it is not the case that japanese restaurants are located in downtowns, we know that tech is clearly an industry still dominated by men.', "Should it be the case that it is not the case that japanese restaurants are located in downtowns, it follows that the notion that 'tech is clearly an industry still dominated by men' is untrue."]
|
It is a fact that either religion includes all aspects of religious belief, observance and practice or universal energy is the basic fabric of everything in the universe. Given that religion includes all aspects of religious belief, observance and practice, it can be inferred that either cargo is located in ships or if blood has magical properties, then either some worms live for years or most objects tend to absorb infrared rather than reflect it. Assuming universal energy is the basic fabric of everything in the universe, we know that either cargo is located in ships or if blood has magical properties, then either some worms live for years or most objects tend to absorb infrared rather than reflect it. Assuming cargo is located in ships, we know that some butterflies eat fluid. Once we know cargo is located in ships, we also know that it is not true that some butterflies eat fluid. So long as if rhizobial bacteria convert atmospheric nitrogen into nitrate fertilizers in a form usable by plants, then recreational fisheries use hook and line, 'if japanese restaurants are located in downtowns, then it is not the case that either some worms live for years or most objects tend to absorb infrared rather than reflect it' is true. Given that rhizobial bacteria convert atmospheric nitrogen into nitrate fertilizers in a form usable by plants, it can be inferred that recreational fisheries use hook and line. Provided that it is not the case that japanese restaurants are located in downtowns, we know that tech is clearly an industry still dominated by men. Should it be the case that it is not the case that japanese restaurants are located in downtowns, it follows that the notion that 'tech is clearly an industry still dominated by men' is untrue.
|
Some people mistakenly believe that blood has magical properties.
|
The statement 'blood is the vehicle used by our bodies to transport nutrients and wastes' can be considered false.
|
Uncertain
|
Modus Tonens:
If [0], then (Either [1] or [2].). [SC1-1]
Not (Either [1] or [2].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [4] or (If [0], then (Either [1] or [2].).). [SC1-2]
Not [4]. [SC2-2]
Therefore, If [0], then (Either [1] or [2].)..
[SC1-2]
Disjunction Elimination:
Either [9] or [10].
If [9], then (Either [4] or (If [0], then (Either [1] or [2].).).).
If [10], then (Either [4] or (If [0], then (Either [1] or [2].).).).
Therefore, Either [4] or (If [0], then (Either [1] or [2].).)..
[SC2-2]
Reductio Ad Absurdum:
If [4], then [7].
If [4], then (Not [7].).
Therefore, Not [4]..
[SC2-1]
Modus Ponens:
If [3], then (Not (Either [1] or [2].).). [SC1-2]
[3] [SC2-2]
Therefore, Not (Either [1] or [2].)..
[SC1-2]
Modus Ponens:
If (If [5], then [6].), then (If [3], then (Not (Either [1] or [2].).).).
If [5], then [6].
Therefore, If [3], then (Not (Either [1] or [2].).)..
[SC2-2]
Reductio Ad Absurdum:
If (Not [3].), then [8].
If (Not [3].), then (Not [8].).
Therefore, [3].
|
{0: 'Blood has magical properties.', 1: 'Some worms live for years.', 2: 'Most objects tend to absorb infrared rather than reflect it.', 3: 'Japanese restaurants are located in downtowns.', 4: 'Cargo is located in ships.', 5: 'Rhizobial bacteria convert atmospheric nitrogen into nitrate fertilizers in a form usable by plants.', 6: 'Recreational fisheries use hook and line.', 7: 'Some butterflies eat fluid.', 8: 'Tech is clearly an industry still dominated by men.', 9: 'Religion includes all aspects of religious belief, observance and practice.', 10: 'Universal energy is the basic fabric of everything in the universe.'}
| 7 |
6,561 |
['Given that the claim that either minimum wage is set by state and federal laws or cOLAs are extra payments, added on to match inflation is false, it can be inferred that fluid power includes hydraulics, which involves liquids, and pneumatics, which involves gases.', 'It is a fact that either either feet have layers or true fish have a skeleton made of bone and are classified in a class called Osteichthyes or most air has moisture.', 'Assuming most air has moisture, we know that the statement that states fluid power includes hydraulics, which involves liquids, and pneumatics, which involves gases is false.', 'Once we know basal cells are responsible for producing the squamous cells in the skin, we also know that group behaviour differs from individual behaviour.', 'When either bones are located in japans or human resources is a graveyard of job applicants is true, it follows that if if basal cells are responsible for producing the squamous cells in the skin, then group behaviour differs from individual behaviour, then if either feet have layers or true fish have a skeleton made of bone and are classified in a class called Osteichthyes, then the statement that states fluid power includes hydraulics, which involves liquids, and pneumatics, which involves gases is false.', 'One may reasonably assume that if some diets cause serious health problems, then either bones are located in japans or human resources is a graveyard of job applicants.', 'There is good reason to believe that either visitation is a tragedy or some diets cause serious health problems.', 'Once we know visitation is a tragedy, we also know that some agricultural practices benefit pheasants at the cost of farm profits.', 'Those that suggest some agricultural practices benefit pheasants at the cost of farm profits are wrong.']
|
Given that the claim that either minimum wage is set by state and federal laws or cOLAs are extra payments, added on to match inflation is false, it can be inferred that fluid power includes hydraulics, which involves liquids, and pneumatics, which involves gases. It is a fact that either either feet have layers or true fish have a skeleton made of bone and are classified in a class called Osteichthyes or most air has moisture. Assuming most air has moisture, we know that the statement that states fluid power includes hydraulics, which involves liquids, and pneumatics, which involves gases is false. Once we know basal cells are responsible for producing the squamous cells in the skin, we also know that group behaviour differs from individual behaviour. When either bones are located in japans or human resources is a graveyard of job applicants is true, it follows that if if basal cells are responsible for producing the squamous cells in the skin, then group behaviour differs from individual behaviour, then if either feet have layers or true fish have a skeleton made of bone and are classified in a class called Osteichthyes, then the statement that states fluid power includes hydraulics, which involves liquids, and pneumatics, which involves gases is false. One may reasonably assume that if some diets cause serious health problems, then either bones are located in japans or human resources is a graveyard of job applicants. There is good reason to believe that either visitation is a tragedy or some diets cause serious health problems. Once we know visitation is a tragedy, we also know that some agricultural practices benefit pheasants at the cost of farm profits. Those that suggest some agricultural practices benefit pheasants at the cost of farm profits are wrong.
|
There is good reason to believe that either minimum wage is set by state and federal laws or cOLAs are extra payments, added on to match inflation.
|
There is good reason to believe that either minimum wage is set by state and federal laws or cOLAs are extra payments, added on to match inflation.
|
TRUE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2].
Not [2]. [SC2-1]
Therefore, Either [0] or [1]..
[SC2-1]
Disjunction Elimination:
Either (Either [3] or [4].) or [5].
If (Either [3] or [4].), then (Not [2].). [SC2-2]
If [5], then (Not [2].).
Therefore, Not [2]..
[SC2-2]
Modus Ponens:
If (If [6], then [7].), then (If (Either [3] or [4].), then (Not [2].).). [SC1-3]
If [6], then [7].
Therefore, If (Either [3] or [4].), then (Not [2].)..
[SC1-3]
Modus Ponens:
If (Either [8] or [9].), then (If (If [6], then [7].), then (If (Either [3] or [4].), then (Not [2].).).).
Either [8] or [9]. [SC2-4]
Therefore, If (If [6], then [7].), then (If (Either [3] or [4].), then (Not [2].).)..
[SC2-4]
Modus Ponens:
If [10], then (Either [8] or [9].).
[10] [SC2-5]
Therefore, Either [8] or [9]..
[SC2-5]
Disjunctive Syllogism:
Either [11] or [10].
Not [11]. [SC2-6]
Therefore, [10].
[SC2-6]
Modus Tonens:
If [11], then [12].
Not [12].
Therefore, Not [11]..
|
{0: 'Minimum wage is set by state and federal laws.', 1: 'COLAs are extra payments, added on to match inflation.', 2: 'Fluid power includes hydraulics, which involves liquids, and pneumatics, which involves gases.', 3: 'Feet have layers.', 4: 'True fish have a skeleton made of bone and are classified in a class called Osteichthyes.', 5: 'Most air has moisture.', 6: 'Basal cells are responsible for producing the squamous cells in the skin.', 7: 'Group behaviour differs from individual behaviour.', 8: 'Bones are located in japans.', 9: 'Human resources is a graveyard of job applicants.', 10: 'Some diets cause serious health problems.', 11: 'Visitation is a tragedy.', 12: 'Some agricultural practices benefit pheasants at the cost of farm profits.'}
| 7 |
6,892 |
['We know that at least one of two things is true: wood is a renewable resource that has a very positive impact on the carbon footprint, or either postgraduate study is also vital to society as a source of knowledge and expertise or people tend to be selfish and self-centered.', 'We know that either most modern motors have a tight bearing housing that stores a generous volume of lubricant or if wood is a renewable resource that has a very positive impact on the carbon footprint, then transportation is a large contributor to greenhouse gas emissions.', 'Either one or both of these statements are true: spiders do best under conditions of high humidity and moderate temperatures, or if either postgraduate study is also vital to society as a source of knowledge and expertise or people tend to be selfish and self-centered, then transportation is a large contributor to greenhouse gas emissions.', 'Those that suggest spiders do best under conditions of high humidity and moderate temperatures are wrong.', 'Given that recycling saves large amounts of energy, it can be inferred that either brain death is the irreversible and permanent loss of all brain function or the statement that states most modern motors have a tight bearing housing that stores a generous volume of lubricant is false.', 'It is fair to say that recycling saves large amounts of energy.', 'The claim that either compactness is solidity or suffixes permit a wide variety of words to be formed from a single word is false.', "Whenever it is true that religious studies provide appreciation and respect for all human life, 'either either compactness is solidity or suffixes permit a wide variety of words to be formed from a single word or the claim that brain death is the irreversible and permanent loss of all brain function has no merit' is true.", 'It is fair to say that religious studies provide appreciation and respect for all human life.']
|
We know that at least one of two things is true: wood is a renewable resource that has a very positive impact on the carbon footprint, or either postgraduate study is also vital to society as a source of knowledge and expertise or people tend to be selfish and self-centered. We know that either most modern motors have a tight bearing housing that stores a generous volume of lubricant or if wood is a renewable resource that has a very positive impact on the carbon footprint, then transportation is a large contributor to greenhouse gas emissions. Either one or both of these statements are true: spiders do best under conditions of high humidity and moderate temperatures, or if either postgraduate study is also vital to society as a source of knowledge and expertise or people tend to be selfish and self-centered, then transportation is a large contributor to greenhouse gas emissions. Those that suggest spiders do best under conditions of high humidity and moderate temperatures are wrong. Given that recycling saves large amounts of energy, it can be inferred that either brain death is the irreversible and permanent loss of all brain function or the statement that states most modern motors have a tight bearing housing that stores a generous volume of lubricant is false. It is fair to say that recycling saves large amounts of energy. The claim that either compactness is solidity or suffixes permit a wide variety of words to be formed from a single word is false. Whenever it is true that religious studies provide appreciation and respect for all human life, 'either either compactness is solidity or suffixes permit a wide variety of words to be formed from a single word or the claim that brain death is the irreversible and permanent loss of all brain function has no merit' is true. It is fair to say that religious studies provide appreciation and respect for all human life.
|
The statement 'transportation is a large contributor to greenhouse gas emissions' is true.
|
Some people mistakenly believe that transportation is a large contributor to greenhouse gas emissions.
|
FALSE
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].).
If [1], then [0]. [SC2-1]
If (Either [2] or [3].), then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [4] or (If [1], then [0].).
Not [4]. [SC2-2]
Therefore, If [1], then [0]..
[SC2-2]
Disjunctive Syllogism:
Either [6] or (Not [4].). [SC1-3]
Not [6]. [SC2-3]
Therefore, Not [4]..
[SC1-3]
Modus Ponens:
If [9], then (Either [6] or (Not [4].).).
[9]
Therefore, Either [6] or (Not [4].)..
[SC2-3]
Disjunctive Syllogism:
Either (Either [7] or [8].) or (Not [6].). [SC1-4]
Not (Either [7] or [8].).
Therefore, Not [6]..
[SC1-4]
Modus Ponens:
If [10], then (Either (Either [7] or [8].) or (Not [6].).).
[10]
Therefore, Either (Either [7] or [8].) or (Not [6].)..
[SC3-1]
Disjunctive Syllogism:
Either [5] or (If (Either [2] or [3].), then [0].).
Not [5].
Therefore, If (Either [2] or [3].), then [0]..
|
{0: 'Transportation is a large contributor to greenhouse gas emissions.', 1: 'Wood is a renewable resource that has a very positive impact on the carbon footprint.', 2: 'Postgraduate study is also vital to society as a source of knowledge and expertise.', 3: 'People tend to be selfish and self-centered.', 4: 'Most modern motors have a tight bearing housing that stores a generous volume of lubricant.', 5: 'Spiders do best under conditions of high humidity and moderate temperatures.', 6: 'Brain death is the irreversible and permanent loss of all brain function.', 7: 'Compactness is solidity.', 8: 'Suffixes permit a wide variety of words to be formed from a single word.', 9: 'Recycling saves large amounts of energy.', 10: 'Religious studies provide appreciation and respect for all human life.'}
| 7 |
6,225 |
['Those that suggest bees also gather resin from other trees to seal their hives with are wrong.', 'Either chrism is olive oil that has been infused with spice or perfume, making the oil fragrant or sharks inhabit shallow water.', 'When chrism is olive oil that has been infused with spice or perfume, making the oil fragrant is true, it follows that either astronomers identify the presence of elements millions of light years away by their spectra or lamarckian evolution is rapid and accumulative.', 'Provided that sharks inhabit shallow water, we know that either astronomers identify the presence of elements millions of light years away by their spectra or lamarckian evolution is rapid and accumulative.', 'The statement that states fronds arise from the rhizome is false.', "Should it be the case that the statement that 'if lamarckian evolution is rapid and accumulative, then differences have consequences' is incorrect, it follows that the statement that states if rocks can become dilatant just before failure because microcracks increase the volume of the rock, then some families own birds is false.", 'Provided that it is a common misconception that if the claim that if astronomers identify the presence of elements millions of light years away by their spectra, then bees also gather resin from other trees to seal their hives with has no merit, then fronds arise from the rhizome, we know that some historians argue that there was no economic decline in the tenth and eleventh century.', 'The claim that some historians argue that there was no economic decline in the tenth and eleventh century does not reflect reality.', "One may reasonably assume that if either speakers are transducers or most raspberry plants tolerate soil conditions, then if the statement that 'if lamarckian evolution is rapid and accumulative, then differences have consequences' is incorrect, then if rocks can become dilatant just before failure because microcracks increase the volume of the rock, then some families own birds.", 'We know that at least one of two things is true: speakers are transducers, or most raspberry plants tolerate soil conditions.']
|
Those that suggest bees also gather resin from other trees to seal their hives with are wrong. Either chrism is olive oil that has been infused with spice or perfume, making the oil fragrant or sharks inhabit shallow water. When chrism is olive oil that has been infused with spice or perfume, making the oil fragrant is true, it follows that either astronomers identify the presence of elements millions of light years away by their spectra or lamarckian evolution is rapid and accumulative. Provided that sharks inhabit shallow water, we know that either astronomers identify the presence of elements millions of light years away by their spectra or lamarckian evolution is rapid and accumulative. The statement that states fronds arise from the rhizome is false. Should it be the case that the statement that 'if lamarckian evolution is rapid and accumulative, then differences have consequences' is incorrect, it follows that the statement that states if rocks can become dilatant just before failure because microcracks increase the volume of the rock, then some families own birds is false. Provided that it is a common misconception that if the claim that if astronomers identify the presence of elements millions of light years away by their spectra, then bees also gather resin from other trees to seal their hives with has no merit, then fronds arise from the rhizome, we know that some historians argue that there was no economic decline in the tenth and eleventh century. The claim that some historians argue that there was no economic decline in the tenth and eleventh century does not reflect reality. One may reasonably assume that if either speakers are transducers or most raspberry plants tolerate soil conditions, then if the statement that 'if lamarckian evolution is rapid and accumulative, then differences have consequences' is incorrect, then if rocks can become dilatant just before failure because microcracks increase the volume of the rock, then some families own birds. We know that at least one of two things is true: speakers are transducers, or most raspberry plants tolerate soil conditions.
|
The statement that states differences have consequences is right.
|
The statement that states differences have consequences is right.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either [2] or [3]. [SC1-2]
If [2], then [1]. [SC2-2]
If [3], then [0]. [SC3-2]
Therefore, Either [1] or [0]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (Either [2] or [3].).
If [6], then (Either [2] or [3].).
Therefore, Either [2] or [3]..
[SC2-2]
Modus Tonens:
If (Not (If [2], then [1].).), then [4]. [SC1-3]
Not [4].
Therefore, If [2], then [1]..
[SC1-3]
Modus Tonens:
If (Not (If (Not (If [2], then [1].).), then [4].).), then [9].
Not [9].
Therefore, If (Not (If [2], then [1].).), then [4]..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If [3], then [0].).), then (If [7], then [8].). [SC1-3]
If (Not (If [3], then [0].).), then (Not (If [7], then [8].).).
Therefore, If [3], then [0]..
[SC1-3]
Modus Ponens:
If (Either [10] or [11].), then (If (Not (If [3], then [0].).), then (If [7], then [8].).).
Either [10] or [11].
Therefore, If (Not (If [3], then [0].).), then (If [7], then [8].)..
|
{0: 'Differences have consequences.', 1: 'Bees also gather resin from other trees to seal their hives with.', 2: 'Astronomers identify the presence of elements millions of light years away by their spectra.', 3: 'Lamarckian evolution is rapid and accumulative.', 4: 'Fronds arise from the rhizome.', 5: 'Chrism is olive oil that has been infused with spice or perfume, making the oil fragrant.', 6: 'Sharks inhabit shallow water.', 7: 'Rocks can become dilatant just before failure because microcracks increase the volume of the rock.', 8: 'Some families own birds.', 9: 'Some historians argue that there was no economic decline in the tenth and eleventh century.', 10: 'Speakers are transducers.', 11: 'Most raspberry plants tolerate soil conditions.'}
| 7 |
6,820 |
['The claim that plains mostly are more suitable for farming than plateaus or mountains has no merit.', 'We know that at least one of two things is true: families have rules, or either plains mostly are more suitable for farming than plateaus or mountains or it is not true that either continental crust varies in p wave velocities both laterally and vertically or depressive symptoms occur on a spectrum ranging from normal to abnormal.', 'Provided that flounder has (part) sections, we know that schistosomiasis is a slow, debilitating infection caught from fresh water in Africa.', "Whenever it is true that schistosomiasis is a slow, debilitating infection caught from fresh water in Africa, 'body weight increases at different rates during pregnancy' is true.", "Whenever it is true that the statement that states if families have rules, then flounder has (part) sections is false, 'if ships carry ballast water to keep the ship stable when it's empty, then stable flies feed on most species of domestic livestock, but are major pests of cattle and horses' is true.", "Whenever it is true that the statement that states if families have rules, then flounder has (part) sections is false, 'the statement, if ships carry ballast water to keep the ship stable when it's empty, then stable flies feed on most species of domestic livestock, but are major pests of cattle and horses, does not hold' is true.", "We know that at least one of two things is true: techniques improve conditions, or the statement 'body weight increases at different rates during pregnancy' can be considered false.", 'It is not true that techniques improve conditions.']
|
The claim that plains mostly are more suitable for farming than plateaus or mountains has no merit. We know that at least one of two things is true: families have rules, or either plains mostly are more suitable for farming than plateaus or mountains or it is not true that either continental crust varies in p wave velocities both laterally and vertically or depressive symptoms occur on a spectrum ranging from normal to abnormal. Provided that flounder has (part) sections, we know that schistosomiasis is a slow, debilitating infection caught from fresh water in Africa. Whenever it is true that schistosomiasis is a slow, debilitating infection caught from fresh water in Africa, 'body weight increases at different rates during pregnancy' is true. Whenever it is true that the statement that states if families have rules, then flounder has (part) sections is false, 'if ships carry ballast water to keep the ship stable when it's empty, then stable flies feed on most species of domestic livestock, but are major pests of cattle and horses' is true. Whenever it is true that the statement that states if families have rules, then flounder has (part) sections is false, 'the statement, if ships carry ballast water to keep the ship stable when it's empty, then stable flies feed on most species of domestic livestock, but are major pests of cattle and horses, does not hold' is true. We know that at least one of two things is true: techniques improve conditions, or the statement 'body weight increases at different rates during pregnancy' can be considered false. It is not true that techniques improve conditions.
|
It is not true that either continental crust varies in p wave velocities both laterally and vertically or depressive symptoms occur on a spectrum ranging from normal to abnormal.
|
It is rational to believe that either continental crust varies in p wave velocities both laterally and vertically or depressive symptoms occur on a spectrum ranging from normal to abnormal.
|
FALSE
|
Disjunctive Syllogism:
Either [2] or (Not (Either [0] or [1].).). [SC1-1]
Not [2].
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (Either [2] or (Not (Either [0] or [1].).).).
Not [3]. [SC2-2]
Therefore, Either [2] or (Not (Either [0] or [1].).)..
[SC2-2]
Modus Tonens:
If [3], then [4]. [SC1-3]
Not [4]. [SC2-3]
Therefore, Not [3]..
[SC1-3]
Hypothetical Syllogism:
If [3], then [5]. [SC1-4]
If [5], then [4].
Therefore, If [3], then [4]..
[SC1-4]
Reductio Ad Absurdum:
If (Not (If [3], then [5].).), then (If [8], then [9].).
If (Not (If [3], then [5].).), then (Not (If [8], then [9].).).
Therefore, If [3], then [5]..
[SC2-3]
Modus Tonens:
If [4], then [6].
Not [6]. [SC2-4]
Therefore, Not [4]..
[SC2-4]
Disjunctive Syllogism:
Either [7] or (Not [6].).
Not [7].
Therefore, Not [6]..
|
{0: 'Continental crust varies in p wave velocities both laterally and vertically.', 1: 'Depressive symptoms occur on a spectrum ranging from normal to abnormal.', 2: 'Plains mostly are more suitable for farming than plateaus or mountains.', 3: 'Families have rules.', 4: 'Schistosomiasis is a slow, debilitating infection caught from fresh water in Africa.', 5: 'Flounder has (part) sections.', 6: 'Body weight increases at different rates during pregnancy.', 7: 'Techniques improve conditions.', 8: "Ships carry ballast water to keep the ship stable when it's empty.", 9: 'Stable flies feed on most species of domestic livestock, but are major pests of cattle and horses.'}
| 7 |
6,369 |
['If nurses are synonymous with a sense of caring and compassion, then either all foods feed candida, especially sugars and starches or depression is an illness just like diabetes or any other other.', 'Should it be the case that school districts serve students, it follows that if nurses are synonymous with a sense of caring and compassion, then we know that the claim that either all foods feed candida, especially sugars and starches or depression is an illness just like diabetes or any other other is false.', 'Assuming homocysteine concentrations are higher in men than women, we know that if nurses are synonymous with a sense of caring and compassion, then we know that the claim that either all foods feed candida, especially sugars and starches or depression is an illness just like diabetes or any other other is false.', 'When families have children is true, it follows that if those that suggest either school districts serve students or homocysteine concentrations are higher in men than women are wrong, then epigraphy is the study of inscriptions or words and text that often survive on stone.', "So long as either horse racing is a small percentage of Internet gambling or pulverized lime is finely ground, 'if those that suggest either school districts serve students or homocysteine concentrations are higher in men than women are wrong, then epigraphy is the study of inscriptions or words and text that often survive on stone' is true.", 'We know that either women devote more time to children than men do or congenital hypothyroidism is a condition in which the thyroid gland is underactive from birth.', 'One may reasonably assume that if women devote more time to children than men do, then if those that suggest either school districts serve students or homocysteine concentrations are higher in men than women are wrong, then the claim that epigraphy is the study of inscriptions or words and text that often survive on stone does not reflect reality.', 'When congenital hypothyroidism is a condition in which the thyroid gland is underactive from birth is true, it follows that if those that suggest either school districts serve students or homocysteine concentrations are higher in men than women are wrong, then the claim that epigraphy is the study of inscriptions or words and text that often survive on stone does not reflect reality.', "The statement that 'catholic schools are special schools' is incorrect.", "One may reasonably assume that if the notion that 'either catholic schools are special schools or either families have children or either horse racing is a small percentage of Internet gambling or pulverized lime is finely ground' is untrue, then smallmouth bass are members of the sunfish family.", "The statement 'smallmouth bass are members of the sunfish family' can be considered false."]
|
If nurses are synonymous with a sense of caring and compassion, then either all foods feed candida, especially sugars and starches or depression is an illness just like diabetes or any other other. Should it be the case that school districts serve students, it follows that if nurses are synonymous with a sense of caring and compassion, then we know that the claim that either all foods feed candida, especially sugars and starches or depression is an illness just like diabetes or any other other is false. Assuming homocysteine concentrations are higher in men than women, we know that if nurses are synonymous with a sense of caring and compassion, then we know that the claim that either all foods feed candida, especially sugars and starches or depression is an illness just like diabetes or any other other is false. When families have children is true, it follows that if those that suggest either school districts serve students or homocysteine concentrations are higher in men than women are wrong, then epigraphy is the study of inscriptions or words and text that often survive on stone. So long as either horse racing is a small percentage of Internet gambling or pulverized lime is finely ground, 'if those that suggest either school districts serve students or homocysteine concentrations are higher in men than women are wrong, then epigraphy is the study of inscriptions or words and text that often survive on stone' is true. We know that either women devote more time to children than men do or congenital hypothyroidism is a condition in which the thyroid gland is underactive from birth. One may reasonably assume that if women devote more time to children than men do, then if those that suggest either school districts serve students or homocysteine concentrations are higher in men than women are wrong, then the claim that epigraphy is the study of inscriptions or words and text that often survive on stone does not reflect reality. When congenital hypothyroidism is a condition in which the thyroid gland is underactive from birth is true, it follows that if those that suggest either school districts serve students or homocysteine concentrations are higher in men than women are wrong, then the claim that epigraphy is the study of inscriptions or words and text that often survive on stone does not reflect reality. The statement that 'catholic schools are special schools' is incorrect. One may reasonably assume that if the notion that 'either catholic schools are special schools or either families have children or either horse racing is a small percentage of Internet gambling or pulverized lime is finely ground' is untrue, then smallmouth bass are members of the sunfish family. The statement 'smallmouth bass are members of the sunfish family' can be considered false.
|
The statement, nurses are synonymous with a sense of caring and compassion, does not hold.
|
The statement, nurses are synonymous with a sense of caring and compassion, does not hold.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then (Either [1] or [2].).
If [0], then (Not (Either [1] or [2].).). [SC2-1]
Therefore, Not [0]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (If [0], then (Not (Either [1] or [2].).).).
If [4], then (If [0], then (Not (Either [1] or [2].).).).
Therefore, If [0], then (Not (Either [1] or [2].).)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [3] or [4].).), then [5]. [SC1-3]
If (Not (Either [3] or [4].).), then (Not [5].). [SC2-3]
Therefore, Either [3] or [4]..
