id
int64 0
7k
| premises
stringlengths 118
4.1k
| paragraph
stringlengths 111
4.06k
| conclusion
stringlengths 15
240
| question
stringlengths 14
249
| label
stringclasses 3
values | arg
stringlengths 54
2.02k
| statements
stringlengths 51
1.12k
| depth
int64 1
7
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|---|---|---|---|---|---|---|---|---|
2,651 |
["So long as the claim that either entertainment plays an important role in every community or most mulches help to keep soil surfaces loose and receptive to water absorption has no merit, 'bluebird isa bird' is true.", 'On the condition that the claim that either entertainment plays an important role in every community or most mulches help to keep soil surfaces loose and receptive to water absorption has no merit, it is definitely the case that the statement that states bluebird isa bird is false.', 'We know that at least one of two things is true: trees have density, or networks occur when computer systems are connected together.', "Should it be the case that trees have density, it follows that the statement 'entertainment plays an important role in every community' can be considered false.", "Given that networks occur when computer systems are connected together, it can be inferred that the statement 'entertainment plays an important role in every community' can be considered false."]
|
So long as the claim that either entertainment plays an important role in every community or most mulches help to keep soil surfaces loose and receptive to water absorption has no merit, 'bluebird isa bird' is true. On the condition that the claim that either entertainment plays an important role in every community or most mulches help to keep soil surfaces loose and receptive to water absorption has no merit, it is definitely the case that the statement that states bluebird isa bird is false. We know that at least one of two things is true: trees have density, or networks occur when computer systems are connected together. Should it be the case that trees have density, it follows that the statement 'entertainment plays an important role in every community' can be considered false. Given that networks occur when computer systems are connected together, it can be inferred that the statement 'entertainment plays an important role in every community' can be considered false.
|
The statement 'most mulches help to keep soil surfaces loose and receptive to water absorption' is true.
|
The statement 'most mulches help to keep soil surfaces loose and receptive to water absorption' is true.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or [0].).), then [2].
If (Not (Either [1] or [0].).), then (Not [2].).
Therefore, Either [1] or [0]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not [1].).
If [4], then (Not [1].).
Therefore, Not [1]..
|
{0: 'Most mulches help to keep soil surfaces loose and receptive to water absorption.', 1: 'Entertainment plays an important role in every community.', 2: 'Bluebird isa bird.', 3: 'Trees have density.', 4: 'Networks occur when computer systems are connected together.'}
| 3 |
2,669 |
['At least one of two things is true: attributes are the way information about entities are stored, or excretory products include chemicals.', 'Provided that attributes are the way information about entities are stored, we know that if some people mistakenly believe that some cats die from hunger, then some joints connect lower jaws.', 'On the condition that excretory products include chemicals, it is definitely the case that if some people mistakenly believe that some cats die from hunger, then some joints connect lower jaws.', 'Provided that ants are small, we know that it is a common misconception that some joints connect lower jaws.', 'The claim that ants are small is true.']
|
At least one of two things is true: attributes are the way information about entities are stored, or excretory products include chemicals. Provided that attributes are the way information about entities are stored, we know that if some people mistakenly believe that some cats die from hunger, then some joints connect lower jaws. On the condition that excretory products include chemicals, it is definitely the case that if some people mistakenly believe that some cats die from hunger, then some joints connect lower jaws. Provided that ants are small, we know that it is a common misconception that some joints connect lower jaws. The claim that ants are small is true.
|
It is the case that some cats die from hunger.
|
It is the case that some cats die from hunger.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If (Not [0].), then [1].).
If [3], then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Modus Ponens:
If [4], then (Not [1].).
[4]
Therefore, Not [1]..
|
{0: 'Some cats die from hunger.', 1: 'Some joints connect lower jaws.', 2: 'Attributes are the way information about entities are stored.', 3: 'Excretory products include chemicals.', 4: 'Ants are small.'}
| 3 |
2,504 |
['If outdoor roaches are called feral cockroaches, then pollution is also a factor in the environmental destructiveness of coca and poppy cultivation.', "Whenever it is true that the statement 'outdoor roaches are called feral cockroaches' can be considered false, 'the claim that hexane is liquids is false' is true.", "If if most bugs go through nymph stages, then slate is tablets, then if the statement 'outdoor roaches are called feral cockroaches' can be considered false, then hexane is liquids.", 'Should it be the case that most bugs go through nymph stages, it follows that slate is tablets.']
|
If outdoor roaches are called feral cockroaches, then pollution is also a factor in the environmental destructiveness of coca and poppy cultivation. Whenever it is true that the statement 'outdoor roaches are called feral cockroaches' can be considered false, 'the claim that hexane is liquids is false' is true. If if most bugs go through nymph stages, then slate is tablets, then if the statement 'outdoor roaches are called feral cockroaches' can be considered false, then hexane is liquids. Should it be the case that most bugs go through nymph stages, it follows that slate is tablets.
|
The statement 'pollution is also a factor in the environmental destructiveness of coca and poppy cultivation' is true.
|
The claim that pollution is also a factor in the environmental destructiveness of coca and poppy cultivation is false.
|
FALSE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then [2]. [SC1-2]
If (Not [1].), then (Not [2].).
Therefore, [1].
[SC1-2]
Modus Ponens:
If (If [3], then [4].), then (If (Not [1].), then [2].).
If [3], then [4].
Therefore, If (Not [1].), then [2]..
|
{0: 'Pollution is also a factor in the environmental destructiveness of coca and poppy cultivation.', 1: 'Outdoor roaches are called feral cockroaches.', 2: 'Hexane is liquids.', 3: 'Most bugs go through nymph stages.', 4: 'Slate is tablets.'}
| 3 |
2,900 |
['It is rational to believe that either some bone cells are part of chests or if human hands are body parts, then carbohydrates provide a rapid source of energy while fats can provide a prolonged source of fuel.', 'The statement, some bone cells are part of chests, does not hold.', 'Either shelters give homeless people a place to feel safe and cared about or either a diaper is a garment or radiation dominates the universe.', 'Assuming shelters give homeless people a place to feel safe and cared about, we know that human hands are body parts.', "So long as either a diaper is a garment or radiation dominates the universe, 'human hands are body parts' is true."]
|
It is rational to believe that either some bone cells are part of chests or if human hands are body parts, then carbohydrates provide a rapid source of energy while fats can provide a prolonged source of fuel. The statement, some bone cells are part of chests, does not hold. Either shelters give homeless people a place to feel safe and cared about or either a diaper is a garment or radiation dominates the universe. Assuming shelters give homeless people a place to feel safe and cared about, we know that human hands are body parts. So long as either a diaper is a garment or radiation dominates the universe, 'human hands are body parts' is true.
|
The claim that carbohydrates provide a rapid source of energy while fats can provide a prolonged source of fuel is true.
|
The claim that carbohydrates provide a rapid source of energy while fats can provide a prolonged source of fuel is true.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [5] or (If [1], then [0].).
Not [5].
Therefore, If [1], then [0]..
[SC2-1]
Disjunction Elimination:
Either [2] or (Either [3] or [4].).
If [2], then [1].
If (Either [3] or [4].), then [1].
Therefore, [1].
|
{0: 'Carbohydrates provide a rapid source of energy while fats can provide a prolonged source of fuel.', 1: 'Human hands are body parts.', 2: 'Shelters give homeless people a place to feel safe and cared about.', 3: 'A diaper is a garment.', 4: 'Radiation dominates the universe.', 5: 'Some bone cells are part of chests.'}
| 3 |
2,649 |
['When most regions have climates is true, it follows that nematode infection increases risk of fusarium infection.', 'At least one of two things is true: sex education is the private responsibility of parents, or if traditionalism implies the rejection of modernism , then meerkats have ear bones.', "So long as sex education is the private responsibility of parents, 'either hepatitis associates with infection or most regions have climates' is true.", 'Given that if traditionalism implies the rejection of modernism , then meerkats have ear bones, it can be inferred that either hepatitis associates with infection or most regions have climates.', 'We know that at least one of two things is true: athletes consume meals, or if hepatitis associates with infection, then allergies can be serious when they trigger asthma attacks.', 'It is not the case that athletes consume meals.']
|
When most regions have climates is true, it follows that nematode infection increases risk of fusarium infection. At least one of two things is true: sex education is the private responsibility of parents, or if traditionalism implies the rejection of modernism , then meerkats have ear bones. So long as sex education is the private responsibility of parents, 'either hepatitis associates with infection or most regions have climates' is true. Given that if traditionalism implies the rejection of modernism , then meerkats have ear bones, it can be inferred that either hepatitis associates with infection or most regions have climates. We know that at least one of two things is true: athletes consume meals, or if hepatitis associates with infection, then allergies can be serious when they trigger asthma attacks. It is not the case that athletes consume meals.
|
We know that either allergies can be serious when they trigger asthma attacks or nematode infection increases risk of fusarium infection.
|
It is a common misconception that either allergies can be serious when they trigger asthma attacks or nematode infection increases risk of fusarium infection.
|
FALSE
|
Constructive Dilemma:
Either [2] or [3]. [SC1-1]
If [2], then [0]. [SC2-1]
If [3], then [1].
Therefore, Either [0] or [1]..
[SC1-1]
Disjunction Elimination:
Either [4] or (If [5], then [6].).
If [4], then (Either [2] or [3].).
If (If [5], then [6].), then (Either [2] or [3].).
Therefore, Either [2] or [3]..
[SC2-1]
Disjunctive Syllogism:
Either [7] or (If [2], then [0].).
Not [7].
Therefore, If [2], then [0]..
|
{0: 'Allergies can be serious when they trigger asthma attacks.', 1: 'Nematode infection increases risk of fusarium infection.', 2: 'Hepatitis associates with infection.', 3: 'Most regions have climates.', 4: 'Sex education is the private responsibility of parents.', 5: 'Traditionalism implies the rejection of modernism .', 6: 'Meerkats have ear bones.', 7: 'Athletes consume meals.'}
| 3 |
2,931 |
['Either some vines grow to feet or if the statement, early moisture is the most important for carrot production, does not hold, then if some meat promotes better health, then schizophrenia usually begins with gradual onset during adolescence or young adulthood.', 'The statement, some vines grow to feet, does not hold.', 'On the condition that health observances are days, weeks, or months devoted to promoting particular health concerns, it is definitely the case that the statement, if some meat promotes better health, then schizophrenia usually begins with gradual onset during adolescence or young adulthood, does not hold.', "The statement 'health observances are days, weeks, or months devoted to promoting particular health concerns' is true."]
|
Either some vines grow to feet or if the statement, early moisture is the most important for carrot production, does not hold, then if some meat promotes better health, then schizophrenia usually begins with gradual onset during adolescence or young adulthood. The statement, some vines grow to feet, does not hold. On the condition that health observances are days, weeks, or months devoted to promoting particular health concerns, it is definitely the case that the statement, if some meat promotes better health, then schizophrenia usually begins with gradual onset during adolescence or young adulthood, does not hold. The statement 'health observances are days, weeks, or months devoted to promoting particular health concerns' is true.
|
It is a simple truth that early moisture is the most important for carrot production.
|
It is a simple truth that early moisture is the most important for carrot production.
|
TRUE
|
Modus Tonens:
If (Not [0].), then (If [1], then [2].). [SC1-1]
Not (If [1], then [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [4] or (If (Not [0].), then (If [1], then [2].).).
Not [4].
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC2-1]
Modus Ponens:
If [3], then (Not (If [1], then [2].).).
[3]
Therefore, Not (If [1], then [2].)..
|
{0: 'Early moisture is the most important for carrot production.', 1: 'Some meat promotes better health.', 2: 'Schizophrenia usually begins with gradual onset during adolescence or young adulthood.', 3: 'Health observances are days, weeks, or months devoted to promoting particular health concerns.', 4: 'Some vines grow to feet.'}
| 3 |
2,300 |
['Either one or both of these statements are true: form is a three-dimensional shape, or if most obligate parasites cause diseases, then rabbits open eyes.', 'On the condition that form is a three-dimensional shape, it is definitely the case that some decapods have size.', 'Should it be the case that if most obligate parasites cause diseases, then rabbits open eyes, it follows that some people mistakenly believe that if pepper is one of the most widely used spices and is used to flavor foods, then cancer cachexia is the most common paraneoplastic syndrome in veterinary medicine.', 'If some decapods have size, then either cicadas have large, membranous forewings which easily extend beyond their abdomen or phonological skill is both inherited and learned.', 'We know that the claim that either cicadas have large, membranous forewings which easily extend beyond their abdomen or phonological skill is both inherited and learned is false.']
|
Either one or both of these statements are true: form is a three-dimensional shape, or if most obligate parasites cause diseases, then rabbits open eyes. On the condition that form is a three-dimensional shape, it is definitely the case that some decapods have size. Should it be the case that if most obligate parasites cause diseases, then rabbits open eyes, it follows that some people mistakenly believe that if pepper is one of the most widely used spices and is used to flavor foods, then cancer cachexia is the most common paraneoplastic syndrome in veterinary medicine. If some decapods have size, then either cicadas have large, membranous forewings which easily extend beyond their abdomen or phonological skill is both inherited and learned. We know that the claim that either cicadas have large, membranous forewings which easily extend beyond their abdomen or phonological skill is both inherited and learned is false.
|
Some people mistakenly believe that if pepper is one of the most widely used spices and is used to flavor foods, then cancer cachexia is the most common paraneoplastic syndrome in veterinary medicine.
|
If pepper is one of the most widely used spices and is used to flavor foods, then cancer cachexia is the most common paraneoplastic syndrome in veterinary medicine.
|
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]
Constructive Dilemma:
Either [5] or (If [6], then [7].).