[SC1-3]
Disjunction Elimination:
Either [8] or (Either [9] or [10].). [SC1-4]
If [8], then (If (Not (Either [3] or [4].).), then [5].).
If (Either [9] or [10].), then (If (Not (Either [3] or [4].).), then [5].).
Therefore, If (Not (Either [3] or [4].).), then [5]..
[SC1-4]
Disjunctive Syllogism:
Either [11] or (Either [8] or (Either [9] or [10].).). [SC1-5]
Not [11].
Therefore, Either [8] or (Either [9] or [10].)..
[SC1-5]
Modus Tonens:
If (Not (Either [11] or (Either [8] or (Either [9] or [10].).).).), then [12].
Not [12].
Therefore, Either [11] or (Either [8] or (Either [9] or [10].).)..
[SC2-3]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If (Not (Either [3] or [4].).), then (Not [5].).).
If [7], then (If (Not (Either [3] or [4].).), then (Not [5].).).
Therefore, If (Not (Either [3] or [4].).), then (Not [5].)..
|
{0: 'Nurses are synonymous with a sense of caring and compassion.', 1: 'All foods feed candida, especially sugars and starches.', 2: 'Depression is an illness just like diabetes or any other other.', 3: 'School districts serve students.', 4: 'Homocysteine concentrations are higher in men than women.', 5: 'Epigraphy is the study of inscriptions or words and text that often survive on stone.', 6: 'Women devote more time to children than men do.', 7: 'Congenital hypothyroidism is a condition in which the thyroid gland is underactive from birth.', 8: 'Families have children.', 9: 'Horse racing is a small percentage of Internet gambling.', 10: 'Pulverized lime is finely ground.', 11: 'Catholic schools are special schools.', 12: 'Smallmouth bass are members of the sunfish family.'}
| 7 |
6,681 |
["The statement that 'spider mites continue to be busy, particularly if plants are located under eaves' is incorrect.", 'We know that either droughts can bring danger to cattle or stress appears to make bighorns susceptible to a variety of bacterial, viral, and fungal infections.', "Whenever it is true that droughts can bring danger to cattle, 'most cellar spiders have eyes' is true.", 'It is the case that wind is assumed to act on a pre-existing wave field.', 'Provided that stress appears to make bighorns susceptible to a variety of bacterial, viral, and fungal infections, we know that vivid colors have high intensity and dull colors have low intensity.', 'When vivid colors have high intensity and dull colors have low intensity is true, it follows that if most electric motors use forces, then spider mites continue to be busy, particularly if plants are located under eaves.', "When yellow drakes continue to appear just at dusk is true, it follows that if wind is assumed to act on a pre-existing wave field, then the statement that 'most cellar spiders have eyes' is incorrect.", "Once we know radiation causes different side effects depending on the area being treated, we also know that if wind is assumed to act on a pre-existing wave field, then the statement that 'most cellar spiders have eyes' is incorrect.", 'Provided that the claim that either yellow drakes continue to appear just at dusk or radiation causes different side effects depending on the area being treated is false, we know that depression is a prevalent mental health problem and it is treatable.', 'On the condition that the claim that either yellow drakes continue to appear just at dusk or radiation causes different side effects depending on the area being treated is false, it is definitely the case that it is a common misconception that depression is a prevalent mental health problem and it is treatable.']
|
The statement that 'spider mites continue to be busy, particularly if plants are located under eaves' is incorrect. We know that either droughts can bring danger to cattle or stress appears to make bighorns susceptible to a variety of bacterial, viral, and fungal infections. Whenever it is true that droughts can bring danger to cattle, 'most cellar spiders have eyes' is true. It is the case that wind is assumed to act on a pre-existing wave field. Provided that stress appears to make bighorns susceptible to a variety of bacterial, viral, and fungal infections, we know that vivid colors have high intensity and dull colors have low intensity. When vivid colors have high intensity and dull colors have low intensity is true, it follows that if most electric motors use forces, then spider mites continue to be busy, particularly if plants are located under eaves. When yellow drakes continue to appear just at dusk is true, it follows that if wind is assumed to act on a pre-existing wave field, then the statement that 'most cellar spiders have eyes' is incorrect. Once we know radiation causes different side effects depending on the area being treated, we also know that if wind is assumed to act on a pre-existing wave field, then the statement that 'most cellar spiders have eyes' is incorrect. Provided that the claim that either yellow drakes continue to appear just at dusk or radiation causes different side effects depending on the area being treated is false, we know that depression is a prevalent mental health problem and it is treatable. On the condition that the claim that either yellow drakes continue to appear just at dusk or radiation causes different side effects depending on the area being treated is false, it is definitely the case that it is a common misconception that depression is a prevalent mental health problem and it is treatable.
|
The statement, most electric motors use forces, does not hold.
|
The statement that states some electric motors are powered by generators is false.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [0], then [1].). [SC1-2]
Not [2]. [SC2-2]
Therefore, If [0], then [1]..
[SC1-2]
Constructive Dilemma:
Either [4] or [5].
If [4], then [2].
If [5], then (If [0], then [1].). [SC3-3]
Therefore, Either [2] or (If [0], then [1].)..
[SC3-3]
Hypothetical Syllogism:
If [5], then [8].
If [8], then (If [0], then [1].).
Therefore, If [5], then (If [0], then [1].)..
[SC2-2]
Modus Ponens:
If [3], then (Not [2].). [SC1-3]
[3]
Therefore, Not [2]..
[SC1-3]
Disjunction Elimination:
Either [6] or [7]. [SC1-4]
If [6], then (If [3], then (Not [2].).).
If [7], then (If [3], then (Not [2].).).
Therefore, If [3], then (Not [2].)..
[SC1-4]
Reductio Ad Absurdum:
If (Not (Either [6] or [7].).), then [9].
If (Not (Either [6] or [7].).), then (Not [9].).
Therefore, Either [6] or [7]..
|
{0: 'Most electric motors use forces.', 1: 'Spider mites continue to be busy, particularly if plants are located under eaves.', 2: 'Most cellar spiders have eyes.', 3: 'Wind is assumed to act on a pre-existing wave field.', 4: 'Droughts can bring danger to cattle.', 5: 'Stress appears to make bighorns susceptible to a variety of bacterial, viral, and fungal infections.', 6: 'Yellow drakes continue to appear just at dusk.', 7: 'Radiation causes different side effects depending on the area being treated.', 8: 'Vivid colors have high intensity and dull colors have low intensity.', 9: 'Depression is a prevalent mental health problem and it is treatable.'}
| 7 |
6,339 |
['The statement that states if natural immunity refers to the protection an animal has when it is born, then assumed planets revolve the sun, but the sun revolves the earth is false.', 'It is rational to believe that either undercoats have (part) guard hair or hellebores are plants.', 'Should it be the case that cartilage is gristle or a firm, elastic, flexible type of connective tissue, it follows that successful churches are large churches.', 'Assuming undercoats have (part) guard hair, we know that if hamsters thrive in cages, then weed control is essential during the earliest stages of development.', 'When if hamsters thrive in cages, then weed control is essential during the earliest stages of development is true, it follows that if we know that the claim that either if natural immunity refers to the protection an animal has when it is born, then assumed planets revolve the sun, but the sun revolves the earth or human beings communicate using a mixture of verbal and non-verbal communication is false, then macro viruses are technically a variation of program viruses.', "So long as the claim that if hellebores are plants, then if we know that the claim that either if natural immunity refers to the protection an animal has when it is born, then assumed planets revolve the sun, but the sun revolves the earth or human beings communicate using a mixture of verbal and non-verbal communication is false, then macro viruses are technically a variation of program viruses does not reflect reality, 'medium colors are ones that bring average price of for extra large' is true.", 'The claim that medium colors are ones that bring average price of for extra large has no merit.', 'There is good reason to believe that either most bushbucks emit bark or if if cartilage is gristle or a firm, elastic, flexible type of connective tissue, then successful churches are large churches, then some people mistakenly believe that macro viruses are technically a variation of program viruses.', 'Those that suggest most bushbucks emit bark are wrong.']
|
The statement that states if natural immunity refers to the protection an animal has when it is born, then assumed planets revolve the sun, but the sun revolves the earth is false. It is rational to believe that either undercoats have (part) guard hair or hellebores are plants. Should it be the case that cartilage is gristle or a firm, elastic, flexible type of connective tissue, it follows that successful churches are large churches. Assuming undercoats have (part) guard hair, we know that if hamsters thrive in cages, then weed control is essential during the earliest stages of development. When if hamsters thrive in cages, then weed control is essential during the earliest stages of development is true, it follows that if we know that the claim that either if natural immunity refers to the protection an animal has when it is born, then assumed planets revolve the sun, but the sun revolves the earth or human beings communicate using a mixture of verbal and non-verbal communication is false, then macro viruses are technically a variation of program viruses. So long as the claim that if hellebores are plants, then if we know that the claim that either if natural immunity refers to the protection an animal has when it is born, then assumed planets revolve the sun, but the sun revolves the earth or human beings communicate using a mixture of verbal and non-verbal communication is false, then macro viruses are technically a variation of program viruses does not reflect reality, 'medium colors are ones that bring average price of for extra large' is true. The claim that medium colors are ones that bring average price of for extra large has no merit. There is good reason to believe that either most bushbucks emit bark or if if cartilage is gristle or a firm, elastic, flexible type of connective tissue, then successful churches are large churches, then some people mistakenly believe that macro viruses are technically a variation of program viruses. Those that suggest most bushbucks emit bark are wrong.
|
It is the case that human beings communicate using a mixture of verbal and non-verbal communication.
|
Human beings celebrate all sorts of occasions.
|
Uncertain
|
Disjunctive Syllogism:
Either (If [1], then [2].) or [0]. [SC1-1]
Not (If [1], then [2].).
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either (If [1], then [2].) or [0].).), then [3]. [SC1-2]
Not [3]. [SC2-2]
Therefore, Either (If [1], then [2].) or [0]..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not (Either (If [1], then [2].) or [0].).), then [3].). [SC2-3]
If [5], then (If (Not (Either (If [1], then [2].) or [0].).), then [3].). [SC3-3]
Therefore, If (Not (Either (If [1], then [2].) or [0].).), then [3]..
[SC2-3]
Hypothetical Syllogism:
If [4], then (If [10], then [11].).
If (If [10], then [11].), then (If (Not (Either (If [1], then [2].) or [0].).), then [3].).
Therefore, If [4], then (If (Not (Either (If [1], then [2].) or [0].).), then [3].)..
[SC3-3]
Modus Tonens:
If (Not (If [5], then (If (Not (Either (If [1], then [2].) or [0].).), then [3].).).), then [9].
Not [9].
Therefore, If [5], then (If (Not (Either (If [1], then [2].) or [0].).), then [3].)..
[SC2-2]
Modus Ponens:
If (If [6], then [7].), then (Not [3].). [SC1-3]
If [6], then [7].
Therefore, Not [3]..
[SC1-3]
Disjunctive Syllogism:
Either [8] or (If (If [6], then [7].), then (Not [3].).).
Not [8].
Therefore, If (If [6], then [7].), then (Not [3].)..
|
{0: 'Human beings communicate using a mixture of verbal and non-verbal communication.', 1: 'Natural immunity refers to the protection an animal has when it is born.', 2: 'Assumed planets revolve the sun, but the sun revolves the earth.', 3: 'Macro viruses are technically a variation of program viruses.', 4: 'Undercoats have (part) guard hair.', 5: 'Hellebores are plants.', 6: 'Cartilage is gristle or a firm, elastic, flexible type of connective tissue.', 7: 'Successful churches are large churches.', 8: 'Most bushbucks emit bark.', 9: 'Medium colors are ones that bring average price of for extra large.', 10: 'Hamsters thrive in cages.', 11: 'Weed control is essential during the earliest stages of development.'}
| 7 |
6,419 |
['We know that at least one of two things is true: either serendipity still plays a role in what people read or different words can mean different things in different languages, or if fiber optics is of major importance in communications and related fields, then weirs have (part) bases.', 'Some people mistakenly believe that either serendipity still plays a role in what people read or different words can mean different things in different languages.', 'We know that the claim that connectivity refers to the type of access including LANs, Internet access type and speed is false.', 'Given that mothers care for infants, it can be inferred that either connectivity refers to the type of access including LANs, Internet access type and speed or the claim that weirs have (part) bases has no merit.', 'At least one of two things is true: plants fail to flower, or either mothers care for infants or hormones enter bloodstreams.', 'One may reasonably assume that if the statement that states if hormones enter bloodstreams, then either connectivity refers to the type of access including LANs, Internet access type and speed or the claim that weirs have (part) bases has no merit is false, then if arthropods has-part extremities, then hikers pass through alpine areas.', 'The statement, if arthropods has-part extremities, then hikers pass through alpine areas, does not hold.', 'It is rational to believe that either either cinders are a type of pyroclastic material or obstructive atelectasis produces characteristic opacities in the lung or true hibernation affects dormouses.', 'Given that either cinders are a type of pyroclastic material or obstructive atelectasis produces characteristic opacities in the lung, it can be inferred that those that suggest plants fail to flower are wrong.', 'On the condition that true hibernation affects dormouses, it is definitely the case that those that suggest plants fail to flower are wrong.']
|
We know that at least one of two things is true: either serendipity still plays a role in what people read or different words can mean different things in different languages, or if fiber optics is of major importance in communications and related fields, then weirs have (part) bases. Some people mistakenly believe that either serendipity still plays a role in what people read or different words can mean different things in different languages. We know that the claim that connectivity refers to the type of access including LANs, Internet access type and speed is false. Given that mothers care for infants, it can be inferred that either connectivity refers to the type of access including LANs, Internet access type and speed or the claim that weirs have (part) bases has no merit. At least one of two things is true: plants fail to flower, or either mothers care for infants or hormones enter bloodstreams. One may reasonably assume that if the statement that states if hormones enter bloodstreams, then either connectivity refers to the type of access including LANs, Internet access type and speed or the claim that weirs have (part) bases has no merit is false, then if arthropods has-part extremities, then hikers pass through alpine areas. The statement, if arthropods has-part extremities, then hikers pass through alpine areas, does not hold. It is rational to believe that either either cinders are a type of pyroclastic material or obstructive atelectasis produces characteristic opacities in the lung or true hibernation affects dormouses. Given that either cinders are a type of pyroclastic material or obstructive atelectasis produces characteristic opacities in the lung, it can be inferred that those that suggest plants fail to flower are wrong. On the condition that true hibernation affects dormouses, it is definitely the case that those that suggest plants fail to flower are wrong.
|
The statement that 'fiber optics is of major importance in communications and related fields' is incorrect.
|
It is not true that fiber optics take communications to the next level .
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either (Either [2] or [3].) or (If [0], then [1].).
Not (Either [2] or [3].).
Therefore, If [0], then [1]..
[SC2-1]
Disjunctive Syllogism:
Either [4] or (Not [1].). [SC1-2]
Not [4].
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6]. [SC1-3]
If [5], then (Either [4] or (Not [1].).).
If [6], then (Either [4] or (Not [1].).). [SC3-3]
Therefore, Either [4] or (Not [1].)..
[SC1-3]
Disjunctive Syllogism:
Either [7] or (Either [5] or [6].).
Not [7]. [SC2-4]
Therefore, Either [5] or [6]..
[SC2-4]
Disjunction Elimination:
Either (Either [10] or [11].) or [12].
If (Either [10] or [11].), then (Not [7].).
If [12], then (Not [7].).
Therefore, Not [7]..
[SC3-3]
Modus Tonens:
If (Not (If [6], then (Either [4] or (Not [1].).).).), then (If [8], then [9].).
Not (If [8], then [9].).
Therefore, If [6], then (Either [4] or (Not [1].).)..
|
{0: 'Fiber optics is of major importance in communications and related fields.', 1: 'Weirs have (part) bases.', 2: 'Serendipity still plays a role in what people read.', 3: 'Different words can mean different things in different languages.', 4: 'Connectivity refers to the type of access including LANs, Internet access type and speed.', 5: 'Mothers care for infants.', 6: 'Hormones enter bloodstreams.', 7: 'Plants fail to flower.', 8: 'Arthropods has-part extremities.', 9: 'Hikers pass through alpine areas.', 10: 'Cinders are a type of pyroclastic material.', 11: 'Obstructive atelectasis produces characteristic opacities in the lung.', 12: 'True hibernation affects dormouses.'}
| 7 |
6,829 |
['Either conscious breathing leads to realizing the link between breathing patterns and mental activity or if the claim that colloidal particles are larger than molecules does not reflect reality, then most meerkats live in burrows.', 'Given that a thyroiditis is a symptom, it can be inferred that if the claim that colloidal particles are larger than molecules does not reflect reality, then we know that the claim that most meerkats live in burrows is false.', 'Provided that sexual harassment can occur in a variety of circumstances, we know that the claim that conscious breathing leads to realizing the link between breathing patterns and mental activity is false.', 'The claim that sexual harassment can occur in a variety of circumstances is true.', 'Should it be the case that it is not the case that either a thyroiditis is a symptom or potassium is found in highest amounts in fresh, unprocessed food, it follows that hands can be in several different positions depending on abdominal strength.', 'Given that it is not the case that either a thyroiditis is a symptom or potassium is found in highest amounts in fresh, unprocessed food, it can be inferred that some people mistakenly believe that hands can be in several different positions depending on abdominal strength.', 'We know that the claim that charter schools are mostly about teaching, learning and educational results is false.', "Should it be the case that those that suggest if the statement that 'if potassium is found in highest amounts in fresh, unprocessed food, then if the claim that colloidal particles are larger than molecules does not reflect reality, then we know that the claim that most meerkats live in burrows is false' is incorrect, then charter schools are mostly about teaching, learning and educational results are wrong, it follows that corrections is a complex field that defies simple analysis.", "If those that suggest if the statement that 'if potassium is found in highest amounts in fresh, unprocessed food, then if the claim that colloidal particles are larger than molecules does not reflect reality, then we know that the claim that most meerkats live in burrows is false' is incorrect, then charter schools are mostly about teaching, learning and educational results are wrong, then the statement 'corrections is a complex field that defies simple analysis' can be considered false."]
|
Either conscious breathing leads to realizing the link between breathing patterns and mental activity or if the claim that colloidal particles are larger than molecules does not reflect reality, then most meerkats live in burrows. Given that a thyroiditis is a symptom, it can be inferred that if the claim that colloidal particles are larger than molecules does not reflect reality, then we know that the claim that most meerkats live in burrows is false. Provided that sexual harassment can occur in a variety of circumstances, we know that the claim that conscious breathing leads to realizing the link between breathing patterns and mental activity is false. The claim that sexual harassment can occur in a variety of circumstances is true. Should it be the case that it is not the case that either a thyroiditis is a symptom or potassium is found in highest amounts in fresh, unprocessed food, it follows that hands can be in several different positions depending on abdominal strength. Given that it is not the case that either a thyroiditis is a symptom or potassium is found in highest amounts in fresh, unprocessed food, it can be inferred that some people mistakenly believe that hands can be in several different positions depending on abdominal strength. We know that the claim that charter schools are mostly about teaching, learning and educational results is false. Should it be the case that those that suggest if the statement that 'if potassium is found in highest amounts in fresh, unprocessed food, then if the claim that colloidal particles are larger than molecules does not reflect reality, then we know that the claim that most meerkats live in burrows is false' is incorrect, then charter schools are mostly about teaching, learning and educational results are wrong, it follows that corrections is a complex field that defies simple analysis. If those that suggest if the statement that 'if potassium is found in highest amounts in fresh, unprocessed food, then if the claim that colloidal particles are larger than molecules does not reflect reality, then we know that the claim that most meerkats live in burrows is false' is incorrect, then charter schools are mostly about teaching, learning and educational results are wrong, then the statement 'corrections is a complex field that defies simple analysis' can be considered false.
|
Many people rightly believe that colloidal particles are larger than molecules.
|
Many people rightly believe that colloidal particles are larger than molecules.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then [1].).
Not [2]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Modus Ponens:
If [7], then (Not [2].).
[7]
Therefore, Not [2]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (If (Not [0].), then (Not [1].).).
If [4], then (If (Not [0].), then (Not [1].).). [SC3-2]
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [3] or [4].).), then [6].
If (Not (Either [3] or [4].).), then (Not [6].).
Therefore, Either [3] or [4]..
[SC3-2]
Modus Tonens:
If (Not (If [4], then (If (Not [0].), then (Not [1].).).).), then [5]. [SC1-3]
Not [5].
Therefore, If [4], then (If (Not [0].), then (Not [1].).)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If (Not (If [4], then (If (Not [0].), then (Not [1].).).).), then [5].).), then [8].
If (Not (If (Not (If [4], then (If (Not [0].), then (Not [1].).).).), then [5].).), then (Not [8].).
Therefore, If (Not (If [4], then (If (Not [0].), then (Not [1].).).).), then [5]..
|
{0: 'Colloidal particles are larger than molecules.', 1: 'Most meerkats live in burrows.', 2: 'Conscious breathing leads to realizing the link between breathing patterns and mental activity.', 3: 'A thyroiditis is a symptom.', 4: 'Potassium is found in highest amounts in fresh, unprocessed food.', 5: 'Charter schools are mostly about teaching, learning and educational results.', 6: 'Hands can be in several different positions depending on abdominal strength.', 7: 'Sexual harassment can occur in a variety of circumstances.', 8: 'Corrections is a complex field that defies simple analysis.'}
| 7 |
6,951 |
['We know that either beer is the product of the fermentation of sugar into alcohol by yeast or faith healers are frauds as are fortune tellers and tele-evangelists.', 'Assuming beer is the product of the fermentation of sugar into alcohol by yeast, we know that if recrudescence is when symptoms return after a symptom-free period, then if cancer is an increasingly prevalent disease, then most skunks have toes.', 'Once we know faith healers are frauds as are fortune tellers and tele-evangelists, we also know that if recrudescence is when symptoms return after a symptom-free period, then if cancer is an increasingly prevalent disease, then most skunks have toes.', "So long as the claim that recrudescence is when symptoms return after a symptom-free period is false, 'men enjoy beers' is true.", 'If the claim that recrudescence is when symptoms return after a symptom-free period is false, then the claim that men enjoy beers has no merit.', "Whenever it is true that it is not true that if either mercury attaches to sulfur or modified mastectomy is the removal of the breast and part of the muscles, then if cancer is an increasingly prevalent disease, then the notion that 'most skunks have toes' is untrue, 'behaviorists are persons who study the behavior of others' is true.", "Given that it is not true that if either mercury attaches to sulfur or modified mastectomy is the removal of the breast and part of the muscles, then if cancer is an increasingly prevalent disease, then the notion that 'most skunks have toes' is untrue, it can be inferred that the statement that 'behaviorists are persons who study the behavior of others' is incorrect.", 'When some people mistakenly believe that either mercury attaches to sulfur or modified mastectomy is the removal of the breast and part of the muscles is true, it follows that factors require investigations.', "Whenever it is true that some people mistakenly believe that either mercury attaches to sulfur or modified mastectomy is the removal of the breast and part of the muscles, 'those that suggest factors require investigations are wrong' is true."]
|
We know that either beer is the product of the fermentation of sugar into alcohol by yeast or faith healers are frauds as are fortune tellers and tele-evangelists. Assuming beer is the product of the fermentation of sugar into alcohol by yeast, we know that if recrudescence is when symptoms return after a symptom-free period, then if cancer is an increasingly prevalent disease, then most skunks have toes. Once we know faith healers are frauds as are fortune tellers and tele-evangelists, we also know that if recrudescence is when symptoms return after a symptom-free period, then if cancer is an increasingly prevalent disease, then most skunks have toes. So long as the claim that recrudescence is when symptoms return after a symptom-free period is false, 'men enjoy beers' is true. If the claim that recrudescence is when symptoms return after a symptom-free period is false, then the claim that men enjoy beers has no merit. Whenever it is true that it is not true that if either mercury attaches to sulfur or modified mastectomy is the removal of the breast and part of the muscles, then if cancer is an increasingly prevalent disease, then the notion that 'most skunks have toes' is untrue, 'behaviorists are persons who study the behavior of others' is true. Given that it is not true that if either mercury attaches to sulfur or modified mastectomy is the removal of the breast and part of the muscles, then if cancer is an increasingly prevalent disease, then the notion that 'most skunks have toes' is untrue, it can be inferred that the statement that 'behaviorists are persons who study the behavior of others' is incorrect. When some people mistakenly believe that either mercury attaches to sulfur or modified mastectomy is the removal of the breast and part of the muscles is true, it follows that factors require investigations. Whenever it is true that some people mistakenly believe that either mercury attaches to sulfur or modified mastectomy is the removal of the breast and part of the muscles, 'those that suggest factors require investigations are wrong' is true.
|
Some people mistakenly believe that cancer is an increasingly prevalent disease.
|
Some people mistakenly believe that cancer is an increasingly prevalent disease.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [4], then (If [0], then [1].). [SC1-2]
[4] [SC2-2]
Therefore, If [0], then [1]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [4], then (If [0], then [1].).).
If [6], then (If [4], then (If [0], then [1].).).
Therefore, If [4], then (If [0], then [1].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not [4].), then [9].
If (Not [4].), then (Not [9].).
Therefore, [4].
[SC2-1]
Modus Ponens:
If (Either [2] or [3].), then (If [0], then (Not [1].).). [SC1-2]
Either [2] or [3]. [SC2-2]
Therefore, If [0], then (Not [1].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Either [2] or [3].), then (If [0], then (Not [1].).).).), then [8].
If (Not (If (Either [2] or [3].), then (If [0], then (Not [1].).).).), then (Not [8].).
Therefore, If (Either [2] or [3].), then (If [0], then (Not [1].).)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (Either [2] or [3].).), then [7].
If (Not (Either [2] or [3].).), then (Not [7].).
Therefore, Either [2] or [3]..
|
{0: 'Cancer is an increasingly prevalent disease.', 1: 'Most skunks have toes.', 2: 'Mercury attaches to sulfur.', 3: 'Modified mastectomy is the removal of the breast and part of the muscles.', 4: 'Recrudescence is when symptoms return after a symptom-free period.', 5: 'Beer is the product of the fermentation of sugar into alcohol by yeast.', 6: 'Faith healers are frauds as are fortune tellers and tele-evangelists.', 7: 'Factors require investigations.', 8: 'Behaviorists are persons who study the behavior of others.', 9: 'Men enjoy beers.'}
| 7 |
6,454 |
["Whenever it is true that fish diversity is low, dominated by Arctic marine species, particularly Arctic cod, 'scanners are a great way to capture photos and even artwork quickly and easily' is true.", "Whenever it is true that most heaters contain sensors, 'either fish diversity is low, dominated by Arctic marine species, particularly Arctic cod or most penguins have behavior' is true.", 'Provided that syphilis causes damage, we know that either fish diversity is low, dominated by Arctic marine species, particularly Arctic cod or most penguins have behavior.', 'At least one of two things is true: expositors are intellectuals, or if most penguins have behavior, then scanners are a great way to capture photos and even artwork quickly and easily.', "The notion that 'expositors are intellectuals' is untrue.", 'Either if rebates are really a form of government spending, then most quartz gems are inexpensive especially the colorless, rose, and other pale colors or jobs are work.', "Whenever it is true that if rebates are really a form of government spending, then most quartz gems are inexpensive especially the colorless, rose, and other pale colors, 'some fish float in rivers' is true.", 'If some fish float in rivers, then most heaters contain sensors.', 'It is a fact that either music is a facilitator for bringing physical responses or if jobs are work, then syphilis causes damage.', 'On the condition that music is a facilitator for bringing physical responses, it is definitely the case that some flatworms use diffusion.', 'Those that suggest some flatworms use diffusion are wrong.']
|
Whenever it is true that fish diversity is low, dominated by Arctic marine species, particularly Arctic cod, 'scanners are a great way to capture photos and even artwork quickly and easily' is true. Whenever it is true that most heaters contain sensors, 'either fish diversity is low, dominated by Arctic marine species, particularly Arctic cod or most penguins have behavior' is true. Provided that syphilis causes damage, we know that either fish diversity is low, dominated by Arctic marine species, particularly Arctic cod or most penguins have behavior. At least one of two things is true: expositors are intellectuals, or if most penguins have behavior, then scanners are a great way to capture photos and even artwork quickly and easily. The notion that 'expositors are intellectuals' is untrue. Either if rebates are really a form of government spending, then most quartz gems are inexpensive especially the colorless, rose, and other pale colors or jobs are work. Whenever it is true that if rebates are really a form of government spending, then most quartz gems are inexpensive especially the colorless, rose, and other pale colors, 'some fish float in rivers' is true. If some fish float in rivers, then most heaters contain sensors. It is a fact that either music is a facilitator for bringing physical responses or if jobs are work, then syphilis causes damage. On the condition that music is a facilitator for bringing physical responses, it is definitely the case that some flatworms use diffusion. Those that suggest some flatworms use diffusion are wrong.
|
It is the case that scanners are a great way to capture photos and even artwork quickly and easily.
|
The claim that scanners are a great way to capture photos and even artwork quickly and easily does not correspond with reality.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (Either [1] or [2].).
If [4], then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC1-2]
Constructive Dilemma:
Either (If [6], then [7].) or [8].
If (If [6], then [7].), then [3]. [SC2-3]
If [8], then [4]. [SC3-3]
Therefore, Either [3] or [4]..
[SC2-3]
Hypothetical Syllogism:
If (If [6], then [7].), then [9].
If [9], then [3].
Therefore, If (If [6], then [7].), then [3]..
[SC3-3]
Disjunctive Syllogism:
Either [10] or (If [8], then [4].).
Not [10]. [SC2-4]
Therefore, If [8], then [4]..
[SC2-4]
Modus Tonens:
If [10], then [11].
Not [11].
Therefore, Not [10]..
[SC3-1]
Disjunctive Syllogism:
Either [5] or (If [2], then [0].).
Not [5].
Therefore, If [2], then [0]..
|
{0: 'Scanners are a great way to capture photos and even artwork quickly and easily.', 1: 'Fish diversity is low, dominated by Arctic marine species, particularly Arctic cod.', 2: 'Most penguins have behavior.', 3: 'Most heaters contain sensors.', 4: 'Syphilis causes damage.', 5: 'Expositors are intellectuals.', 6: 'Rebates are really a form of government spending.', 7: 'Most quartz gems are inexpensive especially the colorless, rose, and other pale colors.', 8: 'Jobs are work.', 9: 'Some fish float in rivers.', 10: 'Music is a facilitator for bringing physical responses.', 11: 'Some flatworms use diffusion.'}
| 7 |
6,063 |
['At least one of two things is true: if most animals have poor vision, then dogs has-part mouths, or excitement is a joy.', 'Assuming excitement is a joy, we know that petroleum technicians need technology.', "Either paella is one of Spain's most well known rice dishes or spiny dogfish are benthopelagic, meaning that they are found just above the bottom of the ocean.", "Given that spiny dogfish are benthopelagic, meaning that they are found just above the bottom of the ocean, it can be inferred that if the notion that 'if if most animals have poor vision, then dogs has-part mouths, then petroleum technicians need technology' is untrue, then vision is imagination.", "Either one or both of these statements are true: hunger is no stranger to the needy people in many parts of the world, or if the notion that 'if if most animals have poor vision, then dogs has-part mouths, then petroleum technicians need technology' is untrue, then it is not the case that vision is imagination.", 'It is not the case that hunger is no stranger to the needy people in many parts of the world.', "Once we know the notion that 'if paella is one of Spain's most well known rice dishes, then either arteries leave leave ventricles or neutered pets tend to be more calmer and content' is untrue, we also know that balanced fertility promotes early development of corn.", 'It is a common misconception that balanced fertility promotes early development of corn.', 'On the condition that either arteries leave leave ventricles or neutered pets tend to be more calmer and content, it is definitely the case that alcoholism is a major social and medical problem in the United States and in most of the world.', "On the condition that alcoholism is a major social and medical problem in the United States and in most of the world, it is definitely the case that if the notion that 'if if most animals have poor vision, then dogs has-part mouths, then petroleum technicians need technology' is untrue, then vision is imagination."]
|
At least one of two things is true: if most animals have poor vision, then dogs has-part mouths, or excitement is a joy. Assuming excitement is a joy, we know that petroleum technicians need technology. Either paella is one of Spain's most well known rice dishes or spiny dogfish are benthopelagic, meaning that they are found just above the bottom of the ocean. Given that spiny dogfish are benthopelagic, meaning that they are found just above the bottom of the ocean, it can be inferred that if the notion that 'if if most animals have poor vision, then dogs has-part mouths, then petroleum technicians need technology' is untrue, then vision is imagination. Either one or both of these statements are true: hunger is no stranger to the needy people in many parts of the world, or if the notion that 'if if most animals have poor vision, then dogs has-part mouths, then petroleum technicians need technology' is untrue, then it is not the case that vision is imagination. It is not the case that hunger is no stranger to the needy people in many parts of the world. Once we know the notion that 'if paella is one of Spain's most well known rice dishes, then either arteries leave leave ventricles or neutered pets tend to be more calmer and content' is untrue, we also know that balanced fertility promotes early development of corn. It is a common misconception that balanced fertility promotes early development of corn. On the condition that either arteries leave leave ventricles or neutered pets tend to be more calmer and content, it is definitely the case that alcoholism is a major social and medical problem in the United States and in most of the world. On the condition that alcoholism is a major social and medical problem in the United States and in most of the world, it is definitely the case that if the notion that 'if if most animals have poor vision, then dogs has-part mouths, then petroleum technicians need technology' is untrue, then vision is imagination.
|
petroleum technicians need technology.
|
Petroleum technicians need technology.
|
TRUE
|
Disjunction Elimination:
Either (If [1], then [2].) or [3].
If (If [1], then [2].), then [0]. [SC2-1]
If [3], then [0].
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (If [1], then [2].), then [0].).), then [4]. [SC1-2]
If (Not (If (If [1], then [2].), then [0].).), then (Not [4].). [SC2-2]
Therefore, If (If [1], then [2].), then [0]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Not (If (If [1], then [2].), then [0].).), then [4].). [SC2-3]
If [6], then (If (Not (If (If [1], then [2].), then [0].).), then [4].).
Therefore, If (Not (If (If [1], then [2].), then [0].).), then [4]..
[SC2-3]
Hypothetical Syllogism:
If [5], then (Either [8] or [9].). [SC1-4]
If (Either [8] or [9].), then (If (Not (If (If [1], then [2].), then [0].).), then [4].). [SC2-4]
Therefore, If [5], then (If (Not (If (If [1], then [2].), then [0].).), then [4].)..
[SC1-4]
Modus Tonens:
If (Not (If [5], then (Either [8] or [9].).).), then [11].
Not [11].
Therefore, If [5], then (Either [8] or [9].)..
[SC2-4]
Hypothetical Syllogism:
If (Either [8] or [9].), then [10].
If [10], then (If (Not (If (If [1], then [2].), then [0].).), then [4].).
Therefore, If (Either [8] or [9].), then (If (Not (If (If [1], then [2].), then [0].).), then [4].)..
[SC2-2]
Disjunctive Syllogism:
Either [7] or (If (Not (If (If [1], then [2].), then [0].).), then (Not [4].).).
Not [7].
Therefore, If (Not (If (If [1], then [2].), then [0].).), then (Not [4].)..
|
{0: 'Petroleum technicians need technology.', 1: 'Most animals have poor vision.', 2: 'Dogs has-part mouths.', 3: 'Excitement is a joy.', 4: 'Vision is imagination.', 5: "Paella is one of Spain's most well known rice dishes.", 6: 'Spiny dogfish are benthopelagic, meaning that they are found just above the bottom of the ocean.', 7: 'Hunger is no stranger to the needy people in many parts of the world.', 8: 'Arteries leave leave ventricles.', 9: 'Neutered pets tend to be more calmer and content.', 10: 'Alcoholism is a major social and medical problem in the United States and in most of the world.', 11: 'Balanced fertility promotes early development of corn.'}
| 7 |
6,759 |
['One may reasonably assume that if many major religions place a significance upon doves, then mucus collects in breathing tubes, but the person has difficulty coughing much out.', 'The statement, mucus collects in breathing tubes, but the person has difficulty coughing much out, does not hold.', 'Given that most syndromes have symptoms, it can be inferred that either many major religions place a significance upon doves or it is not true that if food products contain color, then deer prefer grassland.', 'The claim that bacteria multiply by simple fission or division does not reflect reality.', 'At least one of two things is true: software developer helps designs, or if plants attract goldfinches, then most mountain rivers serve as suitable habitats.', "Whenever it is true that software developer helps designs, 'if globalisation is a new historical era, then most syndromes have symptoms' is true.", 'Should it be the case that if plants attract goldfinches, then most mountain rivers serve as suitable habitats, it follows that if globalisation is a new historical era, then most syndromes have symptoms.', "So long as those that suggest globalisation is a new historical era are wrong, 'toys are located in boxs' is true.", 'On the condition that toys are located in boxs, it is definitely the case that bacteria multiply by simple fission or division.']
|
One may reasonably assume that if many major religions place a significance upon doves, then mucus collects in breathing tubes, but the person has difficulty coughing much out. The statement, mucus collects in breathing tubes, but the person has difficulty coughing much out, does not hold. Given that most syndromes have symptoms, it can be inferred that either many major religions place a significance upon doves or it is not true that if food products contain color, then deer prefer grassland. The claim that bacteria multiply by simple fission or division does not reflect reality. At least one of two things is true: software developer helps designs, or if plants attract goldfinches, then most mountain rivers serve as suitable habitats. Whenever it is true that software developer helps designs, 'if globalisation is a new historical era, then most syndromes have symptoms' is true. Should it be the case that if plants attract goldfinches, then most mountain rivers serve as suitable habitats, it follows that if globalisation is a new historical era, then most syndromes have symptoms. So long as those that suggest globalisation is a new historical era are wrong, 'toys are located in boxs' is true. On the condition that toys are located in boxs, it is definitely the case that bacteria multiply by simple fission or division.
|
It is not true that if food products contain color, then deer prefer grassland.
|
Once we know food products contain color, we also know that deer prefer grassland.
|
FALSE
|
Disjunctive Syllogism:
Either [2] or (Not (If [0], then [1].).). [SC1-1]
Not [2]. [SC2-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Modus Ponens:
If [4], then (Either [2] or (Not (If [0], then [1].).).). [SC1-2]
[4] [SC2-2]
Therefore, Either [2] or (Not (If [0], then [1].).)..
[SC1-2]
Hypothetical Syllogism:
If [4], then [6]. [SC1-3]
If [6], then (Either [2] or (Not (If [0], then [1].).).).
Therefore, If [4], then (Either [2] or (Not (If [0], then [1].).).)..
[SC1-3]
Disjunction Elimination:
Either [8] or (If [9], then [10].).
If [8], then (If [4], then [6].).
If (If [9], then [10].), then (If [4], then [6].).
Therefore, If [4], then [6]..
[SC2-2]
Modus Tonens:
If (Not [4].), then [5]. [SC1-3]
Not [5].
Therefore, [4].
[SC1-3]
Hypothetical Syllogism:
If (Not [4].), then [7].
If [7], then [5].
Therefore, If (Not [4].), then [5]..
[SC2-1]
Modus Tonens:
If [2], then [3].
Not [3].
Therefore, Not [2]..
|
{0: 'Food products contain color.', 1: 'Deer prefer grassland.', 2: 'Many major religions place a significance upon doves.', 3: 'Mucus collects in breathing tubes, but the person has difficulty coughing much out.', 4: 'Globalisation is a new historical era.', 5: 'Bacteria multiply by simple fission or division.', 6: 'Most syndromes have symptoms.', 7: 'Toys are located in boxs.', 8: 'Software developer helps designs.', 9: 'Plants attract goldfinches.', 10: 'Most mountain rivers serve as suitable habitats.'}
| 7 |
6,360 |
['We know that at least one of two things is true: toenails tend to be thicker than fingernails, so the best time for a trim is after a bath or shower, or heartfelt wounds are much like physical wounds.', 'If toenails tend to be thicker than fingernails, so the best time for a trim is after a bath or shower, then raw vegetables are often more appealing than cooked, especially to younger children.', 'If raw vegetables are often more appealing than cooked, especially to younger children, then writing is different than thinking or talking.', 'Given that raw vegetables are often more appealing than cooked, especially to younger children, it can be inferred that it is not true that writing is different than thinking or talking.', 'If fishers have (part) human bodies, then some people mistakenly believe that if a tremolite is asbestos, then a melting point is temperature.', 'If it is not true that either fractals imply nonlinearity in the process which created the fractal process or if heartfelt wounds are much like physical wounds, then fishers have (part) human bodies, then young caterpillars feed on leaves, older ones on flowers.', "Should it be the case that it is not true that either fractals imply nonlinearity in the process which created the fractal process or if heartfelt wounds are much like physical wounds, then fishers have (part) human bodies, it follows that the statement 'young caterpillars feed on leaves, older ones on flowers' can be considered false.", 'Once we know adenoviruses have (part) plasma membranes, we also know that the statement that states fractals imply nonlinearity in the process which created the fractal process is false.', 'It is the case that adenoviruses have (part) plasma membranes.']
|
We know that at least one of two things is true: toenails tend to be thicker than fingernails, so the best time for a trim is after a bath or shower, or heartfelt wounds are much like physical wounds. If toenails tend to be thicker than fingernails, so the best time for a trim is after a bath or shower, then raw vegetables are often more appealing than cooked, especially to younger children. If raw vegetables are often more appealing than cooked, especially to younger children, then writing is different than thinking or talking. Given that raw vegetables are often more appealing than cooked, especially to younger children, it can be inferred that it is not true that writing is different than thinking or talking. If fishers have (part) human bodies, then some people mistakenly believe that if a tremolite is asbestos, then a melting point is temperature. If it is not true that either fractals imply nonlinearity in the process which created the fractal process or if heartfelt wounds are much like physical wounds, then fishers have (part) human bodies, then young caterpillars feed on leaves, older ones on flowers. Should it be the case that it is not true that either fractals imply nonlinearity in the process which created the fractal process or if heartfelt wounds are much like physical wounds, then fishers have (part) human bodies, it follows that the statement 'young caterpillars feed on leaves, older ones on flowers' can be considered false. Once we know adenoviruses have (part) plasma membranes, we also know that the statement that states fractals imply nonlinearity in the process which created the fractal process is false. It is the case that adenoviruses have (part) plasma membranes.
|
Some people mistakenly believe that if a tremolite is asbestos, then a melting point is temperature.
|
The notion that 'tremolites are asbestos' is untrue.
|
Uncertain
|
Disjunctive Syllogism:
Either [2] or (Not (If [0], then [1].).). [SC1-1]
Not [2]. [SC2-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Constructive Dilemma:
Either [3] or [4].
If [3], then [2].
If [4], then (Not (If [0], then [1].).). [SC3-2]
Therefore, Either [2] or (Not (If [0], then [1].).)..
[SC3-2]
Hypothetical Syllogism:
If [4], then [6]. [SC1-3]
If [6], then (Not (If [0], then [1].).).
Therefore, If [4], then (Not (If [0], then [1].).)..
[SC1-3]
Disjunctive Syllogism:
Either [7] or (If [4], then [6].). [SC1-4]
Not [7]. [SC2-4]
Therefore, If [4], then [6]..
[SC1-4]
Reductio Ad Absurdum:
If (Not (Either [7] or (If [4], then [6].).).), then [8].
If (Not (Either [7] or (If [4], then [6].).).), then (Not [8].).
Therefore, Either [7] or (If [4], then [6].)..
[SC2-4]
Modus Ponens:
If [9], then (Not [7].).
[9]
Therefore, Not [7]..
[SC2-1]
Reductio Ad Absurdum:
If [2], then [5].
If [2], then (Not [5].).
Therefore, Not [2]..
|
{0: 'A tremolite is asbestos.', 1: 'A melting point is temperature.', 2: 'Raw vegetables are often more appealing than cooked, especially to younger children.', 3: 'Toenails tend to be thicker than fingernails, so the best time for a trim is after a bath or shower.', 4: 'Heartfelt wounds are much like physical wounds.', 5: 'Writing is different than thinking or talking.', 6: 'Fishers have (part) human bodies.', 7: 'Fractals imply nonlinearity in the process which created the fractal process.', 8: 'Young caterpillars feed on leaves, older ones on flowers.', 9: 'Adenoviruses have (part) plasma membranes.'}
| 7 |
6,237 |
['Either one or both of these statements are true: wild fish migrate freely, or either polytypic values possess polykinded types or internal recycling is common in the metals industry.', 'Assuming wild fish migrate freely, we know that either little guys need moms or shamanism has many fetishistic elements.', 'If either polytypic values possess polykinded types or internal recycling is common in the metals industry, then either little guys need moms or shamanism has many fetishistic elements.', "Once we know the notion that 'if shamanism has many fetishistic elements, then salinity decreases eastward toward Israel because of runoff' is untrue, we also know that rosemaries grow as shrubs.", 'Assuming the claim that if little guys need moms, then salinity decreases eastward toward Israel because of runoff is false, we know that macadamias are nut trees.', 'On the condition that macadamias are nut trees, it is definitely the case that either bread knives are usually about eight inches long or cholesterol is a fatty substance that forms deposits in the blood vessel.', "So long as nuclear transfer is the basic technique used in cloning, 'the claim that either bread knives are usually about eight inches long or cholesterol is a fatty substance that forms deposits in the blood vessel has no merit' is true.", 'It is a simple truth that nuclear transfer is the basic technique used in cloning.', "Given that the statement, if the notion that 'if shamanism has many fetishistic elements, then salinity decreases eastward toward Israel because of runoff' is untrue, then it is not true that rosemaries grow as shrubs, does not hold, it can be inferred that variation depends on interaction.", 'We know that the claim that variation depends on interaction is false.']
|
Either one or both of these statements are true: wild fish migrate freely, or either polytypic values possess polykinded types or internal recycling is common in the metals industry. Assuming wild fish migrate freely, we know that either little guys need moms or shamanism has many fetishistic elements. If either polytypic values possess polykinded types or internal recycling is common in the metals industry, then either little guys need moms or shamanism has many fetishistic elements. Once we know the notion that 'if shamanism has many fetishistic elements, then salinity decreases eastward toward Israel because of runoff' is untrue, we also know that rosemaries grow as shrubs. Assuming the claim that if little guys need moms, then salinity decreases eastward toward Israel because of runoff is false, we know that macadamias are nut trees. On the condition that macadamias are nut trees, it is definitely the case that either bread knives are usually about eight inches long or cholesterol is a fatty substance that forms deposits in the blood vessel. So long as nuclear transfer is the basic technique used in cloning, 'the claim that either bread knives are usually about eight inches long or cholesterol is a fatty substance that forms deposits in the blood vessel has no merit' is true. It is a simple truth that nuclear transfer is the basic technique used in cloning. Given that the statement, if the notion that 'if shamanism has many fetishistic elements, then salinity decreases eastward toward Israel because of runoff' is untrue, then it is not true that rosemaries grow as shrubs, does not hold, it can be inferred that variation depends on interaction. We know that the claim that variation depends on interaction is false.
|
The statement 'salinity decreases eastward toward Israel because of runoff' can be considered true.
|
The statement 'salinity decreases eastward toward Israel because of runoff' can be considered true.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or (Either [4] or [5].).
If [3], then (Either [1] or [2].).
If (Either [4] or [5].), then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC2-1]
Modus Tonens:
If (Not (If [1], then [0].).), then (Either [6] or [7].). [SC1-2]
Not (Either [6] or [7].). [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Hypothetical Syllogism:
If (Not (If [1], then [0].).), then [10].
If [10], then (Either [6] or [7].).
Therefore, If (Not (If [1], then [0].).), then (Either [6] or [7].)..
[SC2-2]
Modus Ponens:
If [11], then (Not (Either [6] or [7].).).
[11]
Therefore, Not (Either [6] or [7].)..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then [0].).), then [8].
If (Not (If [2], then [0].).), then (Not [8].). [SC2-2]
Therefore, If [2], then [0]..
[SC2-2]
Modus Tonens:
If (Not (If (Not (If [2], then [0].).), then (Not [8].).).), then [9].
Not [9].
Therefore, If (Not (If [2], then [0].).), then (Not [8].)..
|
{0: 'Salinity decreases eastward toward Israel because of runoff.', 1: 'Little guys need moms.', 2: 'Shamanism has many fetishistic elements.', 3: 'Wild fish migrate freely.', 4: 'Polytypic values possess polykinded types .', 5: 'Internal recycling is common in the metals industry.', 6: 'Bread knives are usually about eight inches long.', 7: 'Cholesterol is a fatty substance that forms deposits in the blood vessel.', 8: 'Rosemaries grow as shrubs.', 9: 'Variation depends on interaction.', 10: 'Macadamias are nut trees.', 11: 'Nuclear transfer is the basic technique used in cloning.'}
| 7 |
6,112 |
['There is good reason to believe that either artifical corundum is manufactured from bauxite on a large scale or mortality is high in untreated infants and only a few survive to an older age.', "So long as artifical corundum is manufactured from bauxite on a large scale, 'most predators steer clear of skunks, but overly curious dogs tend to be the worst offenders' is true.", 'We know that the claim that if some retinas have ability, then hypertexts take on meaning and structure from the programs they are created in is false.', 'It is rational to believe that either protease is a general term for any enzyme that can cut up proteins or a surge protector is an electrical device.', 'Given that a surge protector is an electrical device, it can be inferred that if the claim that if mortality is high in untreated infants and only a few survive to an older age, then most predators steer clear of skunks, but overly curious dogs tend to be the worst offenders does not correspond with reality, then if some retinas have ability, then hypertexts take on meaning and structure from the programs they are created in.', 'Some people mistakenly believe that if several systems exist in the body to detoxify chemicals, notably the liver enzyme systems, then allelic recombinations contribute to variations in phenotypes of offspring.', 'Either claustrophobia is defined as a fear of enclosed spaces or if a directional microphone is a microphone, then some plants have air.', 'The statement, claustrophobia is defined as a fear of enclosed spaces, does not hold.', 'We know that at least one of two things is true: children begin to make selections of products such as toys and food at a very early age, or if some people mistakenly believe that if if a directional microphone is a microphone, then some plants have air, then if protease is a general term for any enzyme that can cut up proteins, then if the claim that if mortality is high in untreated infants and only a few survive to an older age, then most predators steer clear of skunks, but overly curious dogs tend to be the worst offenders does not correspond with reality, then if some retinas have ability, then hypertexts take on meaning and structure from the programs they are created in, then if several systems exist in the body to detoxify chemicals, notably the liver enzyme systems, then allelic recombinations contribute to variations in phenotypes of offspring.', "The statement 'children begin to make selections of products such as toys and food at a very early age' can be considered false."]
|
There is good reason to believe that either artifical corundum is manufactured from bauxite on a large scale or mortality is high in untreated infants and only a few survive to an older age. So long as artifical corundum is manufactured from bauxite on a large scale, 'most predators steer clear of skunks, but overly curious dogs tend to be the worst offenders' is true. We know that the claim that if some retinas have ability, then hypertexts take on meaning and structure from the programs they are created in is false. It is rational to believe that either protease is a general term for any enzyme that can cut up proteins or a surge protector is an electrical device. Given that a surge protector is an electrical device, it can be inferred that if the claim that if mortality is high in untreated infants and only a few survive to an older age, then most predators steer clear of skunks, but overly curious dogs tend to be the worst offenders does not correspond with reality, then if some retinas have ability, then hypertexts take on meaning and structure from the programs they are created in. Some people mistakenly believe that if several systems exist in the body to detoxify chemicals, notably the liver enzyme systems, then allelic recombinations contribute to variations in phenotypes of offspring. Either claustrophobia is defined as a fear of enclosed spaces or if a directional microphone is a microphone, then some plants have air. The statement, claustrophobia is defined as a fear of enclosed spaces, does not hold. We know that at least one of two things is true: children begin to make selections of products such as toys and food at a very early age, or if some people mistakenly believe that if if a directional microphone is a microphone, then some plants have air, then if protease is a general term for any enzyme that can cut up proteins, then if the claim that if mortality is high in untreated infants and only a few survive to an older age, then most predators steer clear of skunks, but overly curious dogs tend to be the worst offenders does not correspond with reality, then if some retinas have ability, then hypertexts take on meaning and structure from the programs they are created in, then if several systems exist in the body to detoxify chemicals, notably the liver enzyme systems, then allelic recombinations contribute to variations in phenotypes of offspring. The statement 'children begin to make selections of products such as toys and food at a very early age' can be considered false.
|
The statement 'most predators steer clear of skunks, but overly curious dogs tend to be the worst offenders' is true.
|
The statement 'most predators steer clear of skunks, but overly curious dogs tend to be the worst offenders' is true.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC3-1]
Modus Tonens:
If (Not (If [2], then [0].).), then (If [3], then [4].). [SC1-2]
Not (If [3], then [4].).
Therefore, If [2], then [0]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Not (If [2], then [0].).), then (If [3], then [4].).). [SC2-3]
If [6], then (If (Not (If [2], then [0].).), then (If [3], then [4].).).
Therefore, If (Not (If [2], then [0].).), then (If [3], then [4].)..
[SC2-3]
Modus Ponens:
If (If [7], then [8].), then (If [5], then (If (Not (If [2], then [0].).), then (If [3], then [4].).).). [SC1-4]
If [7], then [8]. [SC2-4]
Therefore, If [5], then (If (Not (If [2], then [0].).), then (If [3], then [4].).)..
[SC1-4]
Modus Tonens:
If (Not (If (If [7], then [8].), then (If [5], then (If (Not (If [2], then [0].).), then (If [3], then [4].).).).).), then (If [10], then [11].). [SC1-5]
Not (If [10], then [11].).
Therefore, If (If [7], then [8].), then (If [5], then (If (Not (If [2], then [0].).), then (If [3], then [4].).).)..
[SC1-5]
Disjunctive Syllogism:
Either [12] or (If (Not (If (If [7], then [8].), then (If [5], then (If (Not (If [2], then [0].).), then (If [3], then [4].).).).).), then (If [10], then [11].).).
Not [12].
Therefore, If (Not (If (If [7], then [8].), then (If [5], then (If (Not (If [2], then [0].).), then (If [3], then [4].).).).).), then (If [10], then [11].)..
[SC2-4]
Disjunctive Syllogism:
Either [9] or (If [7], then [8].).
Not [9].