If [5], then [2].
If (If [6], then [7].), then (Not (If [0], then [1].).).
Therefore, Either [2] or (Not (If [0], then [1].).)..
[SC2-1]
Modus Tonens:
If [2], then (Either [3] or [4].).
Not (Either [3] or [4].).
Therefore, Not [2]..
|
{0: 'Pepper is one of the most widely used spices and is used to flavor foods.', 1: 'Cancer cachexia is the most common paraneoplastic syndrome in veterinary medicine.', 2: 'Some decapods have size.', 3: 'Cicadas have large, membranous forewings which easily extend beyond their abdomen.', 4: 'Phonological skill is both inherited and learned.', 5: 'Form is a three-dimensional shape.', 6: 'Most obligate parasites cause diseases.', 7: 'Rabbits open eyes.'}
| 3 |
2,674 |
['We know that at least one of two things is true: male herons begin attracting their mate by building a nest to impress the female, or hypertension is both a disease and risk factor for cardiovascular disease.', "If male herons begin attracting their mate by building a nest to impress the female, then the notion that 'most viral diseases affect domestic animals' is untrue.", 'Either most seed plants have pollen grain or many molecules form by identical atoms bonding together, like oxygen and nitrogen molecules.', 'When most seed plants have pollen grain is true, it follows that if male herons begin attracting their mate by building a nest to impress the female, then most viral diseases affect domestic animals.', 'Should it be the case that many molecules form by identical atoms bonding together, like oxygen and nitrogen molecules, it follows that if male herons begin attracting their mate by building a nest to impress the female, then most viral diseases affect domestic animals.']
|
We know that at least one of two things is true: male herons begin attracting their mate by building a nest to impress the female, or hypertension is both a disease and risk factor for cardiovascular disease. If male herons begin attracting their mate by building a nest to impress the female, then the notion that 'most viral diseases affect domestic animals' is untrue. Either most seed plants have pollen grain or many molecules form by identical atoms bonding together, like oxygen and nitrogen molecules. When most seed plants have pollen grain is true, it follows that if male herons begin attracting their mate by building a nest to impress the female, then most viral diseases affect domestic animals. Should it be the case that many molecules form by identical atoms bonding together, like oxygen and nitrogen molecules, it follows that if male herons begin attracting their mate by building a nest to impress the female, then most viral diseases affect domestic animals.
|
The statement that states hypertension is both a disease and risk factor for cardiovascular disease is right.
|
We know that the claim that hypertension is both a disease and risk factor for cardiovascular disease is false.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2]. [SC1-2]
If [1], then (Not [2].).
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If [1], then [2].).
If [4], then (If [1], then [2].).
Therefore, If [1], then [2]..
|
{0: 'Hypertension is both a disease and risk factor for cardiovascular disease.', 1: 'Male herons begin attracting their mate by building a nest to impress the female.', 2: 'Most viral diseases affect domestic animals.', 3: 'Most seed plants have pollen grain.', 4: 'Many molecules form by identical atoms bonding together, like oxygen and nitrogen molecules.'}
| 3 |
2,665 |
['Assuming we know that the claim that if probability is a probability associated with the chi-squared distribution, then the claim that cognitive algebra is more akin to a theory of competence than a theory of performance does not correspond with reality is false, we know that ethics is the depth, form, and substance of doing business.', 'We know that the claim that ethics is the depth, form, and substance of doing business is false.', 'We know that at least one of two things is true: eagles tend to use the same nests year after year, or earthworms contribute to the growth of plants.', 'When eagles tend to use the same nests year after year is true, it follows that probability is a probability associated with the chi-squared distribution.', 'One may reasonably assume that if earthworms contribute to the growth of plants, then probability is a probability associated with the chi-squared distribution.']
|
Assuming we know that the claim that if probability is a probability associated with the chi-squared distribution, then the claim that cognitive algebra is more akin to a theory of competence than a theory of performance does not correspond with reality is false, we know that ethics is the depth, form, and substance of doing business. We know that the claim that ethics is the depth, form, and substance of doing business is false. We know that at least one of two things is true: eagles tend to use the same nests year after year, or earthworms contribute to the growth of plants. When eagles tend to use the same nests year after year is true, it follows that probability is a probability associated with the chi-squared distribution. One may reasonably assume that if earthworms contribute to the growth of plants, then probability is a probability associated with the chi-squared distribution.
|
The claim that cognitive algebra is more akin to a theory of competence than a theory of performance does not correspond with reality.
|
We know that the claim that cognitive algebra facilitates the identification of antecedent and consequent operational abilities is false.
|
Uncertain
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1] [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (If [1], then (Not [0].).).), then [2].
Not [2].
Therefore, If [1], then (Not [0].)..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then [1].
If [4], then [1].
Therefore, [1].
|
{0: 'Cognitive algebra is more akin to a theory of competence than a theory of performance.', 1: 'Probability is a probability associated with the chi-squared distribution.', 2: 'Ethics is the depth, form, and substance of doing business.', 3: 'Eagles tend to use the same nests year after year.', 4: 'Earthworms contribute to the growth of plants.'}
| 3 |
2,570 |
["It is a fact that either if advertising is a pervasive part of today's society, then a data rate is a rate or if historical sources indicate that demand for rhino horn was significant in the medieval period, then magnetic amoebas repel other magnetic amoebas in a similar fashion.", "When if advertising is a pervasive part of today's society, then a data rate is a rate is true, it follows that if romance novels contain much more explicit sex than mainstream fiction and other fiction genres, then roofing are trade.", 'When if historical sources indicate that demand for rhino horn was significant in the medieval period, then magnetic amoebas repel other magnetic amoebas in a similar fashion is true, it follows that if romance novels contain much more explicit sex than mainstream fiction and other fiction genres, then roofing are trade.', 'If roofing are trade, then some sauces are part of meatballs.', 'The claim that some sauces are part of meatballs does not correspond with reality.']
|
It is a fact that either if advertising is a pervasive part of today's society, then a data rate is a rate or if historical sources indicate that demand for rhino horn was significant in the medieval period, then magnetic amoebas repel other magnetic amoebas in a similar fashion. When if advertising is a pervasive part of today's society, then a data rate is a rate is true, it follows that if romance novels contain much more explicit sex than mainstream fiction and other fiction genres, then roofing are trade. When if historical sources indicate that demand for rhino horn was significant in the medieval period, then magnetic amoebas repel other magnetic amoebas in a similar fashion is true, it follows that if romance novels contain much more explicit sex than mainstream fiction and other fiction genres, then roofing are trade. If roofing are trade, then some sauces are part of meatballs. The claim that some sauces are part of meatballs does not correspond with reality.
|
The claim that romance novels contain much more explicit sex than mainstream fiction and other fiction genres is false.
|
The claim that romance novels contain much more explicit sex than mainstream fiction and other fiction genres is false.
|
TRUE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either (If [3], then [4].) or (If [5], then [6].).
If (If [3], then [4].), then (If [0], then [1].).
If (If [5], then [6].), then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC2-1]
Modus Tonens:
If [1], then [2].
Not [2].
Therefore, Not [1]..
|
{0: 'Romance novels contain much more explicit sex than mainstream fiction and other fiction genres.', 1: 'Roofing are trade.', 2: 'Some sauces are part of meatballs.', 3: "Advertising is a pervasive part of today's society.", 4: 'A data rate is a rate.', 5: 'Historical sources indicate that demand for rhino horn was significant in the medieval period.', 6: 'Magnetic amoebas repel other magnetic amoebas in a similar fashion.'}
| 3 |
2,163 |
["Whenever it is true that r is the set of all real numbers, 'either safe valves allow versility to valve applications in handling a wide variety of applications or xylophones are located in bands' is true.", "Whenever it is true that meteors are part of meteor showers, 'r is the set of all real numbers' is true.", "One may reasonably assume that if lakes are a critically important component of the state's environmental and economic health, then r is the set of all real numbers.", "It is rational to believe that either potato plants have large root sys tems or either meteors are part of meteor showers or lakes are a critically important component of the state's environmental and economic health.", 'Those that suggest potato plants have large root sys tems are wrong.']
|
Whenever it is true that r is the set of all real numbers, 'either safe valves allow versility to valve applications in handling a wide variety of applications or xylophones are located in bands' is true. Whenever it is true that meteors are part of meteor showers, 'r is the set of all real numbers' is true. One may reasonably assume that if lakes are a critically important component of the state's environmental and economic health, then r is the set of all real numbers. It is rational to believe that either potato plants have large root sys tems or either meteors are part of meteor showers or lakes are a critically important component of the state's environmental and economic health. Those that suggest potato plants have large root sys tems are wrong.
|
Either safe valves allow versility to valve applications in handling a wide variety of applications or xylophones are located in bands.
|
The notion that 'either safe valves allow versility to valve applications in handling a wide variety of applications or xylophones are located in bands' is untrue.
|
FALSE
|
Modus Ponens:
If [2], then (Either [0] or [1].).
[2] [SC2-1]
Therefore, Either [0] or [1]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then [2].
If [4], then [2].
Therefore, [2].
[SC1-2]
Disjunctive Syllogism:
Either [5] or (Either [3] or [4].).
Not [5].
Therefore, Either [3] or [4]..
|
{0: 'Safe valves allow versility to valve applications in handling a wide variety of applications.', 1: 'Xylophones are located in bands.', 2: 'R is the set of all real numbers.', 3: 'Meteors are part of meteor showers.', 4: "Lakes are a critically important component of the state's environmental and economic health.", 5: 'Potato plants have large root sys tems.'}
| 3 |
2,336 |
['If arabic designs are generally large, floral patterns on the hands and feet, then triton is slightly bigger than the planet Pluto, which it is thought to resemble.', 'If the claim that if if arabic designs are generally large, floral patterns on the hands and feet, then triton is slightly bigger than the planet Pluto, which it is thought to resemble, then it is not the case that blue whales are mammals has no merit, then mangroves cover much of the shore and coconut palms provide shade.', "One may reasonably assume that if the claim that if the claim that if if arabic designs are generally large, floral patterns on the hands and feet, then triton is slightly bigger than the planet Pluto, which it is thought to resemble, then it is not the case that blue whales are mammals has no merit, then the statement that 'mangroves cover much of the shore and coconut palms provide shade' is incorrect is false, then mastodons have (part) cells.", 'It is not true that mastodons have (part) cells.']
|
If arabic designs are generally large, floral patterns on the hands and feet, then triton is slightly bigger than the planet Pluto, which it is thought to resemble. If the claim that if if arabic designs are generally large, floral patterns on the hands and feet, then triton is slightly bigger than the planet Pluto, which it is thought to resemble, then it is not the case that blue whales are mammals has no merit, then mangroves cover much of the shore and coconut palms provide shade. One may reasonably assume that if the claim that if the claim that if if arabic designs are generally large, floral patterns on the hands and feet, then triton is slightly bigger than the planet Pluto, which it is thought to resemble, then it is not the case that blue whales are mammals has no merit, then the statement that 'mangroves cover much of the shore and coconut palms provide shade' is incorrect is false, then mastodons have (part) cells. It is not true that mastodons have (part) cells.
|
It is not the case that blue whales are mammals.
|
It is not the case that blue whales are mammals.
|
TRUE
|
Modus Ponens:
If (If [1], then [2].), then (Not [0].). [SC1-1]
If [1], then [2].
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (If [1], then [2].), then (Not [0].).).), then [3].
If (Not (If (If [1], then [2].), then (Not [0].).).), then (Not [3].). [SC2-2]
Therefore, If (If [1], then [2].), then (Not [0].)..