Therefore, If [7], then [8]..
|
{0: 'Most predators steer clear of skunks, but overly curious dogs tend to be the worst offenders.', 1: 'Artifical corundum is manufactured from bauxite on a large scale.', 2: 'Mortality is high in untreated infants and only a few survive to an older age.', 3: 'Some retinas have ability.', 4: 'Hypertexts take on meaning and structure from the programs they are created in.', 5: 'Protease is a general term for any enzyme that can cut up proteins.', 6: 'A surge protector is an electrical device.', 7: 'A directional microphone is a microphone.', 8: 'Some plants have air.', 9: 'Claustrophobia is defined as a fear of enclosed spaces.', 10: 'Several systems exist in the body to detoxify chemicals, notably the liver enzyme systems.', 11: 'Allelic recombinations contribute to variations in phenotypes of offspring.', 12: 'Children begin to make selections of products such as toys and food at a very early age.'}
| 7 |
6,640 |
['It is not the case that incontinence is a symptom that can be caused by a wide variety of conditions.', 'The claim that if some demons have a nanorian for a heart, then wind energy is the kinetic energy of the air in motion does not reflect reality.', 'Either one or both of these statements are true: millennium is a small software house supplying system solutions primarily to the travel industry, or if spiders rely on vision, then incontinence is a symptom that can be caused by a wide variety of conditions.', "Assuming the statement that 'if ants perceive their world primarily through their antennae, then bactrian camels live in the Mongolian deserts, where it gets very cold in the winter' is incorrect, we know that diseases flourish in an acidic environment.", 'It is not the case that diseases flourish in an acidic environment.', 'It is a fact that either most thick mucuses are produced by pedal glands or sugar causes tooth decay.', "On the condition that most thick mucuses are produced by pedal glands, it is definitely the case that if the statement that 'either spiders rely on vision or ants perceive their world primarily through their antennae' is incorrect, then if some demons have a nanorian for a heart, then wind energy is the kinetic energy of the air in motion.", "Once we know sugar causes tooth decay, we also know that if the statement that 'either spiders rely on vision or ants perceive their world primarily through their antennae' is incorrect, then if some demons have a nanorian for a heart, then wind energy is the kinetic energy of the air in motion.", "If neem fruits are bitter, purgative, antihemorrhodial and anthelmintic in nature, then the statement 'millennium is a small software house supplying system solutions primarily to the travel industry' can be considered false.", 'Many people rightly believe that neem fruits are bitter, purgative, antihemorrhodial and anthelmintic in nature.']
|
It is not the case that incontinence is a symptom that can be caused by a wide variety of conditions. The claim that if some demons have a nanorian for a heart, then wind energy is the kinetic energy of the air in motion does not reflect reality. Either one or both of these statements are true: millennium is a small software house supplying system solutions primarily to the travel industry, or if spiders rely on vision, then incontinence is a symptom that can be caused by a wide variety of conditions. Assuming the statement that 'if ants perceive their world primarily through their antennae, then bactrian camels live in the Mongolian deserts, where it gets very cold in the winter' is incorrect, we know that diseases flourish in an acidic environment. It is not the case that diseases flourish in an acidic environment. It is a fact that either most thick mucuses are produced by pedal glands or sugar causes tooth decay. On the condition that most thick mucuses are produced by pedal glands, it is definitely the case that if the statement that 'either spiders rely on vision or ants perceive their world primarily through their antennae' is incorrect, then if some demons have a nanorian for a heart, then wind energy is the kinetic energy of the air in motion. Once we know sugar causes tooth decay, we also know that if the statement that 'either spiders rely on vision or ants perceive their world primarily through their antennae' is incorrect, then if some demons have a nanorian for a heart, then wind energy is the kinetic energy of the air in motion. If neem fruits are bitter, purgative, antihemorrhodial and anthelmintic in nature, then the statement 'millennium is a small software house supplying system solutions primarily to the travel industry' can be considered false. Many people rightly believe that neem fruits are bitter, purgative, antihemorrhodial and anthelmintic in nature.
|
Those that suggest bactrian camels live in the Mongolian deserts, where it gets very cold in the winter are right.
|
Bactrian camels are handsome guys With long thick brows around their eyes.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either [2] or [3]. [SC1-2]
If [2], then [1]. [SC2-2]
If [3], then [0]. [SC3-2]
Therefore, Either [1] or [0]..
[SC1-2]
Modus Tonens:
If (Not (Either [2] or [3].).), then (If [5], then [6].). [SC1-3]
Not (If [5], then [6].).
Therefore, Either [2] or [3]..
[SC1-3]
Disjunction Elimination:
Either [9] or [10].
If [9], then (If (Not (Either [2] or [3].).), then (If [5], then [6].).).
If [10], then (If (Not (Either [2] or [3].).), then (If [5], then [6].).).
Therefore, If (Not (Either [2] or [3].).), then (If [5], then [6].)..
[SC2-2]
Disjunctive Syllogism:
Either [7] or (If [2], then [1].).
Not [7]. [SC2-3]
Therefore, If [2], then [1]..
[SC2-3]
Modus Ponens:
If [8], then (Not [7].).
[8]
Therefore, Not [7]..
[SC3-2]
Modus Tonens:
If (Not (If [3], then [0].).), then [4].
Not [4].
Therefore, If [3], then [0]..
|
{0: 'Bactrian camels live in the Mongolian deserts, where it gets very cold in the winter.', 1: 'Incontinence is a symptom that can be caused by a wide variety of conditions.', 2: 'Spiders rely on vision.', 3: 'Ants perceive their world primarily through their antennae.', 4: 'Diseases flourish in an acidic environment.', 5: 'Some demons have a nanorian for a heart.', 6: 'Wind energy is the kinetic energy of the air in motion.', 7: 'Millennium is a small software house supplying system solutions primarily to the travel industry.', 8: 'Neem fruits are bitter, purgative, antihemorrhodial and anthelmintic in nature.', 9: 'Most thick mucuses are produced by pedal glands.', 10: 'Sugar causes tooth decay.'}
| 7 |
6,532 |
['There is good reason to believe that either toddlers tend to like bedtime reading sessions when they are already relaxed or adders have (part) chests.', 'When toddlers tend to like bedtime reading sessions when they are already relaxed is true, it follows that either swans have (part) vacuoles or either simple machines are used in everyday life or food security requires an available and reliable food supply at all times.', 'We know that either all life is beginnings and endings, birth, death, and rebirth or hepatitis b diets improve liver health.', 'Provided that all life is beginnings and endings, birth, death, and rebirth, we know that if swans have (part) vacuoles, then development is a technical term that many places use to talk about fundraising.', 'If hepatitis b diets improve liver health, then if swans have (part) vacuoles, then development is a technical term that many places use to talk about fundraising.', "Whenever it is true that some people mistakenly believe that if either simple machines are used in everyday life or food security requires an available and reliable food supply at all times, then development is a technical term that many places use to talk about fundraising, 'the claim that acquired hydrocephalus can develop at any age as a result of head trauma or illness has no merit' is true.", "Whenever it is true that the claim that if adders have (part) chests, then either swans have (part) vacuoles or either simple machines are used in everyday life or food security requires an available and reliable food supply at all times does not reflect reality, 'mercury freezes at a higher temperature than alcohol does' is true.", 'The claim that mercury freezes at a higher temperature than alcohol does has no merit.', 'Either one or both of these statements are true: either a palomino is a horse or birds are bipedal, but no one suggests that they are closely related to humans, or gentlemen wear hats.', 'On the condition that either a palomino is a horse or birds are bipedal, but no one suggests that they are closely related to humans, it is definitely the case that if some people mistakenly believe that if either simple machines are used in everyday life or food security requires an available and reliable food supply at all times, then development is a technical term that many places use to talk about fundraising, then acquired hydrocephalus can develop at any age as a result of head trauma or illness.', 'It is a fact that either gAG denotes potential sites for the addition of glycosamino glycan side chains or if gentlemen wear hats, then if some people mistakenly believe that if either simple machines are used in everyday life or food security requires an available and reliable food supply at all times, then development is a technical term that many places use to talk about fundraising, then acquired hydrocephalus can develop at any age as a result of head trauma or illness.', 'The claim that gAG denotes potential sites for the addition of glycosamino glycan side chains has no merit.']
|
There is good reason to believe that either toddlers tend to like bedtime reading sessions when they are already relaxed or adders have (part) chests. When toddlers tend to like bedtime reading sessions when they are already relaxed is true, it follows that either swans have (part) vacuoles or either simple machines are used in everyday life or food security requires an available and reliable food supply at all times. We know that either all life is beginnings and endings, birth, death, and rebirth or hepatitis b diets improve liver health. Provided that all life is beginnings and endings, birth, death, and rebirth, we know that if swans have (part) vacuoles, then development is a technical term that many places use to talk about fundraising. If hepatitis b diets improve liver health, then if swans have (part) vacuoles, then development is a technical term that many places use to talk about fundraising. Whenever it is true that some people mistakenly believe that if either simple machines are used in everyday life or food security requires an available and reliable food supply at all times, then development is a technical term that many places use to talk about fundraising, 'the claim that acquired hydrocephalus can develop at any age as a result of head trauma or illness has no merit' is true. Whenever it is true that the claim that if adders have (part) chests, then either swans have (part) vacuoles or either simple machines are used in everyday life or food security requires an available and reliable food supply at all times does not reflect reality, 'mercury freezes at a higher temperature than alcohol does' is true. The claim that mercury freezes at a higher temperature than alcohol does has no merit. Either one or both of these statements are true: either a palomino is a horse or birds are bipedal, but no one suggests that they are closely related to humans, or gentlemen wear hats. On the condition that either a palomino is a horse or birds are bipedal, but no one suggests that they are closely related to humans, it is definitely the case that if some people mistakenly believe that if either simple machines are used in everyday life or food security requires an available and reliable food supply at all times, then development is a technical term that many places use to talk about fundraising, then acquired hydrocephalus can develop at any age as a result of head trauma or illness. It is a fact that either gAG denotes potential sites for the addition of glycosamino glycan side chains or if gentlemen wear hats, then if some people mistakenly believe that if either simple machines are used in everyday life or food security requires an available and reliable food supply at all times, then development is a technical term that many places use to talk about fundraising, then acquired hydrocephalus can develop at any age as a result of head trauma or illness. The claim that gAG denotes potential sites for the addition of glycosamino glycan side chains has no merit.
|
The statement 'development is a technical term that many places use to talk about fundraising' is true.
|
Development is central to policy directed towards climate change.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].). [SC1-1]
If [1], then [0]. [SC2-1]
If (Either [2] or [3].), then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [7] or [8].
If [7], then (Either [1] or (Either [2] or [3].).).
If [8], then (Either [1] or (Either [2] or [3].).). [SC3-2]
Therefore, Either [1] or (Either [2] or [3].)..
[SC3-2]
Modus Tonens:
If (Not (If [8], then (Either [1] or (Either [2] or [3].).).).), then [12].
Not [12].
Therefore, If [8], then (Either [1] or (Either [2] or [3].).)..
[SC2-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [1], then [0].).
If [5], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If (Either [2] or [3].), then [0].).), then [6]. [SC1-2]
If (Not (If (Either [2] or [3].), then [0].).), then (Not [6].).
Therefore, If (Either [2] or [3].), then [0]..
[SC1-2]
Disjunction Elimination:
Either (Either [9] or [10].) or [11].
If (Either [9] or [10].), then (If (Not (If (Either [2] or [3].), then [0].).), then [6].).
If [11], then (If (Not (If (Either [2] or [3].), then [0].).), then [6].). [SC3-3]
Therefore, If (Not (If (Either [2] or [3].), then [0].).), then [6]..
[SC3-3]
Disjunctive Syllogism:
Either [13] or (If [11], then (If (Not (If (Either [2] or [3].), then [0].).), then [6].).).
Not [13].
Therefore, If [11], then (If (Not (If (Either [2] or [3].), then [0].).), then [6].)..
|
{0: 'Development is a technical term that many places use to talk about fundraising.', 1: 'Swans have (part) vacuoles.', 2: 'Simple machines are used in everyday life.', 3: 'Food security requires an available and reliable food supply at all times.', 4: 'All life is beginnings and endings, birth, death, and rebirth.', 5: 'Hepatitis b diets improve liver health.', 6: 'Acquired hydrocephalus can develop at any age as a result of head trauma or illness.', 7: 'Toddlers tend to like bedtime reading sessions when they are already relaxed.', 8: 'Adders have (part) chests.', 9: 'A palomino is a horse.', 10: 'Birds are bipedal, but no one suggests that they are closely related to humans.', 11: 'Gentlemen wear hats.', 12: 'Mercury freezes at a higher temperature than alcohol does.', 13: 'GAG denotes potential sites for the addition of glycosamino glycan side chains.'}
| 7 |
6,126 |
['On the condition that either spreadsheet programs allow the user to enter columns and rows of data or some tea contains chemicals, it is definitely the case that if we know that the claim that chemotherapy is most often the cause of young cancer patients losing their hair is false, then soft bank is one of the major high-tech companies in the world.', 'When if granulomatous inflammation is uncommon in sporotrichosis, then all soils contain certain amounts of clay particles is true, it follows that either spreadsheet programs allow the user to enter columns and rows of data or some tea contains chemicals.', 'Should it be the case that granulomatous inflammation is uncommon in sporotrichosis, it follows that all soils contain certain amounts of clay particles.', 'Given that radiation can also result from a nuclear detonation, it can be inferred that if mynahs have (part) ears, then the claim that soft bank is one of the major high-tech companies in the world does not reflect reality.', 'One may reasonably assume that if humans have minds, then if mynahs have (part) ears, then the claim that soft bank is one of the major high-tech companies in the world does not reflect reality.', 'When the claim that mynahs have (part) ears has no merit is true, it follows that lynxes have (part) ears.', "On the condition that the claim that mynahs have (part) ears has no merit, it is definitely the case that the statement that 'lynxes have (part) ears' is incorrect.", 'When supplies are items consumed during the process of providing services is true, it follows that either radiation can also result from a nuclear detonation or humans have minds.', 'The statement that states supplies are items consumed during the process of providing services is right.']
|
On the condition that either spreadsheet programs allow the user to enter columns and rows of data or some tea contains chemicals, it is definitely the case that if we know that the claim that chemotherapy is most often the cause of young cancer patients losing their hair is false, then soft bank is one of the major high-tech companies in the world. When if granulomatous inflammation is uncommon in sporotrichosis, then all soils contain certain amounts of clay particles is true, it follows that either spreadsheet programs allow the user to enter columns and rows of data or some tea contains chemicals. Should it be the case that granulomatous inflammation is uncommon in sporotrichosis, it follows that all soils contain certain amounts of clay particles. Given that radiation can also result from a nuclear detonation, it can be inferred that if mynahs have (part) ears, then the claim that soft bank is one of the major high-tech companies in the world does not reflect reality. One may reasonably assume that if humans have minds, then if mynahs have (part) ears, then the claim that soft bank is one of the major high-tech companies in the world does not reflect reality. When the claim that mynahs have (part) ears has no merit is true, it follows that lynxes have (part) ears. On the condition that the claim that mynahs have (part) ears has no merit, it is definitely the case that the statement that 'lynxes have (part) ears' is incorrect. When supplies are items consumed during the process of providing services is true, it follows that either radiation can also result from a nuclear detonation or humans have minds. The statement that states supplies are items consumed during the process of providing services is right.
|
The idea that chemotherapy is most often the cause of young cancer patients losing their hair is true.
|
The statement that states chemotherapy is most often the cause of young cancer patients losing their hair is false.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If (Either [2] or [3].), then (If (Not [0].), then [1].).
Either [2] or [3]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Modus Ponens:
If (If [5], then [6].), then (Either [2] or [3].).
If [5], then [6].
Therefore, Either [2] or [3]..
[SC2-1]
Modus Ponens:
If [4], then (Not [1].). [SC1-2]
[4] [SC2-2]
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either [8] or [9]. [SC1-3]
If [8], then (If [4], then (Not [1].).).
If [9], then (If [4], then (Not [1].).).
Therefore, If [4], then (Not [1].)..
[SC1-3]
Modus Ponens:
If [10], then (Either [8] or [9].).
[10]
Therefore, Either [8] or [9]..
[SC2-2]
Reductio Ad Absurdum:
If (Not [4].), then [7].
If (Not [4].), then (Not [7].).
Therefore, [4].
|
{0: 'Chemotherapy is most often the cause of young cancer patients losing their hair.', 1: 'Soft bank is one of the major high-tech companies in the world.', 2: 'Spreadsheet programs allow the user to enter columns and rows of data.', 3: 'Some tea contains chemicals.', 4: 'Mynahs have (part) ears.', 5: 'Granulomatous inflammation is uncommon in sporotrichosis.', 6: 'All soils contain certain amounts of clay particles.', 7: 'Lynxes have (part) ears.', 8: 'Radiation can also result from a nuclear detonation.', 9: 'Humans have minds.', 10: 'Supplies are items consumed during the process of providing services.'}
| 7 |
6,259 |
['It is rational to agree that ostriches usually eat plants, but sometimes they eat small reptiles.', 'It is a fact that either cartoonists are writers whose work depends heavily on hand drawn imagery or obesity is also in vogue.', 'Given that cartoonists are writers whose work depends heavily on hand drawn imagery, it can be inferred that if the claim that if ostriches usually eat plants, but sometimes they eat small reptiles, then the claim that if most horses excrete urine, then ferns retain color does not correspond with reality is false, then a lame duck is an official.', 'Either spider mites on conifers and broadleaved evergreens are cool weather pests or false statements are grounds for disqualification or immediate termination of employment.', "Whenever it is true that spider mites on conifers and broadleaved evergreens are cool weather pests, 'if obesity is also in vogue, then if the claim that if ostriches usually eat plants, but sometimes they eat small reptiles, then the claim that if most horses excrete urine, then ferns retain color does not correspond with reality is false, then a lame duck is an official' is true.", 'When false statements are grounds for disqualification or immediate termination of employment is true, it follows that if obesity is also in vogue, then if the claim that if ostriches usually eat plants, but sometimes they eat small reptiles, then the claim that if most horses excrete urine, then ferns retain color does not correspond with reality is false, then a lame duck is an official.', 'There is good reason to believe that either sin is the problem of the world or dengue fever is caused by a virus spread to humans by mosquitoes.', 'Once we know sin is the problem of the world, we also know that if a lame duck is an official, then if a greyhound is a racer, then wind redistributes sand and other particles especially in arid regions.', 'Once we know dengue fever is caused by a virus spread to humans by mosquitoes, we also know that if a lame duck is an official, then if a greyhound is a racer, then wind redistributes sand and other particles especially in arid regions.', 'Given that if a greyhound is a racer, then wind redistributes sand and other particles especially in arid regions, it can be inferred that vitamin E is an essential antioxidant nutrient which is receiving considerable public attention.', 'One may reasonably assume that if if a greyhound is a racer, then wind redistributes sand and other particles especially in arid regions, then the statement, vitamin E is an essential antioxidant nutrient which is receiving considerable public attention, does not hold.']
|
It is rational to agree that ostriches usually eat plants, but sometimes they eat small reptiles. It is a fact that either cartoonists are writers whose work depends heavily on hand drawn imagery or obesity is also in vogue. Given that cartoonists are writers whose work depends heavily on hand drawn imagery, it can be inferred that if the claim that if ostriches usually eat plants, but sometimes they eat small reptiles, then the claim that if most horses excrete urine, then ferns retain color does not correspond with reality is false, then a lame duck is an official. Either spider mites on conifers and broadleaved evergreens are cool weather pests or false statements are grounds for disqualification or immediate termination of employment. Whenever it is true that spider mites on conifers and broadleaved evergreens are cool weather pests, 'if obesity is also in vogue, then if the claim that if ostriches usually eat plants, but sometimes they eat small reptiles, then the claim that if most horses excrete urine, then ferns retain color does not correspond with reality is false, then a lame duck is an official' is true. When false statements are grounds for disqualification or immediate termination of employment is true, it follows that if obesity is also in vogue, then if the claim that if ostriches usually eat plants, but sometimes they eat small reptiles, then the claim that if most horses excrete urine, then ferns retain color does not correspond with reality is false, then a lame duck is an official. There is good reason to believe that either sin is the problem of the world or dengue fever is caused by a virus spread to humans by mosquitoes. Once we know sin is the problem of the world, we also know that if a lame duck is an official, then if a greyhound is a racer, then wind redistributes sand and other particles especially in arid regions. Once we know dengue fever is caused by a virus spread to humans by mosquitoes, we also know that if a lame duck is an official, then if a greyhound is a racer, then wind redistributes sand and other particles especially in arid regions. Given that if a greyhound is a racer, then wind redistributes sand and other particles especially in arid regions, it can be inferred that vitamin E is an essential antioxidant nutrient which is receiving considerable public attention. One may reasonably assume that if if a greyhound is a racer, then wind redistributes sand and other particles especially in arid regions, then the statement, vitamin E is an essential antioxidant nutrient which is receiving considerable public attention, does not hold.
|
The claim that if most horses excrete urine, then ferns retain color does not correspond with reality.
|
The claim that if most horses excrete urine, then ferns retain color does not correspond with reality.
|
TRUE
|
Modus Ponens:
If [2], then (Not (If [0], then [1].).). [SC1-1]
[2]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Modus Tonens:
If (Not (If [2], then (Not (If [0], then [1].).).).), then [3]. [SC1-2]
Not [3]. [SC2-2]
Therefore, If [2], then (Not (If [0], then [1].).)..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not (If [2], then (Not (If [0], then [1].).).).), then [3].).
If [5], then (If (Not (If [2], then (Not (If [0], then [1].).).).), then [3].). [SC3-3]
Therefore, If (Not (If [2], then (Not (If [0], then [1].).).).), then [3]..
[SC3-3]
Disjunction Elimination:
Either [11] or [12].
If [11], then (If [5], then (If (Not (If [2], then (Not (If [0], then [1].).).).), then [3].).).
If [12], then (If [5], then (If (Not (If [2], then (Not (If [0], then [1].).).).), then [3].).).
Therefore, If [5], then (If (Not (If [2], then (Not (If [0], then [1].).).).), then [3].)..
[SC2-2]
Modus Tonens:
If [3], then (If [6], then [7].). [SC1-3]
Not (If [6], then [7].). [SC2-3]
Therefore, Not [3]..
[SC1-3]
Disjunction Elimination:
Either [8] or [9].
If [8], then (If [3], then (If [6], then [7].).).
If [9], then (If [3], then (If [6], then [7].).).
Therefore, If [3], then (If [6], then [7].)..
[SC2-3]
Reductio Ad Absurdum:
If (If [6], then [7].), then [10].
If (If [6], then [7].), then (Not [10].).
Therefore, Not (If [6], then [7].)..
|
{0: 'Most horses excrete urine.', 1: 'Ferns retain color.', 2: 'Ostriches usually eat plants, but sometimes they eat small reptiles.', 3: 'A lame duck is an official.', 4: 'Cartoonists are writers whose work depends heavily on hand drawn imagery.', 5: 'Obesity is also in vogue.', 6: 'A greyhound is a racer.', 7: 'Wind redistributes sand and other particles especially in arid regions.', 8: 'Sin is the problem of the world.', 9: 'Dengue fever is caused by a virus spread to humans by mosquitoes.', 10: 'Vitamin E is an essential antioxidant nutrient which is receiving considerable public attention.', 11: 'Spider mites on conifers and broadleaved evergreens are cool weather pests.', 12: 'False statements are grounds for disqualification or immediate termination of employment.'}
| 7 |
6,742 |
['Provided that the claim that antibiotics are also responsible for creating new and unusual challenges for the immune system does not correspond with reality, we know that most juvenile birds feed diets.', 'There is good reason to believe that either sterling is money or the statement, most juvenile birds feed diets, does not hold.', 'When sterling is money is true, it follows that biodegradable polymers have important medical and other commercial applications.', 'On the condition that sterling is money, it is definitely the case that alcohol addiction is a major health and social problem in the United States.', "Provided that we know that the claim that either febrile seizures make parents and grandparents very anxious or if alcohol addiction is a major health and social problem in the United States, then the notion that 'biodegradable polymers have important medical and other commercial applications' is untrue is false, we know that stress can irritate asthma and gastrointestinal disorders like ulcers and irritable bowel syndrome.", "When we know that the claim that either febrile seizures make parents and grandparents very anxious or if alcohol addiction is a major health and social problem in the United States, then the notion that 'biodegradable polymers have important medical and other commercial applications' is untrue is false is true, it follows that the statement, stress can irritate asthma and gastrointestinal disorders like ulcers and irritable bowel syndrome, does not hold.", 'Either one or both of these statements are true: tongue depressors are woodwork, or most birds eat nectar.', "Assuming tongue depressors are woodwork, we know that the statement 'febrile seizures make parents and grandparents very anxious' can be considered false.", "On the condition that most birds eat nectar, it is definitely the case that the statement 'febrile seizures make parents and grandparents very anxious' can be considered false."]
|
Provided that the claim that antibiotics are also responsible for creating new and unusual challenges for the immune system does not correspond with reality, we know that most juvenile birds feed diets. There is good reason to believe that either sterling is money or the statement, most juvenile birds feed diets, does not hold. When sterling is money is true, it follows that biodegradable polymers have important medical and other commercial applications. On the condition that sterling is money, it is definitely the case that alcohol addiction is a major health and social problem in the United States. Provided that we know that the claim that either febrile seizures make parents and grandparents very anxious or if alcohol addiction is a major health and social problem in the United States, then the notion that 'biodegradable polymers have important medical and other commercial applications' is untrue is false, we know that stress can irritate asthma and gastrointestinal disorders like ulcers and irritable bowel syndrome. When we know that the claim that either febrile seizures make parents and grandparents very anxious or if alcohol addiction is a major health and social problem in the United States, then the notion that 'biodegradable polymers have important medical and other commercial applications' is untrue is false is true, it follows that the statement, stress can irritate asthma and gastrointestinal disorders like ulcers and irritable bowel syndrome, does not hold. Either one or both of these statements are true: tongue depressors are woodwork, or most birds eat nectar. Assuming tongue depressors are woodwork, we know that the statement 'febrile seizures make parents and grandparents very anxious' can be considered false. On the condition that most birds eat nectar, it is definitely the case that the statement 'febrile seizures make parents and grandparents very anxious' can be considered false.
|
We can assume that antibiotics are also responsible for creating new and unusual challenges for the immune system.
|
Antibiotics are a chemically diverse group of static or cidal compounds produced by microorganisms.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].).
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Reductio Ad Absurdum:
If [2], then [3].
If [2], then (Not [3].). [SC2-3]
Therefore, Not [2]..
[SC2-3]
Hypothetical Syllogism:
If [2], then [4].
If [4], then (Not [3].). [SC2-4]
Therefore, If [2], then (Not [3].)..
[SC2-4]
Disjunctive Syllogism:
Either [5] or (If [4], then (Not [3].).). [SC1-5]
Not [5]. [SC2-5]
Therefore, If [4], then (Not [3].)..
[SC1-5]
Reductio Ad Absurdum:
If (Not (Either [5] or (If [4], then (Not [3].).).).), then [8].
If (Not (Either [5] or (If [4], then (Not [3].).).).), then (Not [8].).
Therefore, Either [5] or (If [4], then (Not [3].).)..
[SC2-5]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Not [5].).
If [7], then (Not [5].).