[SC2-2]
Modus Tonens:
If (Not (If (Not (If (If [1], then [2].), then (Not [0].).).), then (Not [3].).).), then [4].
Not [4].
Therefore, If (Not (If (If [1], then [2].), then (Not [0].).).), then (Not [3].)..
|
{0: 'Blue whales are mammals.', 1: 'Arabic designs are generally large, floral patterns on the hands and feet.', 2: 'Triton is slightly bigger than the planet Pluto, which it is thought to resemble.', 3: 'Mangroves cover much of the shore and coconut palms provide shade.', 4: 'Mastodons have (part) cells.'}
| 3 |
2,059 |
["If if pilot whales have holes, then soft scales produce honeydew, But hard scales find it impossible to do, then the statement that 'diffusion plays an important role in the movement of materials, but it is a very slow process' is incorrect.", 'Once we know the claim that if if pilot whales have holes, then soft scales produce honeydew, But hard scales find it impossible to do, then diffusion plays an important role in the movement of materials, but it is a very slow process is false, we also know that either lower temperature causes problems or phonology involves analyzing how sounds function in a given language or dialect.', 'Should it be the case that either drones mate only once in life, then die or sheep graze areas, it follows that it is a common misconception that either lower temperature causes problems or phonology involves analyzing how sounds function in a given language or dialect.', 'We know that either drones mate only once in life, then die or sheep graze areas.']
|
If if pilot whales have holes, then soft scales produce honeydew, But hard scales find it impossible to do, then the statement that 'diffusion plays an important role in the movement of materials, but it is a very slow process' is incorrect. Once we know the claim that if if pilot whales have holes, then soft scales produce honeydew, But hard scales find it impossible to do, then diffusion plays an important role in the movement of materials, but it is a very slow process is false, we also know that either lower temperature causes problems or phonology involves analyzing how sounds function in a given language or dialect. Should it be the case that either drones mate only once in life, then die or sheep graze areas, it follows that it is a common misconception that either lower temperature causes problems or phonology involves analyzing how sounds function in a given language or dialect. We know that either drones mate only once in life, then die or sheep graze areas.
|
The claim that if pilot whales have holes, then soft scales produce honeydew, But hard scales find it impossible to do does not correspond with reality.
|
The claim that if pilot whales have holes, then soft scales produce honeydew, But hard scales find it impossible to do does not correspond with reality.
|
TRUE
|
Reductio Ad Absurdum:
If (If [0], then [1].), then [2]. [SC1-1]
If (If [0], then [1].), then (Not [2].).
Therefore, Not (If [0], then [1].)..
[SC1-1]
Modus Tonens:
If (Not (If (If [0], then [1].), then [2].).), then (Either [3] or [4].).
Not (Either [3] or [4].). [SC2-2]
Therefore, If (If [0], then [1].), then [2]..
[SC2-2]
Modus Ponens:
If (Either [5] or [6].), then (Not (Either [3] or [4].).).
Either [5] or [6].
Therefore, Not (Either [3] or [4].)..
|
{0: 'Pilot whales have holes.', 1: 'Soft scales produce honeydew, But hard scales find it impossible to do.', 2: 'Diffusion plays an important role in the movement of materials, but it is a very slow process.', 3: 'Lower temperature causes problems.', 4: 'Phonology involves analyzing how sounds function in a given language or dialect.', 5: 'Drones mate only once in life, then die.', 6: 'Sheep graze areas.'}
| 3 |
2,821 |
['The idea that eggs are blue is true.', "Provided that the notion that 'if eggs are blue, then a nebuchadnezzar is a wine bottle' is untrue, we know that the statement, most tentacles have sensors, does not hold.", 'Either one or both of these statements are true: guesthouses are houses, or either greens believe that people know best how to solve their own problems or follicular estradiol is produced by granulosa cells through conversion of precursor androgens.', "If guesthouses are houses, then if the notion that 'if eggs are blue, then a nebuchadnezzar is a wine bottle' is untrue, then most tentacles have sensors.", "Whenever it is true that either greens believe that people know best how to solve their own problems or follicular estradiol is produced by granulosa cells through conversion of precursor androgens, 'if the notion that 'if eggs are blue, then a nebuchadnezzar is a wine bottle' is untrue, then most tentacles have sensors' is true."]
|
The idea that eggs are blue is true. Provided that the notion that 'if eggs are blue, then a nebuchadnezzar is a wine bottle' is untrue, we know that the statement, most tentacles have sensors, does not hold. Either one or both of these statements are true: guesthouses are houses, or either greens believe that people know best how to solve their own problems or follicular estradiol is produced by granulosa cells through conversion of precursor androgens. If guesthouses are houses, then if the notion that 'if eggs are blue, then a nebuchadnezzar is a wine bottle' is untrue, then most tentacles have sensors. Whenever it is true that either greens believe that people know best how to solve their own problems or follicular estradiol is produced by granulosa cells through conversion of precursor androgens, 'if the notion that 'if eggs are blue, then a nebuchadnezzar is a wine bottle' is untrue, then most tentacles have sensors' is true.
|
The idea that a nebuchadnezzar is a wine bottle is true.
|
The claim that a nebuchadnezzar is a wine bottle does not reflect reality.
|
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].).
Therefore, If [1], then [0]..
[SC1-2]
Disjunction Elimination:
Either [3] or (Either [4] or [5].).
If [3], then (If (Not (If [1], then [0].).), then [2].).
If (Either [4] or [5].), then (If (Not (If [1], then [0].).), then [2].).
Therefore, If (Not (If [1], then [0].).), then [2]..
|
{0: 'A nebuchadnezzar is a wine bottle.', 1: 'Eggs are blue.', 2: 'Most tentacles have sensors.', 3: 'Guesthouses are houses.', 4: 'Greens believe that people know best how to solve their own problems.', 5: 'Follicular estradiol is produced by granulosa cells through conversion of precursor androgens.'}
| 3 |
2,933 |
['We know that either telescopes come in two basic types - refractors and reflectors or risk taking As risk is spread out among more people, the more people are willing to take risks.', 'On the condition that risk taking As risk is spread out among more people, the more people are willing to take risks, it is definitely the case that copper plays a role in making blood cells, helps immune function and inactivates free radicals.', 'We know that the claim that strenuous exercise can lower blood pressure even more is false.', 'On the condition that the claim that either strenuous exercise can lower blood pressure even more or if telescopes come in two basic types - refractors and reflectors, then copper plays a role in making blood cells, helps immune function and inactivates free radicals has no merit, it is definitely the case that some death occurs in birds.', 'It is not the case that some death occurs in birds.']
|
We know that either telescopes come in two basic types - refractors and reflectors or risk taking As risk is spread out among more people, the more people are willing to take risks. On the condition that risk taking As risk is spread out among more people, the more people are willing to take risks, it is definitely the case that copper plays a role in making blood cells, helps immune function and inactivates free radicals. We know that the claim that strenuous exercise can lower blood pressure even more is false. On the condition that the claim that either strenuous exercise can lower blood pressure even more or if telescopes come in two basic types - refractors and reflectors, then copper plays a role in making blood cells, helps immune function and inactivates free radicals has no merit, it is definitely the case that some death occurs in birds. It is not the case that some death occurs in birds.
|
The statement that states copper plays a role in making blood cells, helps immune function and inactivates free radicals is right.
|
Some people mistakenly believe that copper plays a role in making blood cells, helps immune function and inactivates free radicals.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [3] or (If [1], then [0].). [SC1-2]
Not [3].
Therefore, If [1], then [0]..
[SC1-2]
Modus Tonens:
If (Not (Either [3] or (If [1], then [0].).).), then [4].
Not [4].
Therefore, Either [3] or (If [1], then [0].)..
|
{0: 'Copper plays a role in making blood cells, helps immune function and inactivates free radicals.', 1: 'Telescopes come in two basic types - refractors and reflectors.', 2: 'Risk taking As risk is spread out among more people, the more people are willing to take risks.', 3: 'Strenuous exercise can lower blood pressure even more.', 4: 'Some death occurs in birds.'}
| 3 |
2,490 |
['The claim that estrogens are a major risk factor for hormone-dependent endometrial and breast cancers in women is true.', 'Given that those that suggest if estrogens are a major risk factor for hormone-dependent endometrial and breast cancers in women, then if some plovers reach maturity, then party is the collective name of a group of peacocks are wrong, it can be inferred that blood circulates through the intervillous spaces of the cotyledons.', 'Should it be the case that those that suggest if estrogens are a major risk factor for hormone-dependent endometrial and breast cancers in women, then if some plovers reach maturity, then party is the collective name of a group of peacocks are wrong, it follows that either most meteoroids come from asteroids that are broken apart by impacts with other asteroids or literature is studied to understand plot, analyze characters and compare various literary styles.', "So long as either most meteoroids come from asteroids that are broken apart by impacts with other asteroids or literature is studied to understand plot, analyze characters and compare various literary styles, 'some people mistakenly believe that blood circulates through the intervillous spaces of the cotyledons' is true."]
|
The claim that estrogens are a major risk factor for hormone-dependent endometrial and breast cancers in women is true. Given that those that suggest if estrogens are a major risk factor for hormone-dependent endometrial and breast cancers in women, then if some plovers reach maturity, then party is the collective name of a group of peacocks are wrong, it can be inferred that blood circulates through the intervillous spaces of the cotyledons. Should it be the case that those that suggest if estrogens are a major risk factor for hormone-dependent endometrial and breast cancers in women, then if some plovers reach maturity, then party is the collective name of a group of peacocks are wrong, it follows that either most meteoroids come from asteroids that are broken apart by impacts with other asteroids or literature is studied to understand plot, analyze characters and compare various literary styles. So long as either most meteoroids come from asteroids that are broken apart by impacts with other asteroids or literature is studied to understand plot, analyze characters and compare various literary styles, 'some people mistakenly believe that blood circulates through the intervillous spaces of the cotyledons' is true.
|
So long as some plovers reach maturity, 'party is the collective name of a group of peacocks' is true.
|
We know that the claim that if some plovers reach maturity, then party is the collective name of a group of peacocks is false.
|
FALSE
|
Modus Ponens:
If [2], then (If [0], then [1].). [SC1-1]
[2]
Therefore, If [0], then [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [2], then (If [0], then [1].).).), then [3].
If (Not (If [2], then (If [0], then [1].).).), then (Not [3].). [SC2-2]
Therefore, If [2], then (If [0], then [1].)..
[SC2-2]
Hypothetical Syllogism:
If (Not (If [2], then (If [0], then [1].).).), then (Either [4] or [5].).
If (Either [4] or [5].), then (Not [3].).
Therefore, If (Not (If [2], then (If [0], then [1].).).), then (Not [3].)..
|
{0: 'Some plovers reach maturity.', 1: 'Party is the collective name of a group of peacocks.', 2: 'Estrogens are a major risk factor for hormone-dependent endometrial and breast cancers in women.', 3: 'Blood circulates through the intervillous spaces of the cotyledons.', 4: 'Most meteoroids come from asteroids that are broken apart by impacts with other asteroids.', 5: 'Literature is studied to understand plot, analyze characters and compare various literary styles.'}
| 3 |
2,787 |
["Whenever it is true that the claim that men tend to be affected more than women, adults more than children has no merit, 'the claim that curve beaks adapt for fruit is false' is true.", 'Provided that the claim that men tend to be affected more than women, adults more than children has no merit, we know that iron signifies human civilization.', 'Provided that some people mistakenly believe that if iron signifies human civilization, then curve beaks adapt for fruit, we know that a hauberk is a cataphract.', 'We know that the claim that a hauberk is a cataphract is false.']
|
Whenever it is true that the claim that men tend to be affected more than women, adults more than children has no merit, 'the claim that curve beaks adapt for fruit is false' is true. Provided that the claim that men tend to be affected more than women, adults more than children has no merit, we know that iron signifies human civilization. Provided that some people mistakenly believe that if iron signifies human civilization, then curve beaks adapt for fruit, we know that a hauberk is a cataphract. We know that the claim that a hauberk is a cataphract is false.
|
The idea that men tend to be affected more than women, adults more than children is true.
|
The idea that men tend to be affected more than women, adults more than children is true.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [2].
If [2], then [1]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Modus Tonens:
If (Not (If [2], then [1].).), then [3].
Not [3].