Therefore, Not [5]..
|
{0: 'Antibiotics are also responsible for creating new and unusual challenges for the immune system.', 1: 'Most juvenile birds feed diets.', 2: 'Sterling is money.', 3: 'Biodegradable polymers have important medical and other commercial applications.', 4: 'Alcohol addiction is a major health and social problem in the United States.', 5: 'Febrile seizures make parents and grandparents very anxious.', 6: 'Tongue depressors are woodwork.', 7: 'Most birds eat nectar.', 8: 'Stress can irritate asthma and gastrointestinal disorders like ulcers and irritable bowel syndrome.'}
| 7 |
6,761 |
['Once we know hedgehogs have long spines, or quills, made of keratin, we also know that either web directories are an index to the topics available on the web or if industrial batik is a complex process, then wetlands also act like humungous natural filters.', 'The claim that hedgehogs have long spines, or quills, made of keratin is true.', "So long as web directories are an index to the topics available on the web, 'laboratory tests have an adjunctive role in the evaluation of depressed patients' is true.", 'On the condition that web directories are an index to the topics available on the web, it is definitely the case that the claim that laboratory tests have an adjunctive role in the evaluation of depressed patients does not correspond with reality.', 'Given that mute swans are an agressive invasive species, it can be inferred that if either antelopes have (part) cytoplasm or shallow earthquakes occur along all plate boundaries, then industrial batik is a complex process.', 'The claim that mute swans are an agressive invasive species is true.', 'At least one of two things is true: a trove is treasure, or most snakes have venom.', 'Should it be the case that a trove is treasure, it follows that either antelopes have (part) cytoplasm or shallow earthquakes occur along all plate boundaries.', 'If most snakes have venom, then either antelopes have (part) cytoplasm or shallow earthquakes occur along all plate boundaries.']
|
Once we know hedgehogs have long spines, or quills, made of keratin, we also know that either web directories are an index to the topics available on the web or if industrial batik is a complex process, then wetlands also act like humungous natural filters. The claim that hedgehogs have long spines, or quills, made of keratin is true. So long as web directories are an index to the topics available on the web, 'laboratory tests have an adjunctive role in the evaluation of depressed patients' is true. On the condition that web directories are an index to the topics available on the web, it is definitely the case that the claim that laboratory tests have an adjunctive role in the evaluation of depressed patients does not correspond with reality. Given that mute swans are an agressive invasive species, it can be inferred that if either antelopes have (part) cytoplasm or shallow earthquakes occur along all plate boundaries, then industrial batik is a complex process. The claim that mute swans are an agressive invasive species is true. At least one of two things is true: a trove is treasure, or most snakes have venom. Should it be the case that a trove is treasure, it follows that either antelopes have (part) cytoplasm or shallow earthquakes occur along all plate boundaries. If most snakes have venom, then either antelopes have (part) cytoplasm or shallow earthquakes occur along all plate boundaries.
|
It is rational to agree that wetlands also act like humungous natural filters.
|
It is rational to agree that wetlands also act like humungous natural filters.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [1], then [0].). [SC1-2]
Not [2]. [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Modus Ponens:
If [7], then (Either [2] or (If [1], then [0].).).
[7]
Therefore, Either [2] or (If [1], then [0].)..
[SC2-2]
Reductio Ad Absurdum:
If [2], then [5].
If [2], then (Not [5].).
Therefore, Not [2]..
[SC2-1]
Modus Ponens:
If (Either [3] or [4].), then [1]. [SC1-2]
Either [3] or [4]. [SC2-2]
Therefore, [1].
[SC1-2]
Modus Ponens:
If [6], then (If (Either [3] or [4].), then [1].).
[6]
Therefore, If (Either [3] or [4].), then [1]..
[SC2-2]
Disjunction Elimination:
Either [8] or [9].
If [8], then (Either [3] or [4].).
If [9], then (Either [3] or [4].).
Therefore, Either [3] or [4]..
|
{0: 'Wetlands also act like humungous natural filters.', 1: 'Industrial batik is a complex process.', 2: 'Web directories are an index to the topics available on the web.', 3: 'Antelopes have (part) cytoplasm.', 4: 'Shallow earthquakes occur along all plate boundaries.', 5: 'Laboratory tests have an adjunctive role in the evaluation of depressed patients.', 6: 'Mute swans are an agressive invasive species.', 7: 'Hedgehogs have long spines, or quills, made of keratin.', 8: 'A trove is treasure.', 9: 'Most snakes have venom.'}
| 7 |
6,137 |
['At least one of two things is true: either arthropods have (part) sections or inroads are invasions, or vIEW is a computer workstation for the blind and visually impaired.', 'Given that the claim that if either arthropods have (part) sections or inroads are invasions, then if the claim that video cameras use an electronic shutter does not correspond with reality, then if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology is false, it can be inferred that most conifers have needles.', "Whenever it is true that the claim that if either arthropods have (part) sections or inroads are invasions, then if the claim that video cameras use an electronic shutter does not correspond with reality, then if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology is false, 'the claim that most conifers have needles is false' is true.", 'Should it be the case that the claim that if vIEW is a computer workstation for the blind and visually impaired, then if the claim that video cameras use an electronic shutter does not correspond with reality, then if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology is false, it follows that passive violence can include prejudice, hatred, and economic oppression.', 'Assuming the claim that if vIEW is a computer workstation for the blind and visually impaired, then if the claim that video cameras use an electronic shutter does not correspond with reality, then if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology is false, we know that the claim that passive violence can include prejudice, hatred, and economic oppression does not correspond with reality.', 'Either human personhood starts at conception or some dye causes eye injuries.', 'On the condition that human personhood starts at conception, it is definitely the case that if if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology, then disarmament reduces tension and thereby the threat of war.', 'Should it be the case that some dye causes eye injuries, it follows that if if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology, then disarmament reduces tension and thereby the threat of war.', "Assuming the notion that 'if if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology, then it is a common misconception that disarmament reduces tension and thereby the threat of war' is untrue, we know that most languages have a syntax and semantics.", "When the notion that 'if if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology, then it is a common misconception that disarmament reduces tension and thereby the threat of war' is untrue is true, it follows that the claim that most languages have a syntax and semantics is false."]
|
At least one of two things is true: either arthropods have (part) sections or inroads are invasions, or vIEW is a computer workstation for the blind and visually impaired. Given that the claim that if either arthropods have (part) sections or inroads are invasions, then if the claim that video cameras use an electronic shutter does not correspond with reality, then if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology is false, it can be inferred that most conifers have needles. Whenever it is true that the claim that if either arthropods have (part) sections or inroads are invasions, then if the claim that video cameras use an electronic shutter does not correspond with reality, then if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology is false, 'the claim that most conifers have needles is false' is true. Should it be the case that the claim that if vIEW is a computer workstation for the blind and visually impaired, then if the claim that video cameras use an electronic shutter does not correspond with reality, then if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology is false, it follows that passive violence can include prejudice, hatred, and economic oppression. Assuming the claim that if vIEW is a computer workstation for the blind and visually impaired, then if the claim that video cameras use an electronic shutter does not correspond with reality, then if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology is false, we know that the claim that passive violence can include prejudice, hatred, and economic oppression does not correspond with reality. Either human personhood starts at conception or some dye causes eye injuries. On the condition that human personhood starts at conception, it is definitely the case that if if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology, then disarmament reduces tension and thereby the threat of war. Should it be the case that some dye causes eye injuries, it follows that if if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology, then disarmament reduces tension and thereby the threat of war. Assuming the notion that 'if if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology, then it is a common misconception that disarmament reduces tension and thereby the threat of war' is untrue, we know that most languages have a syntax and semantics. When the notion that 'if if homologous chromosomes are a pair of chromosomes, then a cryobiology is biology, then it is a common misconception that disarmament reduces tension and thereby the threat of war' is untrue is true, it follows that the claim that most languages have a syntax and semantics is false.
|
Many people rightly believe that video cameras use an electronic shutter.
|
Many people rightly believe that video cameras use an electronic shutter.
|
TRUE
|
Modus Tonens:
If (Not [0].), then (If [1], then [2].). [SC1-1]
Not (If [1], then [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [3] or [4].) or [5].
If (Either [3] or [4].), then (If (Not [0].), then (If [1], then [2].).). [SC2-2]
If [5], then (If (Not [0].), then (If [1], then [2].).). [SC3-2]
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Either [3] or [4].), then (If (Not [0].), then (If [1], then [2].).).).), then [8].
If (Not (If (Either [3] or [4].), then (If (Not [0].), then (If [1], then [2].).).).), then (Not [8].).
Therefore, If (Either [3] or [4].), then (If (Not [0].), then (If [1], then [2].).)..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If [5], then (If (Not [0].), then (If [1], then [2].).).).), then [7].
If (Not (If [5], then (If (Not [0].), then (If [1], then [2].).).).), then (Not [7].).
Therefore, If [5], then (If (Not [0].), then (If [1], then [2].).)..
[SC2-1]
Reductio Ad Absurdum:
If (If [1], then [2].), then [6]. [SC1-2]
If (If [1], then [2].), then (Not [6].). [SC2-2]
Therefore, Not (If [1], then [2].)..
[SC1-2]
Disjunction Elimination:
Either [10] or [11].
If [10], then (If (If [1], then [2].), then [6].).
If [11], then (If (If [1], then [2].), then [6].).
Therefore, If (If [1], then [2].), then [6]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (If [1], then [2].), then (Not [6].).).), then [9].
If (Not (If (If [1], then [2].), then (Not [6].).).), then (Not [9].).
Therefore, If (If [1], then [2].), then (Not [6].)..
|
{0: 'Video cameras use an electronic shutter.', 1: 'Homologous chromosomes are a pair of chromosomes.', 2: 'A cryobiology is biology.', 3: 'Arthropods have (part) sections.', 4: 'Inroads are invasions.', 5: 'VIEW is a computer workstation for the blind and visually impaired.', 6: 'Disarmament reduces tension and thereby the threat of war.', 7: 'Passive violence can include prejudice, hatred, and economic oppression.', 8: 'Most conifers have needles.', 9: 'Most languages have a syntax and semantics.', 10: 'Human personhood starts at conception.', 11: 'Some dye causes eye injuries.'}
| 7 |
6,007 |
["Whenever it is true that either waitresses have (part) personality or nerve fibers connect the thymus, spleen, lymph nodes and bone marrow, 'either humans threaten sharks and their migration success in several ways or funguses are located in fields' is true.", "Whenever it is true that perennial weeds can be a major problem in asparagus plantings, 'either humans threaten sharks and their migration success in several ways or funguses are located in fields' is true.", 'We know that at least one of two things is true: millipedes are omnivores, so they eat pretty much anything and everything, or homicide isa action.', 'If millipedes are omnivores, so they eat pretty much anything and everything, then if humans threaten sharks and their migration success in several ways, then bicycles are a great means of transportation, although most people simply walk.', 'Given that homicide isa action, it can be inferred that if humans threaten sharks and their migration success in several ways, then bicycles are a great means of transportation, although most people simply walk.', 'Given that it is not true that if funguses are located in fields, then bicycles are a great means of transportation, although most people simply walk, it can be inferred that if many experts regard pigs as the most intelligent of domesticated animals, then chemical reaction has consequences.', "So long as it is not true that if funguses are located in fields, then bicycles are a great means of transportation, although most people simply walk, 'it is a common misconception that if many experts regard pigs as the most intelligent of domesticated animals, then chemical reaction has consequences' is true.", 'There is good reason to believe that either salt is a commonly occuring mineral, the technical name of which is sodium chloride or vaccinations are injections of medicines the animal receives to keep it from developing diseases.', 'Given that some plants have waxy surfaces to cut down on evaporation, it can be inferred that if salt is a commonly occuring mineral, the technical name of which is sodium chloride, then either waitresses have (part) personality or nerve fibers connect the thymus, spleen, lymph nodes and bone marrow.', 'It is the case that some plants have waxy surfaces to cut down on evaporation.', 'Either one or both of these statements are true: most insects have origins, or members have capability.', 'Given that most insects have origins, it can be inferred that if vaccinations are injections of medicines the animal receives to keep it from developing diseases, then perennial weeds can be a major problem in asparagus plantings.', 'Given that members have capability, it can be inferred that if vaccinations are injections of medicines the animal receives to keep it from developing diseases, then perennial weeds can be a major problem in asparagus plantings.']
|
Whenever it is true that either waitresses have (part) personality or nerve fibers connect the thymus, spleen, lymph nodes and bone marrow, 'either humans threaten sharks and their migration success in several ways or funguses are located in fields' is true. Whenever it is true that perennial weeds can be a major problem in asparagus plantings, 'either humans threaten sharks and their migration success in several ways or funguses are located in fields' is true. We know that at least one of two things is true: millipedes are omnivores, so they eat pretty much anything and everything, or homicide isa action. If millipedes are omnivores, so they eat pretty much anything and everything, then if humans threaten sharks and their migration success in several ways, then bicycles are a great means of transportation, although most people simply walk. Given that homicide isa action, it can be inferred that if humans threaten sharks and their migration success in several ways, then bicycles are a great means of transportation, although most people simply walk. Given that it is not true that if funguses are located in fields, then bicycles are a great means of transportation, although most people simply walk, it can be inferred that if many experts regard pigs as the most intelligent of domesticated animals, then chemical reaction has consequences. So long as it is not true that if funguses are located in fields, then bicycles are a great means of transportation, although most people simply walk, 'it is a common misconception that if many experts regard pigs as the most intelligent of domesticated animals, then chemical reaction has consequences' is true. There is good reason to believe that either salt is a commonly occuring mineral, the technical name of which is sodium chloride or vaccinations are injections of medicines the animal receives to keep it from developing diseases. Given that some plants have waxy surfaces to cut down on evaporation, it can be inferred that if salt is a commonly occuring mineral, the technical name of which is sodium chloride, then either waitresses have (part) personality or nerve fibers connect the thymus, spleen, lymph nodes and bone marrow. It is the case that some plants have waxy surfaces to cut down on evaporation. Either one or both of these statements are true: most insects have origins, or members have capability. Given that most insects have origins, it can be inferred that if vaccinations are injections of medicines the animal receives to keep it from developing diseases, then perennial weeds can be a major problem in asparagus plantings. Given that members have capability, it can be inferred that if vaccinations are injections of medicines the animal receives to keep it from developing diseases, then perennial weeds can be a major problem in asparagus plantings.
|
The idea that bicycles are a great means of transportation, although most people simply walk is true.
|
The statement that 'bicycles are a great means of transportation, although most people simply walk' is incorrect.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [5] or [6].) or [7]. [SC1-2]
If (Either [5] or [6].), then (Either [1] or [2].).
If [7], then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC1-2]
Constructive Dilemma:
Either [10] or [11].
If [10], then (Either [5] or [6].). [SC2-3]
If [11], then [7]. [SC3-3]
Therefore, Either (Either [5] or [6].) or [7]..
[SC2-3]
Modus Ponens:
If [12], then (If [10], then (Either [5] or [6].).).
[12]
Therefore, If [10], then (Either [5] or [6].)..
[SC3-3]
Disjunction Elimination:
Either [13] or [14].
If [13], then (If [11], then [7].).
If [14], then (If [11], then [7].).
Therefore, If [11], then [7]..
[SC2-1]
Disjunction Elimination:
Either [8] or [9].
If [8], then (If [1], then [0].).
If [9], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then [0].).), then (If [3], then [4].).
If (Not (If [2], then [0].).), then (Not (If [3], then [4].).).
Therefore, If [2], then [0]..
|
{0: 'Bicycles are a great means of transportation, although most people simply walk.', 1: 'Humans threaten sharks and their migration success in several ways.', 2: 'Funguses are located in fields.', 3: 'Many experts regard pigs as the most intelligent of domesticated animals.', 4: 'Chemical reaction has consequences.', 5: 'Waitresses have (part) personality.', 6: 'Nerve fibers connect the thymus, spleen, lymph nodes and bone marrow.', 7: 'Perennial weeds can be a major problem in asparagus plantings.', 8: 'Millipedes are omnivores, so they eat pretty much anything and everything.', 9: 'Homicide isa action.', 10: 'Salt is a commonly occuring mineral, the technical name of which is sodium chloride.', 11: 'Vaccinations are injections of medicines the animal receives to keep it from developing diseases.', 12: 'Some plants have waxy surfaces to cut down on evaporation.', 13: 'Most insects have origins.', 14: 'Members have capability.'}
| 7 |
6,502 |
["So long as some people mistakenly believe that if some female spiders are so much bigger than the males that they sometimes eat their mates, then ordinary laziness is a passive failure to love, 'if cacomistles have (part) faces, then french food is made with heavy sauces that are impossible to make' is true.", "The statement that 'buds have the potential to develop into flowers, leaves, roots, or other stems or branches' is incorrect.", "Should it be the case that income is an eligibility factor for services, it follows that if those that suggest if some female spiders are so much bigger than the males that they sometimes eat their mates, then the statement 'ordinary laziness is a passive failure to love' can be considered false are wrong, then smoking is a major risk factor for coronary artery disease.", 'The claim that income is an eligibility factor for services holds true.', "On the condition that it is not true that if those that suggest if some female spiders are so much bigger than the males that they sometimes eat their mates, then the statement 'ordinary laziness is a passive failure to love' can be considered false are wrong, then the statement that 'smoking is a major risk factor for coronary artery disease' is incorrect, it is definitely the case that leatherjackets can sometimes cause damage to plants.", "If it is not true that if those that suggest if some female spiders are so much bigger than the males that they sometimes eat their mates, then the statement 'ordinary laziness is a passive failure to love' can be considered false are wrong, then the statement that 'smoking is a major risk factor for coronary artery disease' is incorrect, then the statement that 'leatherjackets can sometimes cause damage to plants' is incorrect.", 'We know that either media stereotypes tend to depict people with disabilities as victims employed in low- skilled jobs or laughter also functions with a double meaning in Jazz music.', 'Should it be the case that media stereotypes tend to depict people with disabilities as victims employed in low- skilled jobs, it follows that if if cacomistles have (part) faces, then french food is made with heavy sauces that are impossible to make, then buds have the potential to develop into flowers, leaves, roots, or other stems or branches.', 'Provided that laughter also functions with a double meaning in Jazz music, we know that if if cacomistles have (part) faces, then french food is made with heavy sauces that are impossible to make, then buds have the potential to develop into flowers, leaves, roots, or other stems or branches.']
|
So long as some people mistakenly believe that if some female spiders are so much bigger than the males that they sometimes eat their mates, then ordinary laziness is a passive failure to love, 'if cacomistles have (part) faces, then french food is made with heavy sauces that are impossible to make' is true. The statement that 'buds have the potential to develop into flowers, leaves, roots, or other stems or branches' is incorrect. Should it be the case that income is an eligibility factor for services, it follows that if those that suggest if some female spiders are so much bigger than the males that they sometimes eat their mates, then the statement 'ordinary laziness is a passive failure to love' can be considered false are wrong, then smoking is a major risk factor for coronary artery disease. The claim that income is an eligibility factor for services holds true. On the condition that it is not true that if those that suggest if some female spiders are so much bigger than the males that they sometimes eat their mates, then the statement 'ordinary laziness is a passive failure to love' can be considered false are wrong, then the statement that 'smoking is a major risk factor for coronary artery disease' is incorrect, it is definitely the case that leatherjackets can sometimes cause damage to plants. If it is not true that if those that suggest if some female spiders are so much bigger than the males that they sometimes eat their mates, then the statement 'ordinary laziness is a passive failure to love' can be considered false are wrong, then the statement that 'smoking is a major risk factor for coronary artery disease' is incorrect, then the statement that 'leatherjackets can sometimes cause damage to plants' is incorrect. We know that either media stereotypes tend to depict people with disabilities as victims employed in low- skilled jobs or laughter also functions with a double meaning in Jazz music. Should it be the case that media stereotypes tend to depict people with disabilities as victims employed in low- skilled jobs, it follows that if if cacomistles have (part) faces, then french food is made with heavy sauces that are impossible to make, then buds have the potential to develop into flowers, leaves, roots, or other stems or branches. Provided that laughter also functions with a double meaning in Jazz music, we know that if if cacomistles have (part) faces, then french food is made with heavy sauces that are impossible to make, then buds have the potential to develop into flowers, leaves, roots, or other stems or branches.
|
The notion that 'some female spiders are so much bigger than the males that they sometimes eat their mates' is untrue.
|
The statement that states female spiders wrap their eggs in a silken spun sac is false.
|
Uncertain
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (If [0], then [1].).), then (If [3], then [4].).
Not (If [3], then [4].). [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Modus Tonens:
If (If [3], then [4].), then [5]. [SC1-3]
Not [5].
Therefore, Not (If [3], then [4].)..
[SC1-3]
Disjunction Elimination:
Either [8] or [9].
If [8], then (If (If [3], then [4].), then [5].).
If [9], then (If (If [3], then [4].), then [5].).
Therefore, If (If [3], then [4].), then [5]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [0], then (Not [1].).).), then [2]. [SC1-2]
If (Not (If [0], then (Not [1].).).), then (Not [2].). [SC2-2]
Therefore, If [0], then (Not [1].)..
[SC1-2]
Modus Ponens:
If [7], then (If (Not (If [0], then (Not [1].).).), then [2].).
[7]
Therefore, If (Not (If [0], then (Not [1].).).), then [2]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (If [0], then (Not [1].).).), then (Not [2].).).), then [6].
If (Not (If (Not (If [0], then (Not [1].).).), then (Not [2].).).), then (Not [6].).
Therefore, If (Not (If [0], then (Not [1].).).), then (Not [2].)..
|
{0: 'Some female spiders are so much bigger than the males that they sometimes eat their mates.', 1: 'Ordinary laziness is a passive failure to love.', 2: 'Smoking is a major risk factor for coronary artery disease.', 3: 'Cacomistles have (part) faces.', 4: 'French food is made with heavy sauces that are impossible to make.', 5: 'Buds have the potential to develop into flowers, leaves, roots, or other stems or branches.', 6: 'Leatherjackets can sometimes cause damage to plants.', 7: 'Income is an eligibility factor for services.', 8: 'Media stereotypes tend to depict people with disabilities as victims employed in low- skilled jobs.', 9: 'Laughter also functions with a double meaning in Jazz music.'}
| 7 |
6,831 |
['The statement, if gravity comes from matter, so the presence of matter causes distortions or warps in spacetime, then devils prefer open forest to tall forest, and dry rather than wet forests, does not hold.', 'There is good reason to believe that either attackers use pistols or an exordium is an introduction.', 'When an exordium is an introduction is true, it follows that if those that suggest famine becomes a social rather than a physical phenomenon are wrong, then if gravity comes from matter, so the presence of matter causes distortions or warps in spacetime, then devils prefer open forest to tall forest, and dry rather than wet forests.', 'When sheep graze the open, highland pastures during summer and are rounded up each fall is true, it follows that a wire cutter is an edge tool.', 'One may reasonably assume that if a wire cutter is an edge tool, then most cigarette smoke contains carcinogen.', 'Those that suggest most cigarette smoke contains carcinogen are wrong.', "Once we know it is a common misconception that if the notion that 'if attackers use pistols, then if those that suggest famine becomes a social rather than a physical phenomenon are wrong, then if gravity comes from matter, so the presence of matter causes distortions or warps in spacetime, then devils prefer open forest to tall forest, and dry rather than wet forests' is untrue, then sheep graze the open, highland pastures during summer and are rounded up each fall, we also know that elongated snouts account for the name bottlenose.", "When it is a common misconception that if it is a common misconception that if the notion that 'if attackers use pistols, then if those that suggest famine becomes a social rather than a physical phenomenon are wrong, then if gravity comes from matter, so the presence of matter causes distortions or warps in spacetime, then devils prefer open forest to tall forest, and dry rather than wet forests' is untrue, then sheep graze the open, highland pastures during summer and are rounded up each fall, then we know that the claim that elongated snouts account for the name bottlenose is false is true, it follows that gasoline is relatively non-toxic after a single or acute exposure by all routes.", 'Some people mistakenly believe that gasoline is relatively non-toxic after a single or acute exposure by all routes.']
|
The statement, if gravity comes from matter, so the presence of matter causes distortions or warps in spacetime, then devils prefer open forest to tall forest, and dry rather than wet forests, does not hold. There is good reason to believe that either attackers use pistols or an exordium is an introduction. When an exordium is an introduction is true, it follows that if those that suggest famine becomes a social rather than a physical phenomenon are wrong, then if gravity comes from matter, so the presence of matter causes distortions or warps in spacetime, then devils prefer open forest to tall forest, and dry rather than wet forests. When sheep graze the open, highland pastures during summer and are rounded up each fall is true, it follows that a wire cutter is an edge tool. One may reasonably assume that if a wire cutter is an edge tool, then most cigarette smoke contains carcinogen. Those that suggest most cigarette smoke contains carcinogen are wrong. Once we know it is a common misconception that if the notion that 'if attackers use pistols, then if those that suggest famine becomes a social rather than a physical phenomenon are wrong, then if gravity comes from matter, so the presence of matter causes distortions or warps in spacetime, then devils prefer open forest to tall forest, and dry rather than wet forests' is untrue, then sheep graze the open, highland pastures during summer and are rounded up each fall, we also know that elongated snouts account for the name bottlenose. When it is a common misconception that if it is a common misconception that if the notion that 'if attackers use pistols, then if those that suggest famine becomes a social rather than a physical phenomenon are wrong, then if gravity comes from matter, so the presence of matter causes distortions or warps in spacetime, then devils prefer open forest to tall forest, and dry rather than wet forests' is untrue, then sheep graze the open, highland pastures during summer and are rounded up each fall, then we know that the claim that elongated snouts account for the name bottlenose is false is true, it follows that gasoline is relatively non-toxic after a single or acute exposure by all routes. Some people mistakenly believe that gasoline is relatively non-toxic after a single or acute exposure by all routes.
|
Many people rightly believe that famine becomes a social rather than a physical phenomenon.
|
Famines are extreme shortages of food that cause people to die of starvation.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then (If [1], then [2].). [SC1-1]
Not (If [1], then [2].).
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If (Not [0].), then (If [1], then [2].).). [SC2-2]
If [4], then (If (Not [0].), then (If [1], then [2].).).
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC2-2]
Modus Tonens:
If (Not (If [3], then (If (Not [0].), then (If [1], then [2].).).).), then [5]. [SC1-3]
Not [5]. [SC2-3]
Therefore, If [3], then (If (Not [0].), then (If [1], then [2].).)..
[SC1-3]
Hypothetical Syllogism:
If (Not (If [3], then (If (Not [0].), then (If [1], then [2].).).).), then [6]. [SC1-4]
If [6], then [5].
Therefore, If (Not (If [3], then (If (Not [0].), then (If [1], then [2].).).).), then [5]..
[SC1-4]
Reductio Ad Absurdum:
If (Not (If (Not (If [3], then (If (Not [0].), then (If [1], then [2].).).).), then [6].).), then [8].
If (Not (If (Not (If [3], then (If (Not [0].), then (If [1], then [2].).).).), then [6].).), then (Not [8].). [SC2-5]
Therefore, If (Not (If [3], then (If (Not [0].), then (If [1], then [2].).).).), then [6]..
[SC2-5]
Modus Tonens:
If (Not (If (Not (If (Not (If [3], then (If (Not [0].), then (If [1], then [2].).).).), then [6].).), then (Not [8].).).), then [9].
Not [9].
Therefore, If (Not (If (Not (If [3], then (If (Not [0].), then (If [1], then [2].).).).), then [6].).), then (Not [8].)..