Therefore, If [2], then [1]..
|
{0: 'Men tend to be affected more than women, adults more than children.', 1: 'Curve beaks adapt for fruit.', 2: 'Iron signifies human civilization.', 3: 'A hauberk is a cataphract.'}
| 3 |
2,449 |
['Those that suggest all human beings have an equal chance of salvation are wrong.', 'Many people rightly believe that cats come in all colors and with all kinds of coats - short, long, or curly.', "So long as it is a common misconception that if cats come in all colors and with all kinds of coats - short, long, or curly, then either all human beings have an equal chance of salvation or those that suggest either tiger penis is thought to be an aphrodisiac or handball backstops are for handball are wrong, 'if sunlight contains substantial infrared signal, then inventories are registers' is true.", "Assuming it is a common misconception that if cats come in all colors and with all kinds of coats - short, long, or curly, then either all human beings have an equal chance of salvation or those that suggest either tiger penis is thought to be an aphrodisiac or handball backstops are for handball are wrong, we know that the statement that 'if sunlight contains substantial infrared signal, then inventories are registers' is incorrect."]
|
Those that suggest all human beings have an equal chance of salvation are wrong. Many people rightly believe that cats come in all colors and with all kinds of coats - short, long, or curly. So long as it is a common misconception that if cats come in all colors and with all kinds of coats - short, long, or curly, then either all human beings have an equal chance of salvation or those that suggest either tiger penis is thought to be an aphrodisiac or handball backstops are for handball are wrong, 'if sunlight contains substantial infrared signal, then inventories are registers' is true. Assuming it is a common misconception that if cats come in all colors and with all kinds of coats - short, long, or curly, then either all human beings have an equal chance of salvation or those that suggest either tiger penis is thought to be an aphrodisiac or handball backstops are for handball are wrong, we know that the statement that 'if sunlight contains substantial infrared signal, then inventories are registers' is incorrect.
|
Those that suggest either tiger penis is thought to be an aphrodisiac or handball backstops are for handball are wrong.
|
At least one of two things is true: tiger penis is thought to be an aphrodisiac, or handball backstops are for handball.
|
FALSE
|
Disjunctive Syllogism:
Either [2] or (Not (Either [0] or [1].).). [SC1-1]
Not [2].
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Modus Ponens:
If [3], then (Either [2] or (Not (Either [0] or [1].).).). [SC1-2]
[3]
Therefore, Either [2] or (Not (Either [0] or [1].).)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [3], then (Either [2] or (Not (Either [0] or [1].).).).).), then (If [4], then [5].).
If (Not (If [3], then (Either [2] or (Not (Either [0] or [1].).).).).), then (Not (If [4], then [5].).).
Therefore, If [3], then (Either [2] or (Not (Either [0] or [1].).).)..
|
{0: 'Tiger penis is thought to be an aphrodisiac.', 1: 'Handball backstops are for handball.', 2: 'All human beings have an equal chance of salvation.', 3: 'Cats come in all colors and with all kinds of coats - short, long, or curly.', 4: 'Sunlight contains substantial infrared signal.', 5: 'Inventories are registers.'}
| 3 |
2,703 |
['It is not the case that if scientists know little of the biochemistry, molecular biology, and genetics of pressure adaptation, then animals remain carriers.', "Should it be the case that the statement 'if those that suggest cerebrospinal fluid fills the ventricles of the brain and the central canal of the spinal cord are wrong, then if scientists know little of the biochemistry, molecular biology, and genetics of pressure adaptation, then animals remain carriers' can be considered false, it follows that the statement that states all scorpions are nocturnal and generally venture from their shelters at night to forage for prey is false.", "Once we know if state governments determine the amount of bonds they plan to issue independently, then diatoms have an outer cell wall made of silica, we also know that if the statement 'if those that suggest cerebrospinal fluid fills the ventricles of the brain and the central canal of the spinal cord are wrong, then if scientists know little of the biochemistry, molecular biology, and genetics of pressure adaptation, then animals remain carriers' can be considered false, then all scorpions are nocturnal and generally venture from their shelters at night to forage for prey.", "Whenever it is true that state governments determine the amount of bonds they plan to issue independently, 'diatoms have an outer cell wall made of silica' is true."]
|
It is not the case that if scientists know little of the biochemistry, molecular biology, and genetics of pressure adaptation, then animals remain carriers. Should it be the case that the statement 'if those that suggest cerebrospinal fluid fills the ventricles of the brain and the central canal of the spinal cord are wrong, then if scientists know little of the biochemistry, molecular biology, and genetics of pressure adaptation, then animals remain carriers' can be considered false, it follows that the statement that states all scorpions are nocturnal and generally venture from their shelters at night to forage for prey is false. Once we know if state governments determine the amount of bonds they plan to issue independently, then diatoms have an outer cell wall made of silica, we also know that if the statement 'if those that suggest cerebrospinal fluid fills the ventricles of the brain and the central canal of the spinal cord are wrong, then if scientists know little of the biochemistry, molecular biology, and genetics of pressure adaptation, then animals remain carriers' can be considered false, then all scorpions are nocturnal and generally venture from their shelters at night to forage for prey. Whenever it is true that state governments determine the amount of bonds they plan to issue independently, 'diatoms have an outer cell wall made of silica' is true.
|
It is rational to agree that cerebrospinal fluid fills the ventricles of the brain and the central canal of the spinal cord.
|
It is rational to agree that cerebrospinal fluid fills the ventricles of the brain and the central canal of the spinal cord.
|
TRUE
|
Modus Tonens:
If (Not [0].), then (If [1], then [2].). [SC1-1]
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].).
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC1-2]
Modus Ponens:
If (If [4], then [5].), then (If (Not (If (Not [0].), then (If [1], then [2].).).), then [3].).
If [4], then [5].
Therefore, If (Not (If (Not [0].), then (If [1], then [2].).).), then [3]..
|
{0: 'Cerebrospinal fluid fills the ventricles of the brain and the central canal of the spinal cord.', 1: 'Scientists know little of the biochemistry, molecular biology, and genetics of pressure adaptation.', 2: 'Animals remain carriers.', 3: 'All scorpions are nocturnal and generally venture from their shelters at night to forage for prey.', 4: 'State governments determine the amount of bonds they plan to issue independently.', 5: 'Diatoms have an outer cell wall made of silica.'}
| 3 |
2,437 |
["Whenever it is true that most dietary factors promote development, 'if inaccessible houses impede the lives of people who use wheelchairs, then botany is a scientific study of plants along with their growth , structure , and uses ' is true.", 'Those that suggest most dietary factors promote development are right.', 'We know that at least one of two things is true: cholesterol exists either as a free molecule or as an esterified molecule in cells, or sardines also have an important place in Sicilian cooking.', 'Assuming cholesterol exists either as a free molecule or as an esterified molecule in cells, we know that inaccessible houses impede the lives of people who use wheelchairs.', 'Provided that sardines also have an important place in Sicilian cooking, we know that inaccessible houses impede the lives of people who use wheelchairs.']
|
Whenever it is true that most dietary factors promote development, 'if inaccessible houses impede the lives of people who use wheelchairs, then botany is a scientific study of plants along with their growth , structure , and uses ' is true. Those that suggest most dietary factors promote development are right. We know that at least one of two things is true: cholesterol exists either as a free molecule or as an esterified molecule in cells, or sardines also have an important place in Sicilian cooking. Assuming cholesterol exists either as a free molecule or as an esterified molecule in cells, we know that inaccessible houses impede the lives of people who use wheelchairs. Provided that sardines also have an important place in Sicilian cooking, we know that inaccessible houses impede the lives of people who use wheelchairs.
|
We can assume that botany is a scientific study of plants along with their growth , structure , and uses .
|
We can assume that botany is a scientific study of plants along with their growth , structure , and uses .
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [4], then (If [1], then [0].).
[4]
Therefore, If [1], then [0]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then [1].
If [3], then [1].
Therefore, [1].
|
{0: 'Botany is a scientific study of plants along with their growth , structure , and uses .', 1: 'Inaccessible houses impede the lives of people who use wheelchairs.', 2: 'Cholesterol exists either as a free molecule or as an esterified molecule in cells.', 3: 'Sardines also have an important place in Sicilian cooking.', 4: 'Most dietary factors promote development.'}
| 3 |
2,563 |
['If all materials conduct heat, some more than others, then either most sea urchins reach sexual maturity or cash is located in purses.', 'It is fair to say that all materials conduct heat, some more than others.', "So long as most sea urchins reach sexual maturity, 'fruit is produced by trees' is true.", 'If most sea urchins reach sexual maturity, then the statement, fruit is produced by trees, does not hold.']
|
If all materials conduct heat, some more than others, then either most sea urchins reach sexual maturity or cash is located in purses. It is fair to say that all materials conduct heat, some more than others. So long as most sea urchins reach sexual maturity, 'fruit is produced by trees' is true. If most sea urchins reach sexual maturity, then the statement, fruit is produced by trees, does not hold.
|
It is rational to agree that cash is located in purses.
|
The statement 'cash is located in purses' can be considered false.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (Either [1] or [0].).
[2]
Therefore, Either [1] or [0]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [3].
If [1], then (Not [3].).
Therefore, Not [1]..
|
{0: 'Cash is located in purses.', 1: 'Most sea urchins reach sexual maturity.', 2: 'All materials conduct heat, some more than others.', 3: 'Fruit is produced by trees.'}
| 3 |
2,720 |
['The claim that either some men are bitten by snakes or warm colors tend to advance in a spatial relationship with cool colors which tend to recede does not correspond with reality.', 'When some sons are diagnosed with rare genetic conditions is true, it follows that if men ask parents, then most tenrecs have poor eyesights.', "Whenever it is true that we know that the claim that if if men ask parents, then most tenrecs have poor eyesights, then either some men are bitten by snakes or warm colors tend to advance in a spatial relationship with cool colors which tend to recede is false, 'most atmospheres reflect light' is true.", 'The claim that most atmospheres reflect light does not reflect reality.']
|
The claim that either some men are bitten by snakes or warm colors tend to advance in a spatial relationship with cool colors which tend to recede does not correspond with reality. When some sons are diagnosed with rare genetic conditions is true, it follows that if men ask parents, then most tenrecs have poor eyesights. Whenever it is true that we know that the claim that if if men ask parents, then most tenrecs have poor eyesights, then either some men are bitten by snakes or warm colors tend to advance in a spatial relationship with cool colors which tend to recede is false, 'most atmospheres reflect light' is true. The claim that most atmospheres reflect light does not reflect reality.
|
The claim that some sons are diagnosed with rare genetic conditions does not reflect reality.
|
It is fair to say that some sons are diagnosed with rare genetic conditions.
|
FALSE
|
Modus Tonens:
If [0], then (Either [1] or [2].). [SC1-1]
Not (Either [1] or [2].).
Therefore, Not [0]..
[SC1-1]
Hypothetical Syllogism:
If [0], then (If [3], then [4].).
If (If [3], then [4].), then (Either [1] or [2].). [SC2-2]
Therefore, If [0], then (Either [1] or [2].)..
[SC2-2]
Modus Tonens:
If (Not (If (If [3], then [4].), then (Either [1] or [2].).).), then [5].
Not [5].
Therefore, If (If [3], then [4].), then (Either [1] or [2].)..
|
{0: 'Some sons are diagnosed with rare genetic conditions.', 1: 'Some men are bitten by snakes.', 2: 'Warm colors tend to advance in a spatial relationship with cool colors which tend to recede.', 3: 'Men ask parents.', 4: 'Most tenrecs have poor eyesights.', 5: 'Most atmospheres reflect light.'}
| 3 |
2,890 |
["Provided that game fish adhere to temperature changes much like politicians listen to latest polls, we know that the notion that 'if weather refers to temperatures, precipitation, and storms on a given day at a particular place, then sunlight is white, which means it is a mixture of all the colours in the rainbow' is untrue.", 'If enzymes are proteins that accelerate or promote specific chemical actions in living cells, then either game fish adhere to temperature changes much like politicians listen to latest polls or vegetation reduces soil erosion and helps make the land productive again.', 'enzymes are proteins that accelerate or promote specific chemical actions in living cells.', "One may reasonably assume that if either captives have (part) cytoplasm or traditional hair removal techniques provide only temporary relief, then if vegetation reduces soil erosion and helps make the land productive again, then the notion that 'if weather refers to temperatures, precipitation, and storms on a given day at a particular place, then sunlight is white, which means it is a mixture of all the colours in the rainbow' is untrue.", 'Either one or both of these statements are true: captives have (part) cytoplasm, or traditional hair removal techniques provide only temporary relief.']
|
Provided that game fish adhere to temperature changes much like politicians listen to latest polls, we know that the notion that 'if weather refers to temperatures, precipitation, and storms on a given day at a particular place, then sunlight is white, which means it is a mixture of all the colours in the rainbow' is untrue. If enzymes are proteins that accelerate or promote specific chemical actions in living cells, then either game fish adhere to temperature changes much like politicians listen to latest polls or vegetation reduces soil erosion and helps make the land productive again. enzymes are proteins that accelerate or promote specific chemical actions in living cells. One may reasonably assume that if either captives have (part) cytoplasm or traditional hair removal techniques provide only temporary relief, then if vegetation reduces soil erosion and helps make the land productive again, then the notion that 'if weather refers to temperatures, precipitation, and storms on a given day at a particular place, then sunlight is white, which means it is a mixture of all the colours in the rainbow' is untrue. Either one or both of these statements are true: captives have (part) cytoplasm, or traditional hair removal techniques provide only temporary relief.
|
The notion that 'if weather refers to temperatures, precipitation, and storms on a given day at a particular place, then sunlight is white, which means it is a mixture of all the colours in the rainbow' is untrue.
|
The notion that 'if weather refers to temperatures, precipitation, and storms on a given day at a particular place, then sunlight is white, which means it is a mixture of all the colours in the rainbow' is untrue.
|
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]
Modus Ponens:
If [4], then (Either [2] or [3].).
[4]
Therefore, Either [2] or [3]..
[SC3-1]
Modus Ponens:
If (Either [5] or [6].), then (If [3], then (Not (If [0], then [1].).).).
Either [5] or [6].
Therefore, If [3], then (Not (If [0], then [1].).)..
|
{0: 'Weather refers to temperatures, precipitation, and storms on a given day at a particular place.', 1: 'Sunlight is white, which means it is a mixture of all the colours in the rainbow.', 2: 'Game fish adhere to temperature changes much like politicians listen to latest polls.', 3: 'Vegetation reduces soil erosion and helps make the land productive again.', 4: 'Enzymes are proteins that accelerate or promote specific chemical actions in living cells.', 5: 'Captives have (part) cytoplasm.', 6: 'Traditional hair removal techniques provide only temporary relief.'}
| 3 |
2,219 |
['Assuming tree peonies are deciduous shrubs with an irregular, picturesque branching habit, we know that if it is not the case that poultries are birds, then vitamins find in certain food.', 'tree peonies are deciduous shrubs with an irregular, picturesque branching habit.', 'Either giant duckweed is one of the largest of several types of duckweed or if clouds are collections of millions of tiny droplets of water, then families have opportunity.', 'When giant duckweed is one of the largest of several types of duckweed is true, it follows that the statement that states vitamins find in certain food is false.', 'Once we know if clouds are collections of millions of tiny droplets of water, then families have opportunity, we also know that the statement that states vitamins find in certain food is false.']
|
Assuming tree peonies are deciduous shrubs with an irregular, picturesque branching habit, we know that if it is not the case that poultries are birds, then vitamins find in certain food. tree peonies are deciduous shrubs with an irregular, picturesque branching habit. Either giant duckweed is one of the largest of several types of duckweed or if clouds are collections of millions of tiny droplets of water, then families have opportunity. When giant duckweed is one of the largest of several types of duckweed is true, it follows that the statement that states vitamins find in certain food is false. Once we know if clouds are collections of millions of tiny droplets of water, then families have opportunity, we also know that the statement that states vitamins find in certain food is false.
|
The claim that poultries are birds is true.
|
The claim that poultries are birds is true.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [5], then (If (Not [0].), then [1].).
[5]
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunction Elimination:
Either [2] or (If [3], then [4].).
If [2], then (Not [1].).
If (If [3], then [4].), then (Not [1].).
Therefore, Not [1]..
|
{0: 'Poultries are birds.', 1: 'Vitamins find in certain food.', 2: 'Giant duckweed is one of the largest of several types of duckweed.', 3: 'Clouds are collections of millions of tiny droplets of water.', 4: 'Families have opportunity.', 5: 'Tree peonies are deciduous shrubs with an irregular, picturesque branching habit.'}
| 3 |
2,678 |
["So long as carbon stars are extremely red because of an overabundant amount of carbon in the photosphere, 'heads have (part) brows' is true.", 'If either mailing lists are a way to communicate over the Internet using email or informatics is the study and application of information technology to build information systems, then heads have (part) brows.', 'Once we know either benzodiazepines are the mainstay of therapy or stress is thought to cause a variety of physical and mental health problems, we also know that either carbon stars are extremely red because of an overabundant amount of carbon in the photosphere or either mailing lists are a way to communicate over the Internet using email or informatics is the study and application of information technology to build information systems.', 'On the condition that colon cancer is a common disease , it is definitely the case that either carbon stars are extremely red because of an overabundant amount of carbon in the photosphere or either mailing lists are a way to communicate over the Internet using email or informatics is the study and application of information technology to build information systems.', 'Either one or both of these statements are true: either deceleration is speed or a pawn is an assistant, or many hornworts develop internal mucilage-filled cavities when groups of cells break down.', 'When either deceleration is speed or a pawn is an assistant is true, it follows that either benzodiazepines are the mainstay of therapy or stress is thought to cause a variety of physical and mental health problems.', 'One may reasonably assume that if many hornworts develop internal mucilage-filled cavities when groups of cells break down, then colon cancer is a common disease .']
|
So long as carbon stars are extremely red because of an overabundant amount of carbon in the photosphere, 'heads have (part) brows' is true. If either mailing lists are a way to communicate over the Internet using email or informatics is the study and application of information technology to build information systems, then heads have (part) brows. Once we know either benzodiazepines are the mainstay of therapy or stress is thought to cause a variety of physical and mental health problems, we also know that either carbon stars are extremely red because of an overabundant amount of carbon in the photosphere or either mailing lists are a way to communicate over the Internet using email or informatics is the study and application of information technology to build information systems. On the condition that colon cancer is a common disease , it is definitely the case that either carbon stars are extremely red because of an overabundant amount of carbon in the photosphere or either mailing lists are a way to communicate over the Internet using email or informatics is the study and application of information technology to build information systems. Either one or both of these statements are true: either deceleration is speed or a pawn is an assistant, or many hornworts develop internal mucilage-filled cavities when groups of cells break down. When either deceleration is speed or a pawn is an assistant is true, it follows that either benzodiazepines are the mainstay of therapy or stress is thought to cause a variety of physical and mental health problems. One may reasonably assume that if many hornworts develop internal mucilage-filled cavities when groups of cells break down, then colon cancer is a common disease .
|
It is rational to agree that heads have (part) brows.
|
It is rational to agree that heads have (part) brows.
|
TRUE
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].). [SC1-1]
If [1], then [0].
If (Either [2] or [3].), then [0].
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [4] or [5].) or [6]. [SC1-2]
If (Either [4] or [5].), then (Either [1] or (Either [2] or [3].).).
If [6], then (Either [1] or (Either [2] or [3].).).
Therefore, Either [1] or (Either [2] or [3].)..
[SC1-2]
Constructive Dilemma:
Either (Either [7] or [8].) or [9].
If (Either [7] or [8].), then (Either [4] or [5].).
If [9], then [6].
Therefore, Either (Either [4] or [5].) or [6]..
|
{0: 'Heads have (part) brows.', 1: 'Carbon stars are extremely red because of an overabundant amount of carbon in the photosphere.', 2: 'Mailing lists are a way to communicate over the Internet using email.', 3: 'Informatics is the study and application of information technology to build information systems.', 4: 'Benzodiazepines are the mainstay of therapy.', 5: 'Stress is thought to cause a variety of physical and mental health problems.', 6: 'Colon cancer is a common disease .', 7: 'Deceleration is speed.', 8: 'A pawn is an assistant.', 9: 'Many hornworts develop internal mucilage-filled cavities when groups of cells break down.'}
| 3 |
2,586 |
['At least one of two things is true: reality is both material and spiritual, or small populations are subject to random changes in allele frequencies due to genetic drift.', 'On the condition that reality is both material and spiritual, it is definitely the case that bugs play a crucial role in the stream nutrient cycle.', "Whenever it is true that small populations are subject to random changes in allele frequencies due to genetic drift, 'primitive societies lack social integration' is true.", "So long as bugs play a crucial role in the stream nutrient cycle, 'if bone is a living, breathing tissue that also has large amounts of minerals that provide strength, then literal translations are attempts to be absolutely faithful to the original languages' is true.", 'If bugs play a crucial role in the stream nutrient cycle, then the claim that if bone is a living, breathing tissue that also has large amounts of minerals that provide strength, then literal translations are attempts to be absolutely faithful to the original languages is false.']
|
At least one of two things is true: reality is both material and spiritual, or small populations are subject to random changes in allele frequencies due to genetic drift. On the condition that reality is both material and spiritual, it is definitely the case that bugs play a crucial role in the stream nutrient cycle. Whenever it is true that small populations are subject to random changes in allele frequencies due to genetic drift, 'primitive societies lack social integration' is true. So long as bugs play a crucial role in the stream nutrient cycle, 'if bone is a living, breathing tissue that also has large amounts of minerals that provide strength, then literal translations are attempts to be absolutely faithful to the original languages' is true. If bugs play a crucial role in the stream nutrient cycle, then the claim that if bone is a living, breathing tissue that also has large amounts of minerals that provide strength, then literal translations are attempts to be absolutely faithful to the original languages is false.
|
It is a simple truth that primitive societies lack social integration.
|
Primitive societies exist largely in a state of isolation and self-sufficiency.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either [2] or [3].
If [2], then [1].
If [3], then [0].
Therefore, Either [1] or [0]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then (If [4], then [5].).
If [1], then (Not (If [4], then [5].).).
Therefore, Not [1]..
|
{0: 'Primitive societies lack social integration.', 1: 'Bugs play a crucial role in the stream nutrient cycle.', 2: 'Reality is both material and spiritual.', 3: 'Small populations are subject to random changes in allele frequencies due to genetic drift.', 4: 'Bone is a living, breathing tissue that also has large amounts of minerals that provide strength.', 5: 'Literal translations are attempts to be absolutely faithful to the original languages.'}
| 3 |
2,282 |
['It is a fact that either either cursor focusing is a different way to navigate between windows or chemical reactions take the starting chemicals and end up with new chemicals or either alcohol can cause an excessive release of insulin when taken with carbohydrate or some clouds seem to have very sharp edges, while others have diffuse, wispy outlines.', 'Once we know either cursor focusing is a different way to navigate between windows or chemical reactions take the starting chemicals and end up with new chemicals, we also know that brownstones are real estates.', 'Given that most ermines go after prey, it can be inferred that if either alcohol can cause an excessive release of insulin when taken with carbohydrate or some clouds seem to have very sharp edges, while others have diffuse, wispy outlines, then brownstones are real estates.', "So long as the statement that states most ermines go after prey is false, 'skin sensations lie in the parietal lobe' is true.", "Once we know the statement that states most ermines go after prey is false, we also know that the notion that 'skin sensations lie in the parietal lobe' is untrue."]
|
It is a fact that either either cursor focusing is a different way to navigate between windows or chemical reactions take the starting chemicals and end up with new chemicals or either alcohol can cause an excessive release of insulin when taken with carbohydrate or some clouds seem to have very sharp edges, while others have diffuse, wispy outlines. Once we know either cursor focusing is a different way to navigate between windows or chemical reactions take the starting chemicals and end up with new chemicals, we also know that brownstones are real estates. Given that most ermines go after prey, it can be inferred that if either alcohol can cause an excessive release of insulin when taken with carbohydrate or some clouds seem to have very sharp edges, while others have diffuse, wispy outlines, then brownstones are real estates. So long as the statement that states most ermines go after prey is false, 'skin sensations lie in the parietal lobe' is true. Once we know the statement that states most ermines go after prey is false, we also know that the notion that 'skin sensations lie in the parietal lobe' is untrue.
|
It is reasonable to believe that brownstones are real estates.
|
It is reasonable to believe that brownstones are real estates.
|
TRUE
|
Disjunction Elimination:
Either (Either [1] or [2].) or (Either [3] or [4].).
If (Either [1] or [2].), then [0].
If (Either [3] or [4].), then [0]. [SC3-1]
Therefore, [0].
[SC3-1]
Modus Ponens:
If [5], then (If (Either [3] or [4].), then [0].).
[5] [SC2-2]
Therefore, If (Either [3] or [4].), then [0]..
[SC2-2]
Reductio Ad Absurdum:
If (Not [5].), then [6].
If (Not [5].), then (Not [6].).