[SC2-3]
Modus Tonens:
If [5], then [7].
Not [7].
Therefore, Not [5]..
|
{0: 'Famine becomes a social rather than a physical phenomenon.', 1: 'Gravity comes from matter, so the presence of matter causes distortions or warps in spacetime.', 2: 'Devils prefer open forest to tall forest, and dry rather than wet forests.', 3: 'Attackers use pistols.', 4: 'An exordium is an introduction.', 5: 'A wire cutter is an edge tool.', 6: 'Sheep graze the open, highland pastures during summer and are rounded up each fall.', 7: 'Most cigarette smoke contains carcinogen.', 8: 'Elongated snouts account for the name bottlenose.', 9: 'Gasoline is relatively non-toxic after a single or acute exposure by all routes.'}
| 7 |
6,762 |
["So long as if community service is another form of education that helps make students more complete people, then pubs have (part) floors, 'occasional hurricanes produce major storms and flooding' is true.", 'Provided that either bonds have properties or ministers are used for ceremony, we know that if caimen have (part) cell membranes, then if community service is another form of education that helps make students more complete people, then pubs have (part) floors.', 'Either one or both of these statements are true: bonds have properties, or ministers are used for ceremony.', 'We know that at least one of two things is true: most beetles eat bugs, or walruses have (part) skulls.', "When most beetles eat bugs is true, it follows that either physical change is a key preoccupation for health professions or if possums spend the first four months of their lives in their mother 's pouch , then most species inhabit cold waters.", "Once we know walruses have (part) skulls, we also know that either physical change is a key preoccupation for health professions or if possums spend the first four months of their lives in their mother 's pouch , then most species inhabit cold waters.", 'One may reasonably assume that if talapoins have (part) nuclei, then if physical change is a key preoccupation for health professions, then caimen have (part) cell membranes.', "The statement 'talapoins have (part) nuclei' is true.", "Whenever it is true that it is not true that if if possums spend the first four months of their lives in their mother 's pouch , then most species inhabit cold waters, then caimen have (part) cell membranes, 'either agricultural land comprises two groupings pasture and cropland or horses graze in regions' is true.", 'The claim that either agricultural land comprises two groupings pasture and cropland or horses graze in regions does not reflect reality.']
|
So long as if community service is another form of education that helps make students more complete people, then pubs have (part) floors, 'occasional hurricanes produce major storms and flooding' is true. Provided that either bonds have properties or ministers are used for ceremony, we know that if caimen have (part) cell membranes, then if community service is another form of education that helps make students more complete people, then pubs have (part) floors. Either one or both of these statements are true: bonds have properties, or ministers are used for ceremony. We know that at least one of two things is true: most beetles eat bugs, or walruses have (part) skulls. When most beetles eat bugs is true, it follows that either physical change is a key preoccupation for health professions or if possums spend the first four months of their lives in their mother 's pouch , then most species inhabit cold waters. Once we know walruses have (part) skulls, we also know that either physical change is a key preoccupation for health professions or if possums spend the first four months of their lives in their mother 's pouch , then most species inhabit cold waters. One may reasonably assume that if talapoins have (part) nuclei, then if physical change is a key preoccupation for health professions, then caimen have (part) cell membranes. The statement 'talapoins have (part) nuclei' is true. Whenever it is true that it is not true that if if possums spend the first four months of their lives in their mother 's pouch , then most species inhabit cold waters, then caimen have (part) cell membranes, 'either agricultural land comprises two groupings pasture and cropland or horses graze in regions' is true. The claim that either agricultural land comprises two groupings pasture and cropland or horses graze in regions does not reflect reality.
|
The claim that occasional hurricanes produce major storms and flooding is true.
|
The claim that occasional hurricanes produce major storms and flooding is true.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If [1], then (If [2], then [3].). [SC1-2]
If (If [2], then [3].), then [0].
Therefore, If [1], then [0]..
[SC1-2]
Modus Ponens:
If (Either [7] or [8].), then (If [1], then (If [2], then [3].).).
Either [7] or [8].
Therefore, If [1], then (If [2], then [3].)..
[SC2-1]
Disjunction Elimination:
Either [4] or (If [5], then [6].). [SC1-2]
If [4], then [1]. [SC2-2]
If (If [5], then [6].), then [1]. [SC3-2]
Therefore, [1].
[SC1-2]
Disjunction Elimination:
Either [10] or [11].
If [10], then (Either [4] or (If [5], then [6].).).
If [11], then (Either [4] or (If [5], then [6].).).
Therefore, Either [4] or (If [5], then [6].)..
[SC2-2]
Modus Ponens:
If [9], then (If [4], then [1].).
[9]
Therefore, If [4], then [1]..
[SC3-2]
Modus Tonens:
If (Not (If (If [5], then [6].), then [1].).), then (Either [12] or [13].).
Not (Either [12] or [13].).
Therefore, If (If [5], then [6].), then [1]..
|
{0: 'Occasional hurricanes produce major storms and flooding.', 1: 'Caimen have (part) cell membranes.', 2: 'Community service is another form of education that helps make students more complete people.', 3: 'Pubs have (part) floors.', 4: 'Physical change is a key preoccupation for health professions.', 5: "Possums spend the first four months of their lives in their mother 's pouch .", 6: 'Most species inhabit cold waters.', 7: 'Bonds have properties.', 8: 'Ministers are used for ceremony.', 9: 'Talapoins have (part) nuclei.', 10: 'Most beetles eat bugs.', 11: 'Walruses have (part) skulls.', 12: 'Agricultural land comprises two groupings pasture and cropland.', 13: 'Horses graze in regions.'}
| 7 |
6,851 |
['Should it be the case that many eucalypts also change the shape of their leaves as they get older, it follows that biennials are plants whose entire life cycle occurs within two years.', 'Provided that it is a common misconception that either many eucalypts also change the shape of their leaves as they get older or letters are located in suitcases, we know that plankton is obviously the favorite diet of barnacles.', "The statement that 'plankton is obviously the favorite diet of barnacles' is incorrect.", 'On the condition that bacteria have electrical properties, it is definitely the case that either either homemade oatmeal cookies contain fiber or every molecule absorbs a specific type of light or plants appear to be more robust in open marshes.', "It is a fact that either either histamine is one of the body's triggers for promoting inflammation or shrews vary in size or if either homemade oatmeal cookies contain fiber or every molecule absorbs a specific type of light, then if letters are located in suitcases, then biennials are plants whose entire life cycle occurs within two years.", "Those that suggest either histamine is one of the body's triggers for promoting inflammation or shrews vary in size are wrong.", "Assuming the statement that 'if plants appear to be more robust in open marshes, then if letters are located in suitcases, then biennials are plants whose entire life cycle occurs within two years' is incorrect, we know that plants become loose and wobbly, pulling easily from the soil.", "So long as the statement that 'if plants appear to be more robust in open marshes, then if letters are located in suitcases, then biennials are plants whose entire life cycle occurs within two years' is incorrect, 'it is not the case that plants become loose and wobbly, pulling easily from the soil' is true.", 'Either skateboarders have their own unique style or bacteria have electrical properties.', 'The claim that skateboarders have their own unique style does not reflect reality.']
|
Should it be the case that many eucalypts also change the shape of their leaves as they get older, it follows that biennials are plants whose entire life cycle occurs within two years. Provided that it is a common misconception that either many eucalypts also change the shape of their leaves as they get older or letters are located in suitcases, we know that plankton is obviously the favorite diet of barnacles. The statement that 'plankton is obviously the favorite diet of barnacles' is incorrect. On the condition that bacteria have electrical properties, it is definitely the case that either either homemade oatmeal cookies contain fiber or every molecule absorbs a specific type of light or plants appear to be more robust in open marshes. It is a fact that either either histamine is one of the body's triggers for promoting inflammation or shrews vary in size or if either homemade oatmeal cookies contain fiber or every molecule absorbs a specific type of light, then if letters are located in suitcases, then biennials are plants whose entire life cycle occurs within two years. Those that suggest either histamine is one of the body's triggers for promoting inflammation or shrews vary in size are wrong. Assuming the statement that 'if plants appear to be more robust in open marshes, then if letters are located in suitcases, then biennials are plants whose entire life cycle occurs within two years' is incorrect, we know that plants become loose and wobbly, pulling easily from the soil. So long as the statement that 'if plants appear to be more robust in open marshes, then if letters are located in suitcases, then biennials are plants whose entire life cycle occurs within two years' is incorrect, 'it is not the case that plants become loose and wobbly, pulling easily from the soil' is true. Either skateboarders have their own unique style or bacteria have electrical properties. The claim that skateboarders have their own unique style does not reflect reality.
|
biennials are plants whose entire life cycle occurs within two years.
|
It is a common misconception that biennials are plants whose entire life cycle occurs within two years.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either [1] or [2].).), then [3].
Not [3].
Therefore, Either [1] or [2]..
[SC3-1]
Disjunction Elimination:
Either (Either [4] or [5].) or [6]. [SC1-2]
If (Either [4] or [5].), then (If [2], then [0].). [SC2-2]
If [6], then (If [2], then [0].). [SC3-2]
Therefore, If [2], then [0]..
[SC1-2]
Modus Ponens:
If [10], then (Either (Either [4] or [5].) or [6].).
[10] [SC2-3]
Therefore, Either (Either [4] or [5].) or [6]..
[SC2-3]
Disjunctive Syllogism:
Either [11] or [10].
Not [11].
Therefore, [10].
[SC2-2]
Disjunctive Syllogism:
Either (Either [8] or [9].) or (If (Either [4] or [5].), then (If [2], then [0].).).
Not (Either [8] or [9].).
Therefore, If (Either [4] or [5].), then (If [2], then [0].)..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If [6], then (If [2], then [0].).).), then [7].
If (Not (If [6], then (If [2], then [0].).).), then (Not [7].).
Therefore, If [6], then (If [2], then [0].)..
|
{0: 'Biennials are plants whose entire life cycle occurs within two years.', 1: 'Many eucalypts also change the shape of their leaves as they get older.', 2: 'Letters are located in suitcases.', 3: 'Plankton is obviously the favorite diet of barnacles.', 4: 'Homemade oatmeal cookies contain fiber.', 5: 'Every molecule absorbs a specific type of light.', 6: 'Plants appear to be more robust in open marshes.', 7: 'Plants become loose and wobbly, pulling easily from the soil.', 8: "Histamine is one of the body's triggers for promoting inflammation.", 9: 'Shrews vary in size.', 10: 'Bacteria have electrical properties.', 11: 'Skateboarders have their own unique style.'}
| 7 |
6,407 |
['If the statement, supergiants have even greater luminosities and diameters, does not hold, then an androgen is a sex hormone.', "The statement 'an achiever is a person' can be considered true.", 'The claim that tiger sharks are very large and so they require a considerable amount of wide open space does not correspond with reality.', "Whenever it is true that the statement 'if the claim that if an achiever is a person, then if the statement, supergiants have even greater luminosities and diameters, does not hold, then some people mistakenly believe that an androgen is a sex hormone has no merit, then tiger sharks are very large and so they require a considerable amount of wide open space' can be considered false, 'if lure coursing Many sighthound owners participate in lure coursing with their dogs, then responsible ownership entails restricting the movement of domestic cats' is true.", 'The claim that hens are good winter layers and lay light to dark brown eggs holds true.', "We know that at least one of two things is true: nutritious food is scarce and children are vulnerable to malnutrition, or if hens are good winter layers and lay light to dark brown eggs, then if the statement 'if the claim that if an achiever is a person, then if the statement, supergiants have even greater luminosities and diameters, does not hold, then some people mistakenly believe that an androgen is a sex hormone has no merit, then tiger sharks are very large and so they require a considerable amount of wide open space' can be considered false, then the statement that 'if lure coursing Many sighthound owners participate in lure coursing with their dogs, then responsible ownership entails restricting the movement of domestic cats' is incorrect.", "Should it be the case that some wildfires alter landscapes, it follows that the statement 'nutritious food is scarce and children are vulnerable to malnutrition' can be considered false.", 'It is reasonable to believe that some wildfires alter landscapes.']
|
If the statement, supergiants have even greater luminosities and diameters, does not hold, then an androgen is a sex hormone. The statement 'an achiever is a person' can be considered true. The claim that tiger sharks are very large and so they require a considerable amount of wide open space does not correspond with reality. Whenever it is true that the statement 'if the claim that if an achiever is a person, then if the statement, supergiants have even greater luminosities and diameters, does not hold, then some people mistakenly believe that an androgen is a sex hormone has no merit, then tiger sharks are very large and so they require a considerable amount of wide open space' can be considered false, 'if lure coursing Many sighthound owners participate in lure coursing with their dogs, then responsible ownership entails restricting the movement of domestic cats' is true. The claim that hens are good winter layers and lay light to dark brown eggs holds true. We know that at least one of two things is true: nutritious food is scarce and children are vulnerable to malnutrition, or if hens are good winter layers and lay light to dark brown eggs, then if the statement 'if the claim that if an achiever is a person, then if the statement, supergiants have even greater luminosities and diameters, does not hold, then some people mistakenly believe that an androgen is a sex hormone has no merit, then tiger sharks are very large and so they require a considerable amount of wide open space' can be considered false, then the statement that 'if lure coursing Many sighthound owners participate in lure coursing with their dogs, then responsible ownership entails restricting the movement of domestic cats' is incorrect. Should it be the case that some wildfires alter landscapes, it follows that the statement 'nutritious food is scarce and children are vulnerable to malnutrition' can be considered false. It is reasonable to believe that some wildfires alter landscapes.
|
It is the case that supergiants have even greater luminosities and diameters.
|
Most supergiants end their lives catastrophically as a supernova .
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [2], then (If (Not [0].), then (Not [1].).). [SC1-2]
[2]
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Modus Tonens:
If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then [3]. [SC1-3]
Not [3].
Therefore, If [2], then (If (Not [0].), then (Not [1].).)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then [3].).), then (If [4], then [5].).
If (Not (If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then [3].).), then (Not (If [4], then [5].).). [SC2-4]
Therefore, If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then [3]..
[SC2-4]
Modus Ponens:
If [6], then (If (Not (If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then [3].).), then (Not (If [4], then [5].).).). [SC1-5]
[6]
Therefore, If (Not (If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then [3].).), then (Not (If [4], then [5].).)..
[SC1-5]
Disjunctive Syllogism:
Either [7] or (If [6], then (If (Not (If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then [3].).), then (Not (If [4], then [5].).).).).
Not [7]. [SC2-6]
Therefore, If [6], then (If (Not (If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then [3].).), then (Not (If [4], then [5].).).)..
[SC2-6]
Modus Ponens:
If [8], then (Not [7].).
[8]
Therefore, Not [7]..
|
{0: 'Supergiants have even greater luminosities and diameters.', 1: 'An androgen is a sex hormone.', 2: 'An achiever is a person.', 3: 'Tiger sharks are very large and so they require a considerable amount of wide open space.', 4: 'Lure coursing Many sighthound owners participate in lure coursing with their dogs.', 5: 'Responsible ownership entails restricting the movement of domestic cats.', 6: 'Hens are good winter layers and lay light to dark brown eggs.', 7: 'Nutritious food is scarce and children are vulnerable to malnutrition.', 8: 'Some wildfires alter landscapes.'}
| 7 |
6,692 |
['On the condition that diets include rich food, it is definitely the case that some mangrove trees have tangles.', 'The claim that molten tin is used to float molten glass to produce window glass does not reflect reality.', 'We know that at least one of two things is true: if mining is a very important industry in Chile, then weight training is one of the best ways to maintain muscle mass, or if viruses exist composed of a single strand of nucleic acid enclosed by a capsule of protein, then diets include rich food.', 'The claim that if mining is a very important industry in Chile, then weight training is one of the best ways to maintain muscle mass is false.', 'If islamic teachings require adherents to begin fasting when they have reached the age of puberty, then diets include rich food.', 'When breast cancer strikes one out of every ten American women is true, it follows that either molten tin is used to float molten glass to produce window glass or either viruses exist composed of a single strand of nucleic acid enclosed by a capsule of protein or either ginkgo seeds have irregular germination or carrots are roots.', 'The claim that breast cancer strikes one out of every ten American women is true.', 'We know that at least one of two things is true: anglers have (part) faces, or if either ginkgo seeds have irregular germination or carrots are roots, then islamic teachings require adherents to begin fasting when they have reached the age of puberty.', 'The claim that anglers have (part) faces is false.']
|
On the condition that diets include rich food, it is definitely the case that some mangrove trees have tangles. The claim that molten tin is used to float molten glass to produce window glass does not reflect reality. We know that at least one of two things is true: if mining is a very important industry in Chile, then weight training is one of the best ways to maintain muscle mass, or if viruses exist composed of a single strand of nucleic acid enclosed by a capsule of protein, then diets include rich food. The claim that if mining is a very important industry in Chile, then weight training is one of the best ways to maintain muscle mass is false. If islamic teachings require adherents to begin fasting when they have reached the age of puberty, then diets include rich food. When breast cancer strikes one out of every ten American women is true, it follows that either molten tin is used to float molten glass to produce window glass or either viruses exist composed of a single strand of nucleic acid enclosed by a capsule of protein or either ginkgo seeds have irregular germination or carrots are roots. The claim that breast cancer strikes one out of every ten American women is true. We know that at least one of two things is true: anglers have (part) faces, or if either ginkgo seeds have irregular germination or carrots are roots, then islamic teachings require adherents to begin fasting when they have reached the age of puberty. The claim that anglers have (part) faces is false.
|
It is fair to say that some mangrove trees have tangles.
|
It is fair to say that some mangrove trees have tangles.
|
TRUE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [2] or (Either [3] or [4].). [SC1-2]
If [2], then [1]. [SC2-2]
If (Either [3] or [4].), then [1]. [SC3-2]
Therefore, [1].
[SC1-2]
Disjunctive Syllogism:
Either [8] or (Either [2] or (Either [3] or [4].).). [SC1-3]
Not [8].
Therefore, Either [2] or (Either [3] or [4].)..
[SC1-3]
Modus Ponens:
If [9], then (Either [8] or (Either [2] or (Either [3] or [4].).).).
[9]
Therefore, Either [8] or (Either [2] or (Either [3] or [4].).)..
[SC2-2]
Disjunctive Syllogism:
Either (If [6], then [7].) or (If [2], then [1].).
Not (If [6], then [7].).
Therefore, If [2], then [1]..
[SC3-2]
Hypothetical Syllogism:
If (Either [3] or [4].), then [5]. [SC1-3]
If [5], then [1].
Therefore, If (Either [3] or [4].), then [1]..
[SC1-3]
Disjunctive Syllogism:
Either [10] or (If (Either [3] or [4].), then [5].).
Not [10].
Therefore, If (Either [3] or [4].), then [5]..
|
{0: 'Some mangrove trees have tangles.', 1: 'Diets include rich food.', 2: 'Viruses exist composed of a single strand of nucleic acid enclosed by a capsule of protein.', 3: 'Ginkgo seeds have irregular germination.', 4: 'Carrots are roots.', 5: 'Islamic teachings require adherents to begin fasting when they have reached the age of puberty.', 6: 'Mining is a very important industry in Chile.', 7: 'Weight training is one of the best ways to maintain muscle mass.', 8: 'Molten tin is used to float molten glass to produce window glass.', 9: 'Breast cancer strikes one out of every ten American women.', 10: 'Anglers have (part) faces.'}
| 7 |
6,353 |
["Whenever it is true that vigilantes are workers, 'if if gaurs are able to finally reintegrate their former habitats, then coyotes advertise their location with smells and sounds, such as howling or yapping, then penaeid prawns are the first target of selective breeding programs' is true.", 'We can assume that sheep wool is spun and is used in clothing such sweaters, mitts, and pants.', "Provided that we know that the claim that vigilantes are workers is false, we know that people routinely overestimate a dog's weight, especially if they are on the ground, looking up.", "Whenever it is true that we know that the claim that vigilantes are workers is false, 'it is a common misconception that people routinely overestimate a dog's weight, especially if they are on the ground, looking up' is true.", 'Given that sheep wool is spun and is used in clothing such sweaters, mitts, and pants, it can be inferred that apricots are located in tables.', 'When the claim that if apricots are located in tables, then if gaurs are able to finally reintegrate their former habitats, then coyotes advertise their location with smells and sounds, such as howling or yapping does not correspond with reality is true, it follows that ammonium sulfate is formed and the acid is neutralized.', 'Provided that effective governance is a key factor in social and economic growth, we know that those that suggest ammonium sulfate is formed and the acid is neutralized are wrong.', 'It is a simple truth that effective governance is a key factor in social and economic growth.']
|
Whenever it is true that vigilantes are workers, 'if if gaurs are able to finally reintegrate their former habitats, then coyotes advertise their location with smells and sounds, such as howling or yapping, then penaeid prawns are the first target of selective breeding programs' is true. We can assume that sheep wool is spun and is used in clothing such sweaters, mitts, and pants. Provided that we know that the claim that vigilantes are workers is false, we know that people routinely overestimate a dog's weight, especially if they are on the ground, looking up. Whenever it is true that we know that the claim that vigilantes are workers is false, 'it is a common misconception that people routinely overestimate a dog's weight, especially if they are on the ground, looking up' is true. Given that sheep wool is spun and is used in clothing such sweaters, mitts, and pants, it can be inferred that apricots are located in tables. When the claim that if apricots are located in tables, then if gaurs are able to finally reintegrate their former habitats, then coyotes advertise their location with smells and sounds, such as howling or yapping does not correspond with reality is true, it follows that ammonium sulfate is formed and the acid is neutralized. Provided that effective governance is a key factor in social and economic growth, we know that those that suggest ammonium sulfate is formed and the acid is neutralized are wrong. It is a simple truth that effective governance is a key factor in social and economic growth.
|
The statement 'penaeid prawns are the first target of selective breeding programs' is true.
|
The claim that penaeid prawns are the first target of selective breeding programs is false.
|
FALSE
|
Modus Ponens:
If (If [1], then [2].), then [0]. [SC1-1]
If [1], then [2]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (If (If [1], then [2].), then [0].).
[3] [SC2-2]
Therefore, If (If [1], then [2].), then [0]..
[SC2-2]
Reductio Ad Absurdum:
If (Not [3].), then [6].
If (Not [3].), then (Not [6].).
Therefore, [3].
[SC2-1]
Modus Ponens:
If [4], then (If [1], then [2].). [SC1-2]
[4]
Therefore, If [1], then [2]..
[SC1-2]
Hypothetical Syllogism:
If [4], then [5].
If [5], then (If [1], then [2].). [SC2-3]
Therefore, If [4], then (If [1], then [2].)..
[SC2-3]
Modus Tonens:
If (Not (If [5], then (If [1], then [2].).).), then [7].
Not [7]. [SC2-4]
Therefore, If [5], then (If [1], then [2].)..
[SC2-4]
Modus Ponens:
If [8], then (Not [7].).
[8]
Therefore, Not [7]..
|
{0: 'Penaeid prawns are the first target of selective breeding programs.', 1: 'Gaurs are able to finally reintegrate their former habitats.', 2: 'Coyotes advertise their location with smells and sounds, such as howling or yapping.', 3: 'Vigilantes are workers.', 4: 'Sheep wool is spun and is used in clothing such sweaters, mitts, and pants.', 5: 'Apricots are located in tables.', 6: "People routinely overestimate a dog's weight, especially if they are on the ground, looking up.", 7: 'Ammonium sulfate is formed and the acid is neutralized.', 8: 'Effective governance is a key factor in social and economic growth.'}
| 7 |
6,153 |
['One may reasonably assume that if some starfishs have brains, then juncos like to nest on the ground in mudbanks, tufts of weeds, fallen logs or rock ledges.', "Once we know some people mistakenly believe that if the claim that some starfishs have brains does not correspond with reality, then gold represents power, we also know that the notion that 'tv is made of plastic' is untrue.", "Either pornography causes massive damage in guys' lives and relationships or most juvenile prostitutes are in their mid to late teens.", "Given that pornography causes massive damage in guys' lives and relationships, it can be inferred that we know that the claim that gold represents power is false.", 'Given that most juvenile prostitutes are in their mid to late teens, it can be inferred that we know that the claim that gold represents power is false.', 'Provided that the statement, if the claim that if some people mistakenly believe that if the claim that some starfishs have brains does not correspond with reality, then gold represents power, then tv is made of plastic is false, then central pressure is given in millibars, which is numerically equivalent to hectopascals, does not hold, we know that a coaster brake is a brake.', 'Provided that the statement, if the claim that if some people mistakenly believe that if the claim that some starfishs have brains does not correspond with reality, then gold represents power, then tv is made of plastic is false, then central pressure is given in millibars, which is numerically equivalent to hectopascals, does not hold, we know that it is not true that a coaster brake is a brake.', 'Once we know central pressure is given in millibars, which is numerically equivalent to hectopascals, we also know that cryptobiotic crust is the foundation of life in the high desert.', 'It is not the case that cryptobiotic crust is the foundation of life in the high desert.']
|
One may reasonably assume that if some starfishs have brains, then juncos like to nest on the ground in mudbanks, tufts of weeds, fallen logs or rock ledges. Once we know some people mistakenly believe that if the claim that some starfishs have brains does not correspond with reality, then gold represents power, we also know that the notion that 'tv is made of plastic' is untrue. Either pornography causes massive damage in guys' lives and relationships or most juvenile prostitutes are in their mid to late teens. Given that pornography causes massive damage in guys' lives and relationships, it can be inferred that we know that the claim that gold represents power is false. Given that most juvenile prostitutes are in their mid to late teens, it can be inferred that we know that the claim that gold represents power is false. Provided that the statement, if the claim that if some people mistakenly believe that if the claim that some starfishs have brains does not correspond with reality, then gold represents power, then tv is made of plastic is false, then central pressure is given in millibars, which is numerically equivalent to hectopascals, does not hold, we know that a coaster brake is a brake. Provided that the statement, if the claim that if some people mistakenly believe that if the claim that some starfishs have brains does not correspond with reality, then gold represents power, then tv is made of plastic is false, then central pressure is given in millibars, which is numerically equivalent to hectopascals, does not hold, we know that it is not true that a coaster brake is a brake. Once we know central pressure is given in millibars, which is numerically equivalent to hectopascals, we also know that cryptobiotic crust is the foundation of life in the high desert. It is not the case that cryptobiotic crust is the foundation of life in the high desert.
|
Many people rightly believe that juncos like to nest on the ground in mudbanks, tufts of weeds, fallen logs or rock ledges.
|
Many people rightly believe that juncos like to nest on the ground in mudbanks, tufts of weeds, fallen logs or rock ledges.
|
TRUE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not [1].), then [2]. [SC1-2]
Not [2]. [SC2-2]
Therefore, [1].
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not [1].), then [2].).), then [5]. [SC1-3]
If (Not (If (Not [1].), then [2].).), then (Not [5].).
Therefore, If (Not [1].), then [2]..
[SC1-3]
Modus Tonens:
If (Not (If (Not (If (Not [1].), then [2].).), then [5].).), then [6]. [SC1-4]
Not [6]. [SC2-4]
Therefore, If (Not (If (Not [1].), then [2].).), then [5]..
[SC1-4]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not (If (Not [1].), then [2].).), then [5].).), then [6].).), then [7].
If (Not (If (Not (If (Not (If (Not [1].), then [2].).), then [5].).), then [6].).), then (Not [7].).