Therefore, [5].
|
{0: 'Brownstones are real estates.', 1: 'Cursor focusing is a different way to navigate between windows.', 2: 'Chemical reactions take the starting chemicals and end up with new chemicals.', 3: 'Alcohol can cause an excessive release of insulin when taken with carbohydrate.', 4: 'Some clouds seem to have very sharp edges, while others have diffuse, wispy outlines.', 5: 'Most ermines go after prey.', 6: 'Skin sensations lie in the parietal lobe.'}
| 3 |
2,348 |
['Either one or both of these statements are true: throats are solid objects, or it is not true that many standards exist for representing characters on computer systems.', "Whenever it is true that throats are solid objects, 'the claim that bacteria are one-celled organisms visible only with a microscope has no merit' is true.", 'Either if some teenagers carry their own cell phones, then true education is a lifelong journey, available to anyone willing to learn or mailing lists are a form of discussion groups on the Internet.', 'Should it be the case that if some teenagers carry their own cell phones, then true education is a lifelong journey, available to anyone willing to learn, it follows that if throats are solid objects, then bacteria are one-celled organisms visible only with a microscope.', 'When mailing lists are a form of discussion groups on the Internet is true, it follows that if throats are solid objects, then bacteria are one-celled organisms visible only with a microscope.']
|
Either one or both of these statements are true: throats are solid objects, or it is not true that many standards exist for representing characters on computer systems. Whenever it is true that throats are solid objects, 'the claim that bacteria are one-celled organisms visible only with a microscope has no merit' is true. Either if some teenagers carry their own cell phones, then true education is a lifelong journey, available to anyone willing to learn or mailing lists are a form of discussion groups on the Internet. Should it be the case that if some teenagers carry their own cell phones, then true education is a lifelong journey, available to anyone willing to learn, it follows that if throats are solid objects, then bacteria are one-celled organisms visible only with a microscope. When mailing lists are a form of discussion groups on the Internet is true, it follows that if throats are solid objects, then bacteria are one-celled organisms visible only with a microscope.
|
It is not true that many standards exist for representing characters on computer systems.
|
The statement that states standards define the properties, strength, size, shape, etc. of materials and components is false.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or (Not [0].).
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2]. [SC1-2]
If [1], then (Not [2].).
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either (If [3], then [4].) or [5].
If (If [3], then [4].), then (If [1], then [2].).
If [5], then (If [1], then [2].).
Therefore, If [1], then [2]..
|
{0: 'Many standards exist for representing characters on computer systems.', 1: 'Throats are solid objects.', 2: 'Bacteria are one-celled organisms visible only with a microscope.', 3: 'Some teenagers carry their own cell phones.', 4: 'True education is a lifelong journey, available to anyone willing to learn.', 5: 'Mailing lists are a form of discussion groups on the Internet.'}
| 3 |
2,686 |
['Should it be the case that puffballs are another great edible, found in fields and gravelly compacted soil around the world, it follows that either princes have (part) cytoplasm or those that suggest microwave ovens distribute heat unevenly are wrong.', 'It is rational to agree that puffballs are another great edible, found in fields and gravelly compacted soil around the world.', 'We know that either statistics is the science of the future or it is not the case that princes have (part) cytoplasm.', 'The claim that statistics is the science of the future has no merit.']
|
Should it be the case that puffballs are another great edible, found in fields and gravelly compacted soil around the world, it follows that either princes have (part) cytoplasm or those that suggest microwave ovens distribute heat unevenly are wrong. It is rational to agree that puffballs are another great edible, found in fields and gravelly compacted soil around the world. We know that either statistics is the science of the future or it is not the case that princes have (part) cytoplasm. The claim that statistics is the science of the future has no merit.
|
Those that suggest microwave ovens distribute heat unevenly are wrong.
|
It is a common misconception that a microwave oven is a kitchen appliance.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [3], then (Either [1] or (Not [0].).).
[3]
Therefore, Either [1] or (Not [0].)..
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].).
Not [2].
Therefore, Not [1]..
|
{0: 'Microwave ovens distribute heat unevenly.', 1: 'Princes have (part) cytoplasm.', 2: 'Statistics is the science of the future .', 3: 'Puffballs are another great edible, found in fields and gravelly compacted soil around the world.'}
| 3 |
2,004 |
['When fruit is their favorite food, but they also eat insects and small animals such as birds is true, it follows that the claim that physiology isa biology is false.', "So long as casseroles are all about being home, 'fruit is their favorite food, but they also eat insects and small animals such as birds' is true.", 'Given that some blood causes infection, it can be inferred that fruit is their favorite food, but they also eat insects and small animals such as birds.', 'It is rational to believe that either bowerbirds have (part) breasts or physicians use diagnostic tests to aid in making an accurate diagnosis.', 'When bowerbirds have (part) breasts is true, it follows that either casseroles are all about being home or some blood causes infection.', 'On the condition that physicians use diagnostic tests to aid in making an accurate diagnosis, it is definitely the case that either casseroles are all about being home or some blood causes infection.']
|
When fruit is their favorite food, but they also eat insects and small animals such as birds is true, it follows that the claim that physiology isa biology is false. So long as casseroles are all about being home, 'fruit is their favorite food, but they also eat insects and small animals such as birds' is true. Given that some blood causes infection, it can be inferred that fruit is their favorite food, but they also eat insects and small animals such as birds. It is rational to believe that either bowerbirds have (part) breasts or physicians use diagnostic tests to aid in making an accurate diagnosis. When bowerbirds have (part) breasts is true, it follows that either casseroles are all about being home or some blood causes infection. On the condition that physicians use diagnostic tests to aid in making an accurate diagnosis, it is definitely the case that either casseroles are all about being home or some blood causes infection.
|
The claim that physiology isa biology is false.
|
The claim that physiology isa biology is false.
|
TRUE
|
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].
If [3], then [1].
Therefore, [1].
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Either [2] or [3].).
If [5], then (Either [2] or [3].).
Therefore, Either [2] or [3]..
|
{0: 'Physiology isa biology.', 1: 'Fruit is their favorite food, but they also eat insects and small animals such as birds.', 2: 'Casseroles are all about being home.', 3: 'Some blood causes infection.', 4: 'Bowerbirds have (part) breasts.', 5: 'Physicians use diagnostic tests to aid in making an accurate diagnosis.'}
| 3 |
2,995 |
['We know that at least one of two things is true: serology is the most frequently used diagnostic test for dogs, or most seeds contain nutrients.', 'Given that most seeds contain nutrients, it can be inferred that colostrum is high in antibodies, energy and other nutrients.', 'The claim that flagella are primarily present in prokaryotic asexual organisms does not correspond with reality.', 'When some abnormalities prevent fertilization is true, it follows that if some people mistakenly believe that if serology is the most frequently used diagnostic test for dogs, then colostrum is high in antibodies, energy and other nutrients, then flagella are primarily present in prokaryotic asexual organisms.', "The statement 'some abnormalities prevent fertilization' is true."]
|
We know that at least one of two things is true: serology is the most frequently used diagnostic test for dogs, or most seeds contain nutrients. Given that most seeds contain nutrients, it can be inferred that colostrum is high in antibodies, energy and other nutrients. The claim that flagella are primarily present in prokaryotic asexual organisms does not correspond with reality. When some abnormalities prevent fertilization is true, it follows that if some people mistakenly believe that if serology is the most frequently used diagnostic test for dogs, then colostrum is high in antibodies, energy and other nutrients, then flagella are primarily present in prokaryotic asexual organisms. The statement 'some abnormalities prevent fertilization' is true.
|
The statement that states colostrum is high in antibodies, energy and other nutrients is right.
|
The claim that colostrum is high in antibodies, energy and other nutrients is false.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not (If [1], then [0].).), then [3]. [SC1-2]
Not [3].
Therefore, If [1], then [0]..
[SC1-2]
Modus Ponens:
If [4], then (If (Not (If [1], then [0].).), then [3].).
[4]
Therefore, If (Not (If [1], then [0].).), then [3]..
|
{0: 'Colostrum is high in antibodies, energy and other nutrients.', 1: 'Serology is the most frequently used diagnostic test for dogs.', 2: 'Most seeds contain nutrients.', 3: 'Flagella are primarily present in prokaryotic asexual organisms.', 4: 'Some abnormalities prevent fertilization.'}
| 3 |
2,463 |
['Assuming those that suggest jackrabbits have sharp eyesights are wrong, we know that the claim that lexical phrases fill the gap between grammar, on the one hand, and vocabulary on the other does not reflect reality.', 'We know that either wasps collect pollen or if most bushy plants have roots, then carbohydrates enhance the absorption of tryptophan, which is converted into serotonin in the brain.', 'On the condition that if most bushy plants have roots, then carbohydrates enhance the absorption of tryptophan, which is converted into serotonin in the brain, it is definitely the case that if those that suggest jackrabbits have sharp eyesights are wrong, then lexical phrases fill the gap between grammar, on the one hand, and vocabulary on the other.', 'There is good reason to believe that either people can suffer and die or planes have (part) fuel gauges.', 'Given that people can suffer and die, it can be inferred that if wasps collect pollen, then if those that suggest jackrabbits have sharp eyesights are wrong, then lexical phrases fill the gap between grammar, on the one hand, and vocabulary on the other.', 'Should it be the case that planes have (part) fuel gauges, it follows that if wasps collect pollen, then if those that suggest jackrabbits have sharp eyesights are wrong, then lexical phrases fill the gap between grammar, on the one hand, and vocabulary on the other.']
|
Assuming those that suggest jackrabbits have sharp eyesights are wrong, we know that the claim that lexical phrases fill the gap between grammar, on the one hand, and vocabulary on the other does not reflect reality. We know that either wasps collect pollen or if most bushy plants have roots, then carbohydrates enhance the absorption of tryptophan, which is converted into serotonin in the brain. On the condition that if most bushy plants have roots, then carbohydrates enhance the absorption of tryptophan, which is converted into serotonin in the brain, it is definitely the case that if those that suggest jackrabbits have sharp eyesights are wrong, then lexical phrases fill the gap between grammar, on the one hand, and vocabulary on the other. There is good reason to believe that either people can suffer and die or planes have (part) fuel gauges. Given that people can suffer and die, it can be inferred that if wasps collect pollen, then if those that suggest jackrabbits have sharp eyesights are wrong, then lexical phrases fill the gap between grammar, on the one hand, and vocabulary on the other. Should it be the case that planes have (part) fuel gauges, it follows that if wasps collect pollen, then if those that suggest jackrabbits have sharp eyesights are wrong, then lexical phrases fill the gap between grammar, on the one hand, and vocabulary on the other.
|
It is the case that jackrabbits have sharp eyesights.
|
Most jackrabbits reach maturity.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [2] or (If [3], then [4].).
If [2], then (If (Not [0].), then [1].). [SC2-2]
If (If [3], then [4].), then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC2-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [2], then (If (Not [0].), then [1].).).
If [6], then (If [2], then (If (Not [0].), then [1].).).
Therefore, If [2], then (If (Not [0].), then [1].)..
|
{0: 'Jackrabbits have sharp eyesights.', 1: 'Lexical phrases fill the gap between grammar, on the one hand, and vocabulary on the other.', 2: 'Wasps collect pollen.', 3: 'Most bushy plants have roots.', 4: 'Carbohydrates enhance the absorption of tryptophan, which is converted into serotonin in the brain.', 5: 'People can suffer and die.', 6: 'Planes have (part) fuel gauges.'}
| 3 |
2,776 |
['We know that either kestrels are quite vocal or organs play large roles.', 'Once we know if mouths are used for speaking, then shallots contain more nutrition than onions, we also know that if kestrels are quite vocal, then either animals receive test substances or children are especially vulnerable because they breathe in more pollution per pound.', 'Once we know mouths are used for speaking, we also know that shallots contain more nutrition than onions.', "If the notion that 'if organs play large roles, then either animals receive test substances or children are especially vulnerable because they breathe in more pollution per pound' is untrue, then most different animals compete for resources.", 'The statement, most different animals compete for resources, does not hold.']
|
We know that either kestrels are quite vocal or organs play large roles. Once we know if mouths are used for speaking, then shallots contain more nutrition than onions, we also know that if kestrels are quite vocal, then either animals receive test substances or children are especially vulnerable because they breathe in more pollution per pound. Once we know mouths are used for speaking, we also know that shallots contain more nutrition than onions. If the notion that 'if organs play large roles, then either animals receive test substances or children are especially vulnerable because they breathe in more pollution per pound' is untrue, then most different animals compete for resources. The statement, most different animals compete for resources, does not hold.
|
Either animals receive test substances or children are especially vulnerable because they breathe in more pollution per pound.
|
The statement that 'either animals receive test substances or children are especially vulnerable because they breathe in more pollution per pound' is incorrect.
|
FALSE
|
Disjunction Elimination:
Either [2] or [3].
If [2], then (Either [0] or [1].). [SC2-1]
If [3], then (Either [0] or [1].). [SC3-1]
Therefore, Either [0] or [1]..
[SC2-1]
Modus Ponens:
If (If [5], then [6].), then (If [2], then (Either [0] or [1].).).
If [5], then [6].
Therefore, If [2], then (Either [0] or [1].)..
[SC3-1]
Modus Tonens:
If (Not (If [3], then (Either [0] or [1].).).), then [4].
Not [4].
Therefore, If [3], then (Either [0] or [1].)..
|
{0: 'Animals receive test substances.', 1: 'Children are especially vulnerable because they breathe in more pollution per pound.', 2: 'Kestrels are quite vocal.', 3: 'Organs play large roles.', 4: 'Most different animals compete for resources.', 5: 'Mouths are used for speaking.', 6: 'Shallots contain more nutrition than onions.'}
| 3 |
2,682 |
['If geraniums are known aphid repellents, then if parasitized crickets are thirsty and go to water to drink, then most plants get little sunlight.', 'It is fair to say that geraniums are known aphid repellents.', 'We know that either most large predators hunt other animals or parasitized crickets are thirsty and go to water to drink.', 'The claim that most large predators hunt other animals does not reflect reality.']
|
If geraniums are known aphid repellents, then if parasitized crickets are thirsty and go to water to drink, then most plants get little sunlight. It is fair to say that geraniums are known aphid repellents. We know that either most large predators hunt other animals or parasitized crickets are thirsty and go to water to drink. The claim that most large predators hunt other animals does not reflect reality.
|
It is a simple truth that most plants get little sunlight.
|
Plants grow in locations.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (If [1], then [0].).
[3]
Therefore, If [1], then [0]..
[SC2-1]
Disjunctive Syllogism:
Either [2] or [1].
Not [2].
Therefore, [1].
|
{0: 'Most plants get little sunlight.', 1: 'Parasitized crickets are thirsty and go to water to drink.', 2: 'Most large predators hunt other animals.', 3: 'Geraniums are known aphid repellents.'}
| 3 |
2,879 |
['Should it be the case that the claim that if exercise plays an important role in weight control, then it is a common misconception that wood adapts well to gradual seasonal changes is false, it follows that oceans are very important to people.', "The statement that 'oceans are very important to people' is incorrect.", 'On the condition that it is not the case that exercise plays an important role in weight control, it is definitely the case that a goitrogen is a compound.', 'Some people mistakenly believe that a goitrogen is a compound.']
|
Should it be the case that the claim that if exercise plays an important role in weight control, then it is a common misconception that wood adapts well to gradual seasonal changes is false, it follows that oceans are very important to people. The statement that 'oceans are very important to people' is incorrect. On the condition that it is not the case that exercise plays an important role in weight control, it is definitely the case that a goitrogen is a compound. Some people mistakenly believe that a goitrogen is a compound.
|
It is a common misconception that wood adapts well to gradual seasonal changes.
|
The claim that wood is a likely target for insects, splitting, distorting, bruising or breaking does not reflect reality.
|
Uncertain
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1] [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (If [1], then (Not [0].).).), then [3].
Not [3].
Therefore, If [1], then (Not [0].)..
[SC2-1]
Modus Tonens:
If (Not [1].), then [2].
Not [2].
Therefore, [1].
|
{0: 'Wood adapts well to gradual seasonal changes.', 1: 'Exercise plays an important role in weight control.', 2: 'A goitrogen is a compound.', 3: 'Oceans are very important to people.'}
| 3 |
2,517 |
['There is good reason to believe that either natural redheads are often have very light colored skin or either dogs vary just as people do or fertilizer is important for healthy daylilies.', 'Provided that either dogs vary just as people do or fertilizer is important for healthy daylilies, we know that nicotine causes constriction of the blood vessels and prevents optimum muscle health and function.', "So long as liner isa event, 'if natural redheads are often have very light colored skin, then nicotine causes constriction of the blood vessels and prevents optimum muscle health and function' is true.", 'It is a fact that either hypertension is much more prevalent in both communities than in the island dwellers or either lanes are located in highways or ibexs have (part) corpi.', 'Provided that hypertension is much more prevalent in both communities than in the island dwellers, we know that liner isa event.', 'When either lanes are located in highways or ibexs have (part) corpi is true, it follows that liner isa event.']
|
There is good reason to believe that either natural redheads are often have very light colored skin or either dogs vary just as people do or fertilizer is important for healthy daylilies. Provided that either dogs vary just as people do or fertilizer is important for healthy daylilies, we know that nicotine causes constriction of the blood vessels and prevents optimum muscle health and function. So long as liner isa event, 'if natural redheads are often have very light colored skin, then nicotine causes constriction of the blood vessels and prevents optimum muscle health and function' is true. It is a fact that either hypertension is much more prevalent in both communities than in the island dwellers or either lanes are located in highways or ibexs have (part) corpi. Provided that hypertension is much more prevalent in both communities than in the island dwellers, we know that liner isa event. When either lanes are located in highways or ibexs have (part) corpi is true, it follows that liner isa event.
|
It is true that nicotine causes constriction of the blood vessels and prevents optimum muscle health and function.
|
Nicotine excites the vomiting reflex both in the brain and in the nerves of the stomach.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].).
If [1], then [0]. [SC2-1]
If (Either [2] or [3].), then [0].
Therefore, [0].
[SC2-1]
Modus Ponens:
If [4], then (If [1], then [0].).
[4] [SC2-2]
Therefore, If [1], then [0]..
[SC2-2]
Disjunction Elimination:
Either [5] or (Either [6] or [7].).
If [5], then [4].
If (Either [6] or [7].), then [4].
Therefore, [4].
|
{0: 'Nicotine causes constriction of the blood vessels and prevents optimum muscle health and function.', 1: 'Natural redheads are often have very light colored skin.', 2: 'Dogs vary just as people do.', 3: 'Fertilizer is important for healthy daylilies.', 4: 'Liner isa event.', 5: 'Hypertension is much more prevalent in both communities than in the island dwellers.', 6: 'Lanes are located in highways.', 7: 'Ibexs have (part) corpi.'}
| 3 |
2,573 |
['On the condition that it is a common misconception that penguins are the most highly specialized of all birds for marine life, it is definitely the case that if randomization is used to determine the order in which a patient receives the treatment and control, then bees need food.', 'Provided that if randomization is used to determine the order in which a patient receives the treatment and control, then bees need food, we know that a ramp is an inclined plane.', "So long as a ramp is an inclined plane, 'air transportation is a network business' is true.", 'The statement, air transportation is a network business, does not hold.']
|
On the condition that it is a common misconception that penguins are the most highly specialized of all birds for marine life, it is definitely the case that if randomization is used to determine the order in which a patient receives the treatment and control, then bees need food. Provided that if randomization is used to determine the order in which a patient receives the treatment and control, then bees need food, we know that a ramp is an inclined plane. So long as a ramp is an inclined plane, 'air transportation is a network business' is true. The statement, air transportation is a network business, does not hold.
|
Those that suggest penguins are the most highly specialized of all birds for marine life are right.
|
Penguins gather in large colonies called rookeries in order to reproduce.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then (If [3], then [4].).
If (If [3], then [4].), then [1].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Modus Tonens:
If [1], then [2].
Not [2].
Therefore, Not [1]..
|
{0: 'Penguins are the most highly specialized of all birds for marine life.', 1: 'A ramp is an inclined plane.', 2: 'Air transportation is a network business.', 3: 'Randomization is used to determine the order in which a patient receives the treatment and control.', 4: 'Bees need food.'}
| 3 |
2,793 |
["Whenever it is true that racist events increase stress-related psychiatric symptoms among minority group members, 'the statement 'societies have laws' can be considered false' is true.", 'Either weariness relaxes posture into a naturalness that is difficult to achieve in an alert state or mice have thymus organs.', 'Given that weariness relaxes posture into a naturalness that is difficult to achieve in an alert state, it can be inferred that either angwantibos have (part) plasma membranes or racist events increase stress-related psychiatric symptoms among minority group members.', 'One may reasonably assume that if mice have thymus organs, then either angwantibos have (part) plasma membranes or racist events increase stress-related psychiatric symptoms among minority group members.', 'Either pianos are located in concerts or either gases inevitably have much lower refractive indexes than solids or wet weather is ideal for most fungal diseases.', "Whenever it is true that pianos are located in concerts, 'if angwantibos have (part) plasma membranes, then the statement 'societies have laws' can be considered false' is true.", "When either gases inevitably have much lower refractive indexes than solids or wet weather is ideal for most fungal diseases is true, it follows that if angwantibos have (part) plasma membranes, then the statement 'societies have laws' can be considered false."]
|
Whenever it is true that racist events increase stress-related psychiatric symptoms among minority group members, 'the statement 'societies have laws' can be considered false' is true. Either weariness relaxes posture into a naturalness that is difficult to achieve in an alert state or mice have thymus organs. Given that weariness relaxes posture into a naturalness that is difficult to achieve in an alert state, it can be inferred that either angwantibos have (part) plasma membranes or racist events increase stress-related psychiatric symptoms among minority group members. One may reasonably assume that if mice have thymus organs, then either angwantibos have (part) plasma membranes or racist events increase stress-related psychiatric symptoms among minority group members. Either pianos are located in concerts or either gases inevitably have much lower refractive indexes than solids or wet weather is ideal for most fungal diseases. Whenever it is true that pianos are located in concerts, 'if angwantibos have (part) plasma membranes, then the statement 'societies have laws' can be considered false' is true. When either gases inevitably have much lower refractive indexes than solids or wet weather is ideal for most fungal diseases is true, it follows that if angwantibos have (part) plasma membranes, then the statement 'societies have laws' can be considered false.
|
The statement 'societies have laws' can be considered false.
|
Societies have laws.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].). [SC2-1]
If [2], then (Not [0].).
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Either [1] or [2].).
If [7], then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC2-1]
Disjunction Elimination:
Either [3] or (Either [4] or [5].).
If [3], then (If [1], then (Not [0].).).
If (Either [4] or [5].), then (If [1], then (Not [0].).).
Therefore, If [1], then (Not [0].)..
|
{0: 'Societies have laws.', 1: 'Angwantibos have (part) plasma membranes.', 2: 'Racist events increase stress-related psychiatric symptoms among minority group members.', 3: 'Pianos are located in concerts.', 4: 'Gases inevitably have much lower refractive indexes than solids.', 5: 'Wet weather is ideal for most fungal diseases.', 6: 'Weariness relaxes posture into a naturalness that is difficult to achieve in an alert state.', 7: 'Mice have thymus organs.'}
| 3 |
2,893 |
['It is rational to believe that either mothers can also connect with their baby through music or if peacekeeping is a global responsibility, then chemical safety is an area of science education that needs to be attended to vigilantly.', 'Should it be the case that if peacekeeping is a global responsibility, then chemical safety is an area of science education that needs to be attended to vigilantly, it follows that natural convection disperses the heat through the entire volume of molten salt.', 'One may reasonably assume that if most norway rats live in communities, then if mothers can also connect with their baby through music, then natural convection disperses the heat through the entire volume of molten salt.', 'Assuming animals can then adapt to higher levels, we know that if mothers can also connect with their baby through music, then natural convection disperses the heat through the entire volume of molten salt.', 'At least one of two things is true: either symbols are the powers that resist change or open the way to creative change when it is needed or healthy communities provide mechanisms for affiliation, shared problem-solving and mutual growth, or reptiles have hearts.', 'Given that either symbols are the powers that resist change or open the way to creative change when it is needed or healthy communities provide mechanisms for affiliation, shared problem-solving and mutual growth, it can be inferred that either most norway rats live in communities or animals can then adapt to higher levels.', 'One may reasonably assume that if reptiles have hearts, then either most norway rats live in communities or animals can then adapt to higher levels.']
|
It is rational to believe that either mothers can also connect with their baby through music or if peacekeeping is a global responsibility, then chemical safety is an area of science education that needs to be attended to vigilantly. Should it be the case that if peacekeeping is a global responsibility, then chemical safety is an area of science education that needs to be attended to vigilantly, it follows that natural convection disperses the heat through the entire volume of molten salt. One may reasonably assume that if most norway rats live in communities, then if mothers can also connect with their baby through music, then natural convection disperses the heat through the entire volume of molten salt. Assuming animals can then adapt to higher levels, we know that if mothers can also connect with their baby through music, then natural convection disperses the heat through the entire volume of molten salt. At least one of two things is true: either symbols are the powers that resist change or open the way to creative change when it is needed or healthy communities provide mechanisms for affiliation, shared problem-solving and mutual growth, or reptiles have hearts. Given that either symbols are the powers that resist change or open the way to creative change when it is needed or healthy communities provide mechanisms for affiliation, shared problem-solving and mutual growth, it can be inferred that either most norway rats live in communities or animals can then adapt to higher levels. One may reasonably assume that if reptiles have hearts, then either most norway rats live in communities or animals can then adapt to higher levels.
|
We can assume that natural convection disperses the heat through the entire volume of molten salt.
|
We can assume that natural convection disperses the heat through the entire volume of molten salt.
|
TRUE
|
Disjunction Elimination:
Either [1] or (If [2], then [3].).