Therefore, If (Not (If (Not (If (Not [1].), then [2].).), then [5].).), then [6]..
[SC2-4]
Modus Tonens:
If [6], then [8].
Not [8].
Therefore, Not [6]..
[SC2-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not [2].).
If [4], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Juncos like to nest on the ground in mudbanks, tufts of weeds, fallen logs or rock ledges.', 1: 'Some starfishs have brains.', 2: 'Gold represents power.', 3: "Pornography causes massive damage in guys' lives and relationships.", 4: 'Most juvenile prostitutes are in their mid to late teens.', 5: 'Tv is made of plastic.', 6: 'Central pressure is given in millibars, which is numerically equivalent to hectopascals.', 7: 'A coaster brake is a brake.', 8: 'Cryptobiotic crust is the foundation of life in the high desert.'}
| 7 |
6,566 |
["The statement that 'a rand is an unit' is incorrect.", 'Once we know the claim that either a rand is an unit or if tomatillos are part of tomatillos, then tolerance refers to an increase in the amount of a drug necessary toexperience the same effect has no merit, we also know that coherence measures the degree of synchronisation between signals.', "The notion that 'coherence measures the degree of synchronisation between signals' is untrue.", 'It is a fact that either lemurs are located in nature or constrictors have (part) nuclei.', "Once we know constrictors have (part) nuclei, we also know that either old men are fathers or the statement that 'tolerance refers to an increase in the amount of a drug necessary toexperience the same effect' is incorrect.", 'Assuming old men are fathers, we know that vertebrates descend from ancestors.', 'On the condition that old men are fathers, it is definitely the case that the statement, vertebrates descend from ancestors, does not hold.', "Provided that the claim that if lemurs are located in nature, then either old men are fathers or the statement that 'tolerance refers to an increase in the amount of a drug necessary toexperience the same effect' is incorrect does not correspond with reality, we know that either catalysts are central to modern chemical manufacturing as well as to life or a pedicure is attention.", "Should it be the case that the claim that if lemurs are located in nature, then either old men are fathers or the statement that 'tolerance refers to an increase in the amount of a drug necessary toexperience the same effect' is incorrect does not correspond with reality, it follows that those that suggest either catalysts are central to modern chemical manufacturing as well as to life or a pedicure is attention are wrong."]
|
The statement that 'a rand is an unit' is incorrect. Once we know the claim that either a rand is an unit or if tomatillos are part of tomatillos, then tolerance refers to an increase in the amount of a drug necessary toexperience the same effect has no merit, we also know that coherence measures the degree of synchronisation between signals. The notion that 'coherence measures the degree of synchronisation between signals' is untrue. It is a fact that either lemurs are located in nature or constrictors have (part) nuclei. Once we know constrictors have (part) nuclei, we also know that either old men are fathers or the statement that 'tolerance refers to an increase in the amount of a drug necessary toexperience the same effect' is incorrect. Assuming old men are fathers, we know that vertebrates descend from ancestors. On the condition that old men are fathers, it is definitely the case that the statement, vertebrates descend from ancestors, does not hold. Provided that the claim that if lemurs are located in nature, then either old men are fathers or the statement that 'tolerance refers to an increase in the amount of a drug necessary toexperience the same effect' is incorrect does not correspond with reality, we know that either catalysts are central to modern chemical manufacturing as well as to life or a pedicure is attention. Should it be the case that the claim that if lemurs are located in nature, then either old men are fathers or the statement that 'tolerance refers to an increase in the amount of a drug necessary toexperience the same effect' is incorrect does not correspond with reality, it follows that those that suggest either catalysts are central to modern chemical manufacturing as well as to life or a pedicure is attention are wrong.
|
Those that suggest tomatillos are part of tomatillos are wrong.
|
The claim that tomatillos have a tangy, lemony flavor does not reflect reality.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [0], then [1].). [SC1-2]
Not [2].
Therefore, If [0], then [1]..
[SC1-2]
Modus Tonens:
If (Not (Either [2] or (If [0], then [1].).).), then [7].
Not [7].
Therefore, Either [2] or (If [0], then [1].)..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (Not [1].). [SC1-2]
Not [3]. [SC2-2]
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (Either [3] or (Not [1].).). [SC2-3]
If [6], then (Either [3] or (Not [1].).).
Therefore, Either [3] or (Not [1].)..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If [5], then (Either [3] or (Not [1].).).).), then (Either [8] or [9].).
If (Not (If [5], then (Either [3] or (Not [1].).).).), then (Not (Either [8] or [9].).).
Therefore, If [5], then (Either [3] or (Not [1].).)..
[SC2-2]
Reductio Ad Absurdum:
If [3], then [4].
If [3], then (Not [4].).
Therefore, Not [3]..
|
{0: 'Tomatillos are part of tomatillos.', 1: 'Tolerance refers to an increase in the amount of a drug necessary toexperience the same effect.', 2: 'A rand is an unit.', 3: 'Old men are fathers.', 4: 'Vertebrates descend from ancestors.', 5: 'Lemurs are located in nature.', 6: 'Constrictors have (part) nuclei.', 7: 'Coherence measures the degree of synchronisation between signals.', 8: 'Catalysts are central to modern chemical manufacturing as well as to life.', 9: 'A pedicure is attention.'}
| 7 |
6,542 |
['The statement, many people believe that language is a unique capacity of humans, does not hold.', 'On the condition that the claim that either automobiles have (part) petrol engines or either many people believe that language is a unique capacity of humans or the claim that either playschool isa institution or jerboas have (part) chest cavities does not correspond with reality is false, it is definitely the case that a paleface is White.', 'We know that at least one of two things is true: forensic psychologists are active in the applied and clinical aspects of psychology and law, or if the claim that either automobiles have (part) petrol engines or either many people believe that language is a unique capacity of humans or the claim that either playschool isa institution or jerboas have (part) chest cavities does not correspond with reality is false, then the claim that a paleface is White does not reflect reality.', 'It is a common misconception that forensic psychologists are active in the applied and clinical aspects of psychology and law.', 'If the claim that if twigs are slender and stunted, then some people mistakenly believe that automobiles have (part) petrol engines does not correspond with reality, then a churchyard is a yard.', 'The statement, a churchyard is a yard, does not hold.', 'Once we know it is a common misconception that twigs are slender and stunted, we also know that electricity flows through any electric conducting material.', 'The statement that states electricity flows through any electric conducting material is false.']
|
The statement, many people believe that language is a unique capacity of humans, does not hold. On the condition that the claim that either automobiles have (part) petrol engines or either many people believe that language is a unique capacity of humans or the claim that either playschool isa institution or jerboas have (part) chest cavities does not correspond with reality is false, it is definitely the case that a paleface is White. We know that at least one of two things is true: forensic psychologists are active in the applied and clinical aspects of psychology and law, or if the claim that either automobiles have (part) petrol engines or either many people believe that language is a unique capacity of humans or the claim that either playschool isa institution or jerboas have (part) chest cavities does not correspond with reality is false, then the claim that a paleface is White does not reflect reality. It is a common misconception that forensic psychologists are active in the applied and clinical aspects of psychology and law. If the claim that if twigs are slender and stunted, then some people mistakenly believe that automobiles have (part) petrol engines does not correspond with reality, then a churchyard is a yard. The statement, a churchyard is a yard, does not hold. Once we know it is a common misconception that twigs are slender and stunted, we also know that electricity flows through any electric conducting material. The statement that states electricity flows through any electric conducting material is false.
|
The claim that either playschool isa institution or jerboas have (part) chest cavities does not correspond with reality.
|
The claim that either playschool isa institution or jerboas have (part) chest cavities does not correspond with reality.
|
TRUE
|
Disjunctive Syllogism:
Either [2] or (Not (Either [0] or [1].).). [SC1-1]
Not [2].
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (Either [2] or (Not (Either [0] or [1].).).). [SC1-2]
Not [3]. [SC2-2]
Therefore, Either [2] or (Not (Either [0] or [1].).)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [3] or (Either [2] or (Not (Either [0] or [1].).).).).), then [4].
If (Not (Either [3] or (Either [2] or (Not (Either [0] or [1].).).).).), then (Not [4].). [SC2-3]
Therefore, Either [3] or (Either [2] or (Not (Either [0] or [1].).).)..
[SC2-3]
Disjunctive Syllogism:
Either [8] or (If (Not (Either [3] or (Either [2] or (Not (Either [0] or [1].).).).).), then (Not [4].).).
Not [8].
Therefore, If (Not (Either [3] or (Either [2] or (Not (Either [0] or [1].).).).).), then (Not [4].)..
[SC2-2]
Modus Ponens:
If [5], then (Not [3].). [SC1-3]
[5] [SC2-3]
Therefore, Not [3]..
[SC1-3]
Modus Tonens:
If (Not (If [5], then (Not [3].).).), then [6].
Not [6].
Therefore, If [5], then (Not [3].)..
[SC2-3]
Modus Tonens:
If (Not [5].), then [7].
Not [7].
Therefore, [5].
|
{0: 'Playschool isa institution.', 1: 'Jerboas have (part) chest cavities.', 2: 'Many people believe that language is a unique capacity of humans.', 3: 'Automobiles have (part) petrol engines.', 4: 'A paleface is White.', 5: 'Twigs are slender and stunted.', 6: 'A churchyard is a yard.', 7: 'Electricity flows through any electric conducting material.', 8: 'Forensic psychologists are active in the applied and clinical aspects of psychology and law.'}
| 7 |
6,343 |
['If the statement that states if energy is delivered to the brain by the oxidation of glucose from the blood, then if jaws have forces, then the claim that artillery are the same as crossbows has no merit is false, then most species try to dominate their sites through all sorts of means.', "So long as the statement that states if energy is delivered to the brain by the oxidation of glucose from the blood, then if jaws have forces, then the claim that artillery are the same as crossbows has no merit is false, 'the statement, most species try to dominate their sites through all sorts of means, does not hold' is true.", 'It is rational to believe that either some States also have low cost dental and eye care schemes for the aged or energy is delivered to the brain by the oxidation of glucose from the blood.', 'Some people mistakenly believe that some States also have low cost dental and eye care schemes for the aged.', 'We know that at least one of two things is true: sport hunting takes the place of natural predators, or all human blood runs red.', "So long as sport hunting takes the place of natural predators, 'either most houseplants thrive in moderate to bright, indirect light or jaws have forces' is true.", 'Assuming all human blood runs red, we know that either most houseplants thrive in moderate to bright, indirect light or jaws have forces.', 'Given that police suicides that occur on duty are often the result of rage at the police bureaucracy, it can be inferred that some people mistakenly believe that most houseplants thrive in moderate to bright, indirect light.', 'Many people rightly believe that police suicides that occur on duty are often the result of rage at the police bureaucracy.']
|
If the statement that states if energy is delivered to the brain by the oxidation of glucose from the blood, then if jaws have forces, then the claim that artillery are the same as crossbows has no merit is false, then most species try to dominate their sites through all sorts of means. So long as the statement that states if energy is delivered to the brain by the oxidation of glucose from the blood, then if jaws have forces, then the claim that artillery are the same as crossbows has no merit is false, 'the statement, most species try to dominate their sites through all sorts of means, does not hold' is true. It is rational to believe that either some States also have low cost dental and eye care schemes for the aged or energy is delivered to the brain by the oxidation of glucose from the blood. Some people mistakenly believe that some States also have low cost dental and eye care schemes for the aged. We know that at least one of two things is true: sport hunting takes the place of natural predators, or all human blood runs red. So long as sport hunting takes the place of natural predators, 'either most houseplants thrive in moderate to bright, indirect light or jaws have forces' is true. Assuming all human blood runs red, we know that either most houseplants thrive in moderate to bright, indirect light or jaws have forces. Given that police suicides that occur on duty are often the result of rage at the police bureaucracy, it can be inferred that some people mistakenly believe that most houseplants thrive in moderate to bright, indirect light. Many people rightly believe that police suicides that occur on duty are often the result of rage at the police bureaucracy.
|
The claim that artillery are the same as crossbows has no merit.
|
It is a common misconception that artillery is an armament.
|
Uncertain
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1] [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [3], then (If [1], then (Not [0].).). [SC1-2]
[3] [SC2-2]
Therefore, If [1], then (Not [0].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [3], then (If [1], then (Not [0].).).).), then [4].
If (Not (If [3], then (If [1], then (Not [0].).).).), then (Not [4].).
Therefore, If [3], then (If [1], then (Not [0].).)..
[SC2-2]
Disjunctive Syllogism:
Either [7] or [3].
Not [7].
Therefore, [3].
[SC2-1]
Disjunctive Syllogism:
Either [2] or [1]. [SC1-2]
Not [2]. [SC2-2]
Therefore, [1].
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (Either [2] or [1].).
If [6], then (Either [2] or [1].).
Therefore, Either [2] or [1]..
[SC2-2]
Modus Ponens:
If [8], then (Not [2].).
[8]
Therefore, Not [2]..
|
{0: 'Artillery are the same as crossbows.', 1: 'Jaws have forces.', 2: 'Most houseplants thrive in moderate to bright, indirect light.', 3: 'Energy is delivered to the brain by the oxidation of glucose from the blood.', 4: 'Most species try to dominate their sites through all sorts of means.', 5: 'Sport hunting takes the place of natural predators.', 6: 'All human blood runs red.', 7: 'Some States also have low cost dental and eye care schemes for the aged.', 8: 'Police suicides that occur on duty are often the result of rage at the police bureaucracy.'}
| 7 |
6,887 |
['culture has festivals.', 'Assuming the statement, if it is not true that if culture has festivals, then we know that the claim that disability comes in many forms - some visible, some invisible is false, then powdery mildew is the oldest of the fungal diseases affecting hops, does not hold, we know that the claim that rain is defined as liquid precipitation has no merit.', 'It is a fact that either fax machines are communication devices or families often keep the body alive for days or even weeks refusing to accept the person has died.', 'Provided that fax machines are communication devices, we know that if the statement, if it is not true that if culture has festivals, then we know that the claim that disability comes in many forms - some visible, some invisible is false, then powdery mildew is the oldest of the fungal diseases affecting hops, does not hold, then rain is defined as liquid precipitation.', "Whenever it is true that families often keep the body alive for days or even weeks refusing to accept the person has died, 'if the statement, if it is not true that if culture has festivals, then we know that the claim that disability comes in many forms - some visible, some invisible is false, then powdery mildew is the oldest of the fungal diseases affecting hops, does not hold, then rain is defined as liquid precipitation' is true.", 'Given that it is not the case that if it is not true that if culture has festivals, then we know that the claim that disability comes in many forms - some visible, some invisible is false, then child care is an essential family support, it can be inferred that pharmacists also use computers to control inventory and print labels.', 'We know that the claim that pharmacists also use computers to control inventory and print labels is false.', 'We know that at least one of two things is true: tapirs are active at night, or some species reproduce only asexually.', 'One may reasonably assume that if tapirs are active at night, then if child care is an essential family support, then those that suggest powdery mildew is the oldest of the fungal diseases affecting hops are wrong.', 'One may reasonably assume that if some species reproduce only asexually, then if child care is an essential family support, then those that suggest powdery mildew is the oldest of the fungal diseases affecting hops are wrong.']
|
culture has festivals. Assuming the statement, if it is not true that if culture has festivals, then we know that the claim that disability comes in many forms - some visible, some invisible is false, then powdery mildew is the oldest of the fungal diseases affecting hops, does not hold, we know that the claim that rain is defined as liquid precipitation has no merit. It is a fact that either fax machines are communication devices or families often keep the body alive for days or even weeks refusing to accept the person has died. Provided that fax machines are communication devices, we know that if the statement, if it is not true that if culture has festivals, then we know that the claim that disability comes in many forms - some visible, some invisible is false, then powdery mildew is the oldest of the fungal diseases affecting hops, does not hold, then rain is defined as liquid precipitation. Whenever it is true that families often keep the body alive for days or even weeks refusing to accept the person has died, 'if the statement, if it is not true that if culture has festivals, then we know that the claim that disability comes in many forms - some visible, some invisible is false, then powdery mildew is the oldest of the fungal diseases affecting hops, does not hold, then rain is defined as liquid precipitation' is true. Given that it is not the case that if it is not true that if culture has festivals, then we know that the claim that disability comes in many forms - some visible, some invisible is false, then child care is an essential family support, it can be inferred that pharmacists also use computers to control inventory and print labels. We know that the claim that pharmacists also use computers to control inventory and print labels is false. We know that at least one of two things is true: tapirs are active at night, or some species reproduce only asexually. One may reasonably assume that if tapirs are active at night, then if child care is an essential family support, then those that suggest powdery mildew is the oldest of the fungal diseases affecting hops are wrong. One may reasonably assume that if some species reproduce only asexually, then if child care is an essential family support, then those that suggest powdery mildew is the oldest of the fungal diseases affecting hops are wrong.
|
We know that the claim that disability comes in many forms - some visible, some invisible is false.
|
It is fair to say that disability comes in many forms - some visible, some invisible.
|
FALSE
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [1], then (Not [0].).).), then [2]. [SC1-2]
If (Not (If [1], then (Not [0].).).), then (Not [2].). [SC2-2]
Therefore, If [1], then (Not [0].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (If [1], then (Not [0].).).), then [2].).), then [4]. [SC1-3]
If (Not (If (Not (If [1], then (Not [0].).).), then [2].).), then (Not [4].).
Therefore, If (Not (If [1], then (Not [0].).).), then [2]..
[SC1-3]
Disjunction Elimination:
Either [8] or [9].
If [8], then (If (Not (If (Not (If [1], then (Not [0].).).), then [2].).), then [4].).
If [9], then (If (Not (If (Not (If [1], then (Not [0].).).), then [2].).), then [4].).
Therefore, If (Not (If (Not (If [1], then (Not [0].).).), then [2].).), then [4]..
[SC2-2]
Hypothetical Syllogism:
If (Not (If [1], then (Not [0].).).), then [3]. [SC1-3]
If [3], then (Not [2].). [SC2-3]
Therefore, If (Not (If [1], then (Not [0].).).), then (Not [2].)..
[SC1-3]
Modus Tonens:
If (Not (If (Not (If [1], then (Not [0].).).), then [3].).), then [5].
Not [5].
Therefore, If (Not (If [1], then (Not [0].).).), then [3]..
[SC2-3]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If [3], then (Not [2].).).
If [7], then (If [3], then (Not [2].).).
Therefore, If [3], then (Not [2].)..
|
{0: 'Disability comes in many forms - some visible, some invisible.', 1: 'Culture has festivals.', 2: 'Powdery mildew is the oldest of the fungal diseases affecting hops.', 3: 'Child care is an essential family support.', 4: 'Rain is defined as liquid precipitation.', 5: 'Pharmacists also use computers to control inventory and print labels.', 6: 'Tapirs are active at night.', 7: 'Some species reproduce only asexually.', 8: 'Fax machines are communication devices.', 9: 'Families often keep the body alive for days or even weeks refusing to accept the person has died.'}
| 7 |
6,997 |
["Whenever it is true that it is not true that chlorine is virtually ineffective on crypto at levels typically used for disinfection, 'the claim that if most tarsiers have fur, then cloves are used in cooking, whole or ground is false' is true.", 'One may reasonably assume that if the statement, if it is not true that chlorine is virtually ineffective on crypto at levels typically used for disinfection, then if most tarsiers have fur, then cloves are used in cooking, whole or ground, does not hold, then weak points are liabilities.', 'current research focuses on the life history and feeding habits of estuarine fishes.', 'The claim that many people believe in reincarnation is false.', 'At least one of two things is true: some intestines help food, or education systems are, of course, closely related to national cultures and identities.', 'Should it be the case that some intestines help food, it follows that if current research focuses on the life history and feeding habits of estuarine fishes, then if the statement, if it is not true that chlorine is virtually ineffective on crypto at levels typically used for disinfection, then if most tarsiers have fur, then cloves are used in cooking, whole or ground, does not hold, then the statement, green tea produces a yellowish-green brew and is milder tasting than black teas, does not hold.', 'Should it be the case that education systems are, of course, closely related to national cultures and identities, it follows that if current research focuses on the life history and feeding habits of estuarine fishes, then if the statement, if it is not true that chlorine is virtually ineffective on crypto at levels typically used for disinfection, then if most tarsiers have fur, then cloves are used in cooking, whole or ground, does not hold, then the statement, green tea produces a yellowish-green brew and is milder tasting than black teas, does not hold.', 'It is rational to believe that either sperm competition is responsible for many sexually selected traits in gastropods or some organisms use cilia.', 'If sperm competition is responsible for many sexually selected traits in gastropods, then many people believe in reincarnation .', 'One may reasonably assume that if some organisms use cilia, then if weak points are liabilities, then green tea produces a yellowish-green brew and is milder tasting than black teas.']
|
Whenever it is true that it is not true that chlorine is virtually ineffective on crypto at levels typically used for disinfection, 'the claim that if most tarsiers have fur, then cloves are used in cooking, whole or ground is false' is true. One may reasonably assume that if the statement, if it is not true that chlorine is virtually ineffective on crypto at levels typically used for disinfection, then if most tarsiers have fur, then cloves are used in cooking, whole or ground, does not hold, then weak points are liabilities. current research focuses on the life history and feeding habits of estuarine fishes. The claim that many people believe in reincarnation is false. At least one of two things is true: some intestines help food, or education systems are, of course, closely related to national cultures and identities. Should it be the case that some intestines help food, it follows that if current research focuses on the life history and feeding habits of estuarine fishes, then if the statement, if it is not true that chlorine is virtually ineffective on crypto at levels typically used for disinfection, then if most tarsiers have fur, then cloves are used in cooking, whole or ground, does not hold, then the statement, green tea produces a yellowish-green brew and is milder tasting than black teas, does not hold. Should it be the case that education systems are, of course, closely related to national cultures and identities, it follows that if current research focuses on the life history and feeding habits of estuarine fishes, then if the statement, if it is not true that chlorine is virtually ineffective on crypto at levels typically used for disinfection, then if most tarsiers have fur, then cloves are used in cooking, whole or ground, does not hold, then the statement, green tea produces a yellowish-green brew and is milder tasting than black teas, does not hold. It is rational to believe that either sperm competition is responsible for many sexually selected traits in gastropods or some organisms use cilia. If sperm competition is responsible for many sexually selected traits in gastropods, then many people believe in reincarnation . One may reasonably assume that if some organisms use cilia, then if weak points are liabilities, then green tea produces a yellowish-green brew and is milder tasting than black teas.
|
The idea that chlorine is virtually ineffective on crypto at levels typically used for disinfection is true.
|
Chlorine is also important in the manufacture of paints, aerosol propellants and plastics.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then (If [1], then [2].). [SC1-1]
If (Not [0].), then (Not (If [1], then [2].).).
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then (If [1], then [2].).).), then [3]. [SC1-2]
If (Not (If (Not [0].), then (If [1], then [2].).).), then (Not [3].). [SC2-2]
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC1-2]
Hypothetical Syllogism:
If (Not (If (Not [0].), then (If [1], then [2].).).), then [5].
If [5], then [3]. [SC2-3]
Therefore, If (Not (If (Not [0].), then (If [1], then [2].).).), then [3]..
[SC2-3]
Disjunctive Syllogism:
Either [8] or (If [5], then [3].). [SC1-4]
Not [8].
Therefore, If [5], then [3]..
[SC1-4]
Constructive Dilemma:
Either [9] or [10].
If [9], then [8].
If [10], then (If [5], then [3].).
Therefore, Either [8] or (If [5], then [3].)..
[SC2-2]
Modus Ponens:
If [4], then (If (Not (If (Not [0].), then (If [1], then [2].).).), then (Not [3].).). [SC1-3]
[4]
Therefore, If (Not (If (Not [0].), then (If [1], then [2].).).), then (Not [3].)..
[SC1-3]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If [4], then (If (Not (If (Not [0].), then (If [1], then [2].).).), then (Not [3].).).).
If [7], then (If [4], then (If (Not (If (Not [0].), then (If [1], then [2].).).), then (Not [3].).).).
Therefore, If [4], then (If (Not (If (Not [0].), then (If [1], then [2].).).), then (Not [3].).)..
|
{0: 'Chlorine is virtually ineffective on crypto at levels typically used for disinfection.', 1: 'Most tarsiers have fur.', 2: 'Cloves are used in cooking, whole or ground.', 3: 'Green tea produces a yellowish-green brew and is milder tasting than black teas.', 4: 'Current research focuses on the life history and feeding habits of estuarine fishes.', 5: 'Weak points are liabilities.', 6: 'Some intestines help food.', 7: 'Education systems are, of course, closely related to national cultures and identities.', 8: 'Many people believe in reincarnation .', 9: 'Sperm competition is responsible for many sexually selected traits in gastropods.', 10: 'Some organisms use cilia.'}
| 7 |
6,825 |
['Assuming the claim that most large particles have structures does not correspond with reality, we know that some insects eat matter.', 'Once we know some insects eat matter, we also know that either meanness is evil or some bikes have windshields.', "Whenever it is true that some insects eat matter, 'sports are athletes' is true.", 'The claim that evidence shows contribute factors holds true.', "Given that the statement 'if evidence shows contribute factors, then if sports are athletes, then the claim that either meanness is evil or some bikes have windshields has no merit' can be considered false, it can be inferred that the claim that sighting produces bias does not reflect reality.", "It is a fact that either most hornets survive heat or if the statement 'if evidence shows contribute factors, then if sports are athletes, then the claim that either meanness is evil or some bikes have windshields has no merit' can be considered false, then sighting produces bias.", 'Provided that most hornets survive heat, we know that more muscles help with bladder control.', 'If most hornets survive heat, then the claim that more muscles help with bladder control is false.']
|
Assuming the claim that most large particles have structures does not correspond with reality, we know that some insects eat matter. Once we know some insects eat matter, we also know that either meanness is evil or some bikes have windshields. Whenever it is true that some insects eat matter, 'sports are athletes' is true. The claim that evidence shows contribute factors holds true. Given that the statement 'if evidence shows contribute factors, then if sports are athletes, then the claim that either meanness is evil or some bikes have windshields has no merit' can be considered false, it can be inferred that the claim that sighting produces bias does not reflect reality. It is a fact that either most hornets survive heat or if the statement 'if evidence shows contribute factors, then if sports are athletes, then the claim that either meanness is evil or some bikes have windshields has no merit' can be considered false, then sighting produces bias. Provided that most hornets survive heat, we know that more muscles help with bladder control. If most hornets survive heat, then the claim that more muscles help with bladder control is false.
|
Many people rightly believe that most large particles have structures.
|
Some people mistakenly believe that most large particles have structures.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If [1], then (Either [2] or [3].).
If [1], then (Not (Either [2] or [3].).). [SC2-2]
Therefore, Not [1]..
[SC2-2]
Hypothetical Syllogism:
If [1], then [4].
If [4], then (Not (Either [2] or [3].).). [SC2-3]
Therefore, If [1], then (Not (Either [2] or [3].).)..
[SC2-3]
Modus Ponens:
If [5], then (If [4], then (Not (Either [2] or [3].).).). [SC1-4]
[5]
Therefore, If [4], then (Not (Either [2] or [3].).)..
[SC1-4]
Reductio Ad Absurdum:
If (Not (If [5], then (If [4], then (Not (Either [2] or [3].).).).).), then [6]. [SC1-5]
If (Not (If [5], then (If [4], then (Not (Either [2] or [3].).).).).), then (Not [6].).