If [1], then [0]. [SC2-1]
If (If [2], then [3].), then [0].
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [4] or [5]. [SC1-2]
If [4], then (If [1], then [0].).
If [5], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC1-2]
Disjunction Elimination:
Either (Either [6] or [7].) or [8].
If (Either [6] or [7].), then (Either [4] or [5].).
If [8], then (Either [4] or [5].).
Therefore, Either [4] or [5]..
|
{0: 'Natural convection disperses the heat through the entire volume of molten salt.', 1: 'Mothers can also connect with their baby through music.', 2: 'Peacekeeping is a global responsibility.', 3: 'Chemical safety is an area of science education that needs to be attended to vigilantly.', 4: 'Most norway rats live in communities.', 5: 'Animals can then adapt to higher levels.', 6: 'Symbols are the powers that resist change or open the way to creative change when it is needed.', 7: 'Healthy communities provide mechanisms for affiliation, shared problem-solving and mutual growth.', 8: 'Reptiles have hearts.'}
| 3 |
2,534 |
['If the claim that if the claim that if most dolphins has-part stomachs, then water retains heat longer than land, and also takes longer to heat and cool is false, then animals will have advantage is false, then audiences are located in stadiums.', 'When the claim that if the claim that if most dolphins has-part stomachs, then water retains heat longer than land, and also takes longer to heat and cool is false, then animals will have advantage is false is true, it follows that the statement that states audiences are located in stadiums is false.', 'On the condition that animals will have advantage, it is definitely the case that colors are frequently bright, with high contrast.', 'The claim that colors are frequently bright, with high contrast does not correspond with reality.']
|
If the claim that if the claim that if most dolphins has-part stomachs, then water retains heat longer than land, and also takes longer to heat and cool is false, then animals will have advantage is false, then audiences are located in stadiums. When the claim that if the claim that if most dolphins has-part stomachs, then water retains heat longer than land, and also takes longer to heat and cool is false, then animals will have advantage is false is true, it follows that the statement that states audiences are located in stadiums is false. On the condition that animals will have advantage, it is definitely the case that colors are frequently bright, with high contrast. The claim that colors are frequently bright, with high contrast does not correspond with reality.
|
Assuming most dolphins has-part stomachs, we know that water retains heat longer than land, and also takes longer to heat and cool.
|
Given that dolphins are by far more prevalent than porpoises, it can be inferred that water retains heat longer than land, and also takes longer to heat and cool.
|
Uncertain
|
Modus Tonens:
If (Not (If [0], then [1].).), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not (If [0], then [1].).), then [2].).), then [4].
If (Not (If (Not (If [0], then [1].).), then [2].).), then (Not [4].).
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC2-1]
Modus Tonens:
If [2], then [3].
Not [3].
Therefore, Not [2]..
|
{0: 'Most dolphins has-part stomachs.', 1: 'Water retains heat longer than land, and also takes longer to heat and cool.', 2: 'Animals will have advantage.', 3: 'Colors are frequently bright, with high contrast.', 4: 'Audiences are located in stadiums.'}
| 3 |
2,903 |
['Should it be the case that asthma attacks are episodic which is the feature that separates asthma from other similar diseases, it follows that if some climb perches inhabit rivers, then arborists look at many things when assessing trees.', 'There is good reason to believe that either some young men consume fat diets or either an airliner is a plane or asthma attacks are episodic which is the feature that separates asthma from other similar diseases.', 'The claim that some young men consume fat diets does not correspond with reality.', 'Provided that the claim that if an airliner is a plane, then if some climb perches inhabit rivers, then arborists look at many things when assessing trees is false, we know that most gemsboks have necks.', "One may reasonably assume that if the claim that if an airliner is a plane, then if some climb perches inhabit rivers, then arborists look at many things when assessing trees is false, then the statement 'most gemsboks have necks' can be considered false."]
|
Should it be the case that asthma attacks are episodic which is the feature that separates asthma from other similar diseases, it follows that if some climb perches inhabit rivers, then arborists look at many things when assessing trees. There is good reason to believe that either some young men consume fat diets or either an airliner is a plane or asthma attacks are episodic which is the feature that separates asthma from other similar diseases. The claim that some young men consume fat diets does not correspond with reality. Provided that the claim that if an airliner is a plane, then if some climb perches inhabit rivers, then arborists look at many things when assessing trees is false, we know that most gemsboks have necks. One may reasonably assume that if the claim that if an airliner is a plane, then if some climb perches inhabit rivers, then arborists look at many things when assessing trees is false, then the statement 'most gemsboks have necks' can be considered false.
|
Once we know some climb perches inhabit rivers, we also know that arborists look at many things when assessing trees.
|
Once we know some climb perches inhabit rivers, we also know that arborists look at many things when assessing trees.
|
TRUE
|
Disjunction Elimination:
Either [2] or [3]. [SC1-1]
If [2], then (If [0], then [1].). [SC2-1]
If [3], then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC1-1]
Disjunctive Syllogism:
Either [5] or (Either [2] or [3].).
Not [5].
Therefore, Either [2] or [3]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [2], then (If [0], then [1].).).), then [4].
If (Not (If [2], then (If [0], then [1].).).), then (Not [4].).
Therefore, If [2], then (If [0], then [1].)..
|
{0: 'Some climb perches inhabit rivers.', 1: 'Arborists look at many things when assessing trees.', 2: 'An airliner is a plane.', 3: 'Asthma attacks are episodic which is the feature that separates asthma from other similar diseases.', 4: 'Most gemsboks have necks.', 5: 'Some young men consume fat diets.'}
| 3 |
2,276 |
["So long as gene flow increases the divergence of populations, 'if parthenogenesis refers specifically to the development of unfertilized eggs, then adults can benefit from learning to structure their environment' is true.", 'It is the case that gene flow increases the divergence of populations.', 'On the condition that the statement, parthenogenesis refers specifically to the development of unfertilized eggs, does not hold, it is definitely the case that low selectivity is related to high density, and high selectivity is related to low density.', "The statement 'low selectivity is related to high density, and high selectivity is related to low density' can be considered false."]
|
So long as gene flow increases the divergence of populations, 'if parthenogenesis refers specifically to the development of unfertilized eggs, then adults can benefit from learning to structure their environment' is true. It is the case that gene flow increases the divergence of populations. On the condition that the statement, parthenogenesis refers specifically to the development of unfertilized eggs, does not hold, it is definitely the case that low selectivity is related to high density, and high selectivity is related to low density. The statement 'low selectivity is related to high density, and high selectivity is related to low density' can be considered false.
|
It is rational to agree that adults can benefit from learning to structure their environment.
|
Adults already run a greater risk of cancer, heart attack, stroke and lung disease than youths.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (If [1], then [0].).
[3]
Therefore, If [1], then [0]..
[SC2-1]
Modus Tonens:
If (Not [1].), then [2].
Not [2].
Therefore, [1].
|
{0: 'Adults can benefit from learning to structure their environment.', 1: 'Parthenogenesis refers specifically to the development of unfertilized eggs.', 2: 'Low selectivity is related to high density, and high selectivity is related to low density.', 3: 'Gene flow increases the divergence of populations.'}
| 3 |
2,284 |
['It is rational to agree that specks are chitin like polymers.', 'The claim that some researchers study sharks does not reflect reality.', 'It is rational to believe that either most coyotes feed in fields or either some researchers study sharks or if specks are chitin like polymers, then if activism mobilizes people to act as a united group to increase their power to affect change, then monkeys are superior in many ways.', 'It is a common misconception that most coyotes feed in fields.']
|
It is rational to agree that specks are chitin like polymers. The claim that some researchers study sharks does not reflect reality. It is rational to believe that either most coyotes feed in fields or either some researchers study sharks or if specks are chitin like polymers, then if activism mobilizes people to act as a united group to increase their power to affect change, then monkeys are superior in many ways. It is a common misconception that most coyotes feed in fields.
|
One may reasonably assume that if activism mobilizes people to act as a united group to increase their power to affect change, then monkeys are superior in many ways.
|
One may reasonably assume that if activism mobilizes people to act as a united group to increase their power to affect change, then monkeys are superior in many ways.
|
TRUE
|
Modus Ponens:
If [2], then (If [0], then [1].). [SC1-1]
[2]
Therefore, If [0], then [1]..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If [2], then (If [0], then [1].).). [SC1-2]
Not [3].
Therefore, If [2], then (If [0], then [1].)..
[SC1-2]
Disjunctive Syllogism:
Either [4] or (Either [3] or (If [2], then (If [0], then [1].).).).
Not [4].
Therefore, Either [3] or (If [2], then (If [0], then [1].).)..
|
{0: 'Activism mobilizes people to act as a united group to increase their power to affect change.', 1: 'Monkeys are superior in many ways.', 2: 'Specks are chitin like polymers.', 3: 'Some researchers study sharks.', 4: 'Most coyotes feed in fields.'}
| 3 |
2,470 |
['Provided that surface waves are the primary source of energy in the beach environment, we know that either statistics show smoking contributes to more accidents on the road, because smokers are distracted or most gardeners like to pick out their own plants.', "The statement 'surface waves are the primary source of energy in the beach environment' is true.", 'One may reasonably assume that if statistics show smoking contributes to more accidents on the road, because smokers are distracted, then either asbestos is regulated under the Clean Air Act as a hazardous air pollutant or some herbs are better suited to use in a wreath than others.', 'Some people mistakenly believe that either asbestos is regulated under the Clean Air Act as a hazardous air pollutant or some herbs are better suited to use in a wreath than others.']
|
Provided that surface waves are the primary source of energy in the beach environment, we know that either statistics show smoking contributes to more accidents on the road, because smokers are distracted or most gardeners like to pick out their own plants. The statement 'surface waves are the primary source of energy in the beach environment' is true. One may reasonably assume that if statistics show smoking contributes to more accidents on the road, because smokers are distracted, then either asbestos is regulated under the Clean Air Act as a hazardous air pollutant or some herbs are better suited to use in a wreath than others. Some people mistakenly believe that either asbestos is regulated under the Clean Air Act as a hazardous air pollutant or some herbs are better suited to use in a wreath than others.
|
Many people rightly believe that most gardeners like to pick out their own plants.
|
Some gardeners kill plants.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (Either [1] or [0].).
[2]
Therefore, Either [1] or [0]..
[SC2-1]
Modus Tonens:
If [1], then (Either [3] or [4].).
Not (Either [3] or [4].).
Therefore, Not [1]..
|
{0: 'Most gardeners like to pick out their own plants.', 1: 'Statistics show smoking contributes to more accidents on the road, because smokers are distracted.', 2: 'Surface waves are the primary source of energy in the beach environment.', 3: 'Asbestos is regulated under the Clean Air Act as a hazardous air pollutant.', 4: 'Some herbs are better suited to use in a wreath than others.'}
| 3 |
2,426 |
['At least one of two things is true: either proper names are the names of people, countries, etc, businesses and organisations or most engineers work in industries, or if internet radio is probably one of the most popular forms of streaming media, then retention is the ability of a tag to stay in a fish over a period of time.', 'Assuming either proper names are the names of people, countries, etc, businesses and organisations or most engineers work in industries, we know that if nautical charts are some of the best tools to map routes and determine water depth, then large brooms are relatively warm in winter and cool in summer.', 'When if internet radio is probably one of the most popular forms of streaming media, then retention is the ability of a tag to stay in a fish over a period of time is true, it follows that if nautical charts are some of the best tools to map routes and determine water depth, then large brooms are relatively warm in winter and cool in summer.', 'At least one of two things is true: lead poisoning occurs when lead is inhaled or ingested, or men make up more than half of Internet users, but women are rapidly narrowing the gap.', 'Assuming lead poisoning occurs when lead is inhaled or ingested, we know that it is not true that large brooms are relatively warm in winter and cool in summer.', 'Once we know men make up more than half of Internet users, but women are rapidly narrowing the gap, we also know that it is not true that large brooms are relatively warm in winter and cool in summer.']
|
At least one of two things is true: either proper names are the names of people, countries, etc, businesses and organisations or most engineers work in industries, or if internet radio is probably one of the most popular forms of streaming media, then retention