Therefore, If [5], then (If [4], then (Not (Either [2] or [3].).).)..
[SC1-5]
Disjunctive Syllogism:
Either [7] or (If (Not (If [5], then (If [4], then (Not (Either [2] or [3].).).).).), then [6].).
Not [7]. [SC2-6]
Therefore, If (Not (If [5], then (If [4], then (Not (Either [2] or [3].).).).).), then [6]..
[SC2-6]
Reductio Ad Absurdum:
If [7], then [8].
If [7], then (Not [8].).
Therefore, Not [7]..
|
{0: 'Most large particles have structures.', 1: 'Some insects eat matter.', 2: 'Meanness is evil.', 3: 'Some bikes have windshields.', 4: 'Sports are athletes.', 5: 'Evidence shows contribute factors.', 6: 'Sighting produces bias.', 7: 'Most hornets survive heat.', 8: 'More muscles help with bladder control.'}
| 7 |
6,056 |
['It is a common misconception that perfection is the clerkly way of doing things.', "Whenever it is true that sole mothers risk poverty both on pensions and in the workforce, 'human beings form social systems' is true.", 'Given that the claim that if human beings form social systems, then perfection is the clerkly way of doing things is false, it can be inferred that asthma attacks are when the bronchial tubes tighten and a lake of breath occurs.', 'Should it be the case that the claim that if most scientific calculators have a key for converting easily between polar and rectangular forms, then if the claim that if human beings form social systems, then perfection is the clerkly way of doing things is false, then we know that the claim that asthma attacks are when the bronchial tubes tighten and a lake of breath occurs is false has no merit, it follows that web catalogs are database that are compiled from the web and stored on the web site.', "Assuming the claim that if most scientific calculators have a key for converting easily between polar and rectangular forms, then if the claim that if human beings form social systems, then perfection is the clerkly way of doing things is false, then we know that the claim that asthma attacks are when the bronchial tubes tighten and a lake of breath occurs is false has no merit, we know that the notion that 'web catalogs are database that are compiled from the web and stored on the web site' is untrue.", 'It is not true that either some metaphase is part of meiosis or mothers experience deliveries.', 'It is a fact that either women have options or telomeres form large loop structures called telomere loops, or T-loops.', 'Should it be the case that women have options, it follows that either either some metaphase is part of meiosis or mothers experience deliveries or most scientific calculators have a key for converting easily between polar and rectangular forms.', 'Once we know telomeres form large loop structures called telomere loops, or T-loops, we also know that either either some metaphase is part of meiosis or mothers experience deliveries or most scientific calculators have a key for converting easily between polar and rectangular forms.']
|
It is a common misconception that perfection is the clerkly way of doing things. Whenever it is true that sole mothers risk poverty both on pensions and in the workforce, 'human beings form social systems' is true. Given that the claim that if human beings form social systems, then perfection is the clerkly way of doing things is false, it can be inferred that asthma attacks are when the bronchial tubes tighten and a lake of breath occurs. Should it be the case that the claim that if most scientific calculators have a key for converting easily between polar and rectangular forms, then if the claim that if human beings form social systems, then perfection is the clerkly way of doing things is false, then we know that the claim that asthma attacks are when the bronchial tubes tighten and a lake of breath occurs is false has no merit, it follows that web catalogs are database that are compiled from the web and stored on the web site. Assuming the claim that if most scientific calculators have a key for converting easily between polar and rectangular forms, then if the claim that if human beings form social systems, then perfection is the clerkly way of doing things is false, then we know that the claim that asthma attacks are when the bronchial tubes tighten and a lake of breath occurs is false has no merit, we know that the notion that 'web catalogs are database that are compiled from the web and stored on the web site' is untrue. It is not true that either some metaphase is part of meiosis or mothers experience deliveries. It is a fact that either women have options or telomeres form large loop structures called telomere loops, or T-loops. Should it be the case that women have options, it follows that either either some metaphase is part of meiosis or mothers experience deliveries or most scientific calculators have a key for converting easily between polar and rectangular forms. Once we know telomeres form large loop structures called telomere loops, or T-loops, we also know that either either some metaphase is part of meiosis or mothers experience deliveries or most scientific calculators have a key for converting easily between polar and rectangular forms.
|
Some people mistakenly believe that sole mothers risk poverty both on pensions and in the workforce.
|
It is the case that sole mothers risk poverty both on pensions and in the workforce.
|
FALSE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Hypothetical Syllogism:
If [0], then [2].
If [2], then [1]. [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [2], then [1].).), then [3].
If (Not (If [2], then [1].).), then (Not [3].). [SC2-3]
Therefore, If [2], then [1]..
[SC2-3]
Modus Ponens:
If [4], then (If (Not (If [2], then [1].).), then (Not [3].).). [SC1-4]
[4] [SC2-4]
Therefore, If (Not (If [2], then [1].).), then (Not [3].)..
[SC1-4]
Reductio Ad Absurdum:
If (Not (If [4], then (If (Not (If [2], then [1].).), then (Not [3].).).).), then [7].
If (Not (If [4], then (If (Not (If [2], then [1].).), then (Not [3].).).).), then (Not [7].).
Therefore, If [4], then (If (Not (If [2], then [1].).), then (Not [3].).)..
[SC2-4]
Disjunctive Syllogism:
Either (Either [5] or [6].) or [4]. [SC1-5]
Not (Either [5] or [6].).
Therefore, [4].
[SC1-5]
Disjunction Elimination:
Either [8] or [9].
If [8], then (Either (Either [5] or [6].) or [4].).
If [9], then (Either (Either [5] or [6].) or [4].).
Therefore, Either (Either [5] or [6].) or [4]..
|
{0: 'Sole mothers risk poverty both on pensions and in the workforce.', 1: 'Perfection is the clerkly way of doing things.', 2: 'Human beings form social systems.', 3: 'Asthma attacks are when the bronchial tubes tighten and a lake of breath occurs.', 4: 'Most scientific calculators have a key for converting easily between polar and rectangular forms.', 5: 'Some metaphase is part of meiosis.', 6: 'Mothers experience deliveries.', 7: 'Web catalogs are database that are compiled from the web and stored on the web site.', 8: 'Women have options.', 9: 'Telomeres form large loop structures called telomere loops, or T-loops.'}
| 7 |
6,400 |
['Some people mistakenly believe that surface tension has the dimension of force per unit length , or of energy per unit area .', "Should it be the case that most fiber helps bacterium levels, it follows that if the notion that 'plants provide habitat for animals' is untrue, then surface tension has the dimension of force per unit length , or of energy per unit area .", 'On the condition that the claim that either either ciliates have a gullet and a contractile vacuole which is used to regulate water balance or atheism is a non prophet organisation or most fiber helps bacterium levels does not reflect reality, it is definitely the case that some goldeneyes eat insects.', 'It is not true that some goldeneyes eat insects.', "Should it be the case that the statement, if either ciliates have a gullet and a contractile vacuole which is used to regulate water balance or atheism is a non prophet organisation, then if the notion that 'plants provide habitat for animals' is untrue, then surface tension has the dimension of force per unit length , or of energy per unit area , does not hold, it follows that if china is still one of the world leaders in the tea industry today, then triggerfish have (part) cytoplasm.", 'If if china is still one of the world leaders in the tea industry today, then triggerfish have (part) cytoplasm, then destruction can occur from both natural and human causes.', 'It is rational to believe that either spectrum lines are part of spectrums or some mammals find along coasts.', "Whenever it is true that some mammals find along coasts, 'the statement that states destruction can occur from both natural and human causes is false' is true.", 'When raw opium is placed in an open cooking pot of boiling water is true, it follows that if spectrum lines are part of spectrums, then the statement that states destruction can occur from both natural and human causes is false.', 'We can assume that raw opium is placed in an open cooking pot of boiling water.']
|
Some people mistakenly believe that surface tension has the dimension of force per unit length , or of energy per unit area . Should it be the case that most fiber helps bacterium levels, it follows that if the notion that 'plants provide habitat for animals' is untrue, then surface tension has the dimension of force per unit length , or of energy per unit area . On the condition that the claim that either either ciliates have a gullet and a contractile vacuole which is used to regulate water balance or atheism is a non prophet organisation or most fiber helps bacterium levels does not reflect reality, it is definitely the case that some goldeneyes eat insects. It is not true that some goldeneyes eat insects. Should it be the case that the statement, if either ciliates have a gullet and a contractile vacuole which is used to regulate water balance or atheism is a non prophet organisation, then if the notion that 'plants provide habitat for animals' is untrue, then surface tension has the dimension of force per unit length , or of energy per unit area , does not hold, it follows that if china is still one of the world leaders in the tea industry today, then triggerfish have (part) cytoplasm. If if china is still one of the world leaders in the tea industry today, then triggerfish have (part) cytoplasm, then destruction can occur from both natural and human causes. It is rational to believe that either spectrum lines are part of spectrums or some mammals find along coasts. Whenever it is true that some mammals find along coasts, 'the statement that states destruction can occur from both natural and human causes is false' is true. When raw opium is placed in an open cooking pot of boiling water is true, it follows that if spectrum lines are part of spectrums, then the statement that states destruction can occur from both natural and human causes is false. We can assume that raw opium is placed in an open cooking pot of boiling water.
|
Many people rightly believe that plants provide habitat for animals.
|
Many people rightly believe that plants provide habitat for animals.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [2] or [3].) or [4]. [SC1-2]
If (Either [2] or [3].), then (If (Not [0].), then [1].). [SC2-2]
If [4], then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Tonens:
If (Not (Either (Either [2] or [3].) or [4].).), then [6].
Not [6].
Therefore, Either (Either [2] or [3].) or [4]..
[SC2-2]
Modus Tonens:
If (Not (If (Either [2] or [3].), then (If (Not [0].), then [1].).).), then [5]. [SC1-3]
Not [5]. [SC2-3]
Therefore, If (Either [2] or [3].), then (If (Not [0].), then [1].)..
[SC1-3]
Hypothetical Syllogism:
If (Not (If (Either [2] or [3].), then (If (Not [0].), then [1].).).), then (If [7], then [8].).
If (If [7], then [8].), then [5].
Therefore, If (Not (If (Either [2] or [3].), then (If (Not [0].), then [1].).).), then [5]..
[SC2-3]
Disjunction Elimination:
Either [9] or [10].
If [9], then (Not [5].). [SC2-4]
If [10], then (Not [5].).
Therefore, Not [5]..
[SC2-4]
Modus Ponens:
If [11], then (If [9], then (Not [5].).).
[11]
Therefore, If [9], then (Not [5].)..
|
{0: 'Plants provide habitat for animals.', 1: 'Surface tension has the dimension of force per unit length , or of energy per unit area .', 2: 'Ciliates have a gullet and a contractile vacuole which is used to regulate water balance.', 3: 'Atheism is a non prophet organisation.', 4: 'Most fiber helps bacterium levels.', 5: 'Destruction can occur from both natural and human causes.', 6: 'Some goldeneyes eat insects.', 7: 'China is still one of the world leaders in the tea industry today.', 8: 'Triggerfish have (part) cytoplasm.', 9: 'Spectrum lines are part of spectrums.', 10: 'Some mammals find along coasts.', 11: 'Raw opium is placed in an open cooking pot of boiling water.'}
| 7 |
6,572 |
['The statement that states notebooks are laptop computers that weigh between five and seven pounds is right.', 'The claim that flat feet are fairly normal in infants and toddlers is false.', 'At least one of two things is true: laurels are the most common family of trees in the forest, or hermit crabs are nocturnal.', "So long as the claim that if the notion that 'if the statement that states if notebooks are laptop computers that weigh between five and seven pounds, then petal blight is caused by an airborne fungus which over-winters on the spent flowers is false, then diarrhea is really deadly for guinea pigs' is untrue, then flat feet are fairly normal in infants and toddlers is false, 'opossums also eat considerable amounts of vegetable matter, especially fruits and grains' is true.", "If the claim that if the notion that 'if the statement that states if notebooks are laptop computers that weigh between five and seven pounds, then petal blight is caused by an airborne fungus which over-winters on the spent flowers is false, then diarrhea is really deadly for guinea pigs' is untrue, then flat feet are fairly normal in infants and toddlers is false, then the statement 'opossums also eat considerable amounts of vegetable matter, especially fruits and grains' can be considered false.", "Provided that chronic headaches can virtually destroy families and relationships, we know that if laurels are the most common family of trees in the forest, then if the statement that states if notebooks are laptop computers that weigh between five and seven pounds, then petal blight is caused by an airborne fungus which over-winters on the spent flowers is false, then the statement that 'diarrhea is really deadly for guinea pigs' is incorrect.", 'Those that suggest chronic headaches can virtually destroy families and relationships are right.', "Once we know the statement that 'if hermit crabs are nocturnal, then if the statement that states if notebooks are laptop computers that weigh between five and seven pounds, then petal blight is caused by an airborne fungus which over-winters on the spent flowers is false, then the statement that 'diarrhea is really deadly for guinea pigs' is incorrect' is incorrect, we also know that antimicrobial resistance can reduce the power of once life-saving medicines to that of a sugar pill.", 'Those that suggest antimicrobial resistance can reduce the power of once life-saving medicines to that of a sugar pill are wrong.']
|
The statement that states notebooks are laptop computers that weigh between five and seven pounds is right. The claim that flat feet are fairly normal in infants and toddlers is false. At least one of two things is true: laurels are the most common family of trees in the forest, or hermit crabs are nocturnal. So long as the claim that if the notion that 'if the statement that states if notebooks are laptop computers that weigh between five and seven pounds, then petal blight is caused by an airborne fungus which over-winters on the spent flowers is false, then diarrhea is really deadly for guinea pigs' is untrue, then flat feet are fairly normal in infants and toddlers is false, 'opossums also eat considerable amounts of vegetable matter, especially fruits and grains' is true. If the claim that if the notion that 'if the statement that states if notebooks are laptop computers that weigh between five and seven pounds, then petal blight is caused by an airborne fungus which over-winters on the spent flowers is false, then diarrhea is really deadly for guinea pigs' is untrue, then flat feet are fairly normal in infants and toddlers is false, then the statement 'opossums also eat considerable amounts of vegetable matter, especially fruits and grains' can be considered false. Provided that chronic headaches can virtually destroy families and relationships, we know that if laurels are the most common family of trees in the forest, then if the statement that states if notebooks are laptop computers that weigh between five and seven pounds, then petal blight is caused by an airborne fungus which over-winters on the spent flowers is false, then the statement that 'diarrhea is really deadly for guinea pigs' is incorrect. Those that suggest chronic headaches can virtually destroy families and relationships are right. Once we know the statement that 'if hermit crabs are nocturnal, then if the statement that states if notebooks are laptop computers that weigh between five and seven pounds, then petal blight is caused by an airborne fungus which over-winters on the spent flowers is false, then the statement that 'diarrhea is really deadly for guinea pigs' is incorrect' is incorrect, we also know that antimicrobial resistance can reduce the power of once life-saving medicines to that of a sugar pill. Those that suggest antimicrobial resistance can reduce the power of once life-saving medicines to that of a sugar pill are wrong.
|
It is fair to say that petal blight is caused by an airborne fungus which over-winters on the spent flowers.
|
The statement that 'petal blight is caused by an airborne fungus which over-winters on the spent flowers' is incorrect.
|
FALSE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [1], then [0].).), then [2]. [SC1-2]
If (Not (If [1], then [0].).), then (Not [2].). [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Modus Tonens:
If (Not (If (Not (If [1], then [0].).), then [2].).), then [3]. [SC1-3]
Not [3].
Therefore, If (Not (If [1], then [0].).), then [2]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not (If [1], then [0].).), then [2].).), then [3].).), then [7].
If (Not (If (Not (If (Not (If [1], then [0].).), then [2].).), then [3].).), then (Not [7].).
Therefore, If (Not (If (Not (If [1], then [0].).), then [2].).), then [3]..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not (If [1], then [0].).), then (Not [2].).). [SC2-3]
If [5], then (If (Not (If [1], then [0].).), then (Not [2].).). [SC3-3]
Therefore, If (Not (If [1], then [0].).), then (Not [2].)..
[SC2-3]
Modus Ponens:
If [6], then (If [4], then (If (Not (If [1], then [0].).), then (Not [2].).).).
[6]
Therefore, If [4], then (If (Not (If [1], then [0].).), then (Not [2].).)..
[SC3-3]
Modus Tonens:
If (Not (If [5], then (If (Not (If [1], then [0].).), then (Not [2].).).).), then [8].
Not [8].
Therefore, If [5], then (If (Not (If [1], then [0].).), then (Not [2].).)..
|
{0: 'Petal blight is caused by an airborne fungus which over-winters on the spent flowers.', 1: 'Notebooks are laptop computers that weigh between five and seven pounds.', 2: 'Diarrhea is really deadly for guinea pigs.', 3: 'Flat feet are fairly normal in infants and toddlers.', 4: 'Laurels are the most common family of trees in the forest.', 5: 'Hermit crabs are nocturnal.', 6: 'Chronic headaches can virtually destroy families and relationships.', 7: 'Opossums also eat considerable amounts of vegetable matter, especially fruits and grains.', 8: 'Antimicrobial resistance can reduce the power of once life-saving medicines to that of a sugar pill.'}
| 7 |
6,473 |
['Either one or both of these statements are true: vegetation cover is affected by building facilities for and path damage, or either sugar builds up in the blood to high levels or liquids are located in cups.', 'One may reasonably assume that if vegetation cover is affected by building facilities for and path damage, then some people mistakenly believe that television is located in living rooms.', 'Should it be the case that either sugar builds up in the blood to high levels or liquids are located in cups, it follows that life cycles vary by species.', 'Once we know life cycles vary by species, we also know that tree frogs are frogs.', 'On the condition that genetic variability exists between all individuals to one degree or another, it is definitely the case that if tree frogs are frogs, then culture is growth.', 'It is reasonable to believe that genetic variability exists between all individuals to one degree or another.', 'Once we know chemical weapons fly, everything from deadly gas to poison powders, we also know that if culture is growth, then some people mistakenly believe that television is located in living rooms.', 'Provided that chrysotile asbestos is the main cause of pleural mesothelioma, we know that if culture is growth, then some people mistakenly believe that television is located in living rooms.', 'If the claim that either chemical weapons fly, everything from deadly gas to poison powders or chrysotile asbestos is the main cause of pleural mesothelioma has no merit, then either people are most likely to be exposed to methyl mercury through eating contaminated fish or prophets are the last word throughout the Bible.', 'It is a common misconception that either people are most likely to be exposed to methyl mercury through eating contaminated fish or prophets are the last word throughout the Bible.']
|
Either one or both of these statements are true: vegetation cover is affected by building facilities for and path damage, or either sugar builds up in the blood to high levels or liquids are located in cups. One may reasonably assume that if vegetation cover is affected by building facilities for and path damage, then some people mistakenly believe that television is located in living rooms. Should it be the case that either sugar builds up in the blood to high levels or liquids are located in cups, it follows that life cycles vary by species. Once we know life cycles vary by species, we also know that tree frogs are frogs. On the condition that genetic variability exists between all individuals to one degree or another, it is definitely the case that if tree frogs are frogs, then culture is growth. It is reasonable to believe that genetic variability exists between all individuals to one degree or another. Once we know chemical weapons fly, everything from deadly gas to poison powders, we also know that if culture is growth, then some people mistakenly believe that television is located in living rooms. Provided that chrysotile asbestos is the main cause of pleural mesothelioma, we know that if culture is growth, then some people mistakenly believe that television is located in living rooms. If the claim that either chemical weapons fly, everything from deadly gas to poison powders or chrysotile asbestos is the main cause of pleural mesothelioma has no merit, then either people are most likely to be exposed to methyl mercury through eating contaminated fish or prophets are the last word throughout the Bible. It is a common misconception that either people are most likely to be exposed to methyl mercury through eating contaminated fish or prophets are the last word throughout the Bible.
|
Some people mistakenly believe that television is located in living rooms.
|
The statement that states television has a way of making everything appear smaller than real life is false.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].).
If [1], then (Not [0].).
If (Either [2] or [3].), then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC3-1]
Hypothetical Syllogism:
If (Either [2] or [3].), then [4]. [SC1-2]
If [4], then (Not [0].). [SC2-2]
Therefore, If (Either [2] or [3].), then (Not [0].)..
[SC1-2]
Hypothetical Syllogism:
If (Either [2] or [3].), then [5].
If [5], then [4].
Therefore, If (Either [2] or [3].), then [4]..
[SC2-2]
Hypothetical Syllogism:
If [4], then [6]. [SC1-3]
If [6], then (Not [0].). [SC2-3]
Therefore, If [4], then (Not [0].)..
[SC1-3]
Modus Ponens:
If [7], then (If [4], then [6].).
[7]
Therefore, If [4], then [6]..
[SC2-3]
Disjunction Elimination:
Either [8] or [9]. [SC1-4]
If [8], then (If [6], then (Not [0].).).
If [9], then (If [6], then (Not [0].).).
Therefore, If [6], then (Not [0].)..
[SC1-4]
Modus Tonens:
If (Not (Either [8] or [9].).), then (Either [10] or [11].).
Not (Either [10] or [11].).
Therefore, Either [8] or [9]..
|
{0: 'Television is located in living rooms.', 1: 'Vegetation cover is affected by building facilities for and path damage.', 2: 'Sugar builds up in the blood to high levels.', 3: 'Liquids are located in cups.', 4: 'Tree frogs are frogs.', 5: 'Life cycles vary by species.', 6: 'Culture is growth.', 7: 'Genetic variability exists between all individuals to one degree or another.', 8: 'Chemical weapons fly, everything from deadly gas to poison powders.', 9: 'Chrysotile asbestos is the main cause of pleural mesothelioma.', 10: 'People are most likely to be exposed to methyl mercury through eating contaminated fish.', 11: 'Prophets are the last word throughout the Bible.'}
| 7 |
6,468 |
["Whenever it is true that it is not true that threats are warning, 'either hypnosis is a technique in which an individual s susceptibility to suggestion is heightened or praseodymium is a silvery rare-earth metal that is soft, malleable and ductile' is true.", 'It is a fact that either details are facts or american foods have their origins in other culture.', 'Provided that american foods have their origins in other culture, we know that if it is not true that threats are warning, then the claim that either hypnosis is a technique in which an individual s susceptibility to suggestion is heightened or praseodymium is a silvery rare-earth metal that is soft, malleable and ductile does not correspond with reality.', 'Provided that the claim that if details are facts, then if it is not true that threats are warning, then the claim that either hypnosis is a technique in which an individual s susceptibility to suggestion is heightened or praseodymium is a silvery rare-earth metal that is soft, malleable and ductile does not correspond with reality does not correspond with reality, we know that some people mistakenly believe that darkness never dispels light.', 'One may reasonably assume that if mumps is an acute infectious disease, then acne affects adolescents at a time they are developing their personalities.', "So long as acne affects adolescents at a time they are developing their personalities, 'if the claim that if details are facts, then if it is not true that threats are warning, then the claim that either hypnosis is a technique in which an individual s susceptibility to suggestion is heightened or praseodymium is a silvery rare-earth metal that is soft, malleable and ductile does not correspond with reality does not correspond with reality, then darkness never dispels light' is true.", 'It is reasonable to believe that many companies have policies that discourage their employees from giving or receiving gifts.', 'We know that either frequent harvesting is the key to keeping mint plants at their best or if many companies have policies that discourage their employees from giving or receiving gifts, then mumps is an acute infectious disease.', 'Those that suggest frequent harvesting is the key to keeping mint plants at their best are wrong.']
|
Whenever it is true that it is not true that threats are warning, 'either hypnosis is a technique in which an individual s susceptibility to suggestion is heightened or praseodymium is a silvery rare-earth metal that is soft, malleable and ductile' is true. It is a fact that either details are facts or american foods have their origins in other culture. Provided that american foods have their origins in other culture, we know that if it is not true that threats are warning, then the claim that either hypnosis is a technique in which an individual s susceptibility to suggestion is heightened or praseodymium is a silvery rare-earth metal that is soft, malleable and ductile does not correspond with reality. Provided that the claim that if details are facts, then if it is not true that threats are warning, then the claim that either hypnosis is a technique in which an individual s susceptibility to suggestion is heightened or praseodymium is a silvery rare-earth metal that is soft, malleable and ductile does not correspond with reality does not correspond with reality, we know that some people mistakenly believe that darkness never dispels light. One may reasonably assume that if mumps is an acute infectious disease, then acne affects adolescents at a time they are developing their personalities. So long as acne affects adolescents at a time they are developing their personalities, 'if the claim that if details are facts, then if it is not true that threats are warning, then the claim that either hypnosis is a technique in which an individual s susceptibility to suggestion is heightened or praseodymium is a silvery rare-earth metal that is soft, malleable and ductile does not correspond with reality does not correspond with reality, then darkness never dispels light' is true. It is reasonable to believe that many companies have policies that discourage their employees from giving or receiving gifts. We know that either frequent harvesting is the key to keeping mint plants at their best or if many companies have policies that discourage their employees from giving or receiving gifts, then mumps is an acute infectious disease. Those that suggest frequent harvesting is the key to keeping mint plants at their best are wrong.
|
We can assume that threats are warning.
|
We can assume that threats are warning.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then (Either [1] or [2].).
If (Not [0].), then (Not (Either [1] or [2].).). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If (Not [0].), then (Not (Either [1] or [2].).).). [SC2-2]
If [4], then (If (Not [0].), then (Not (Either [1] or [2].).).).
Therefore, If (Not [0].), then (Not (Either [1] or [2].).)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [3], then (If (Not [0].), then (Not (Either [1] or [2].).).).).), then [5]. [SC1-3]
If (Not (If [3], then (If (Not [0].), then (Not (Either [1] or [2].).).).).), then (Not [5].).
Therefore, If [3], then (If (Not [0].), then (Not (Either [1] or [2].).).)..
[SC1-3]
Modus Ponens:
If [6], then (If (Not (If [3], then (If (Not [0].), then (Not (Either [1] or [2].).).).).), then [5].). [SC1-4]
[6] [SC2-4]
Therefore, If (Not (If [3], then (If (Not [0].), then (Not (Either [1] or [2].).).).).), then [5]..
[SC1-4]
Hypothetical Syllogism:
If [6], then [7].
If [7], then (If (Not (If [3], then (If (Not [0].), then (Not (Either [1] or [2].).).).).), then [5].).
Therefore, If [6], then (If (Not (If [3], then (If (Not [0].), then (Not (Either [1] or [2].).).).).), then [5].)..
[SC2-4]
Modus Ponens:
If [8], then [6]. [SC1-5]
[8]
Therefore, [6].
[SC1-5]
Disjunctive Syllogism:
Either [9] or (If [8], then [6].).
Not [9].
Therefore, If [8], then [6]..
|
{0: 'Threats are warning.', 1: 'Hypnosis is a technique in which an individual s susceptibility to suggestion is heightened.', 2: 'Praseodymium is a silvery rare-earth metal that is soft, malleable and ductile.', 3: 'Details are facts.', 4: 'American foods have their origins in other culture.', 5: 'Darkness never dispels light.', 6: 'Mumps is an acute infectious disease.', 7: 'Acne affects adolescents at a time they are developing their personalities.', 8: 'Many companies have policies that discourage their employees from giving or receiving gifts.', 9: 'Frequent harvesting is the key to keeping mint plants at their best.'}
| 7 |
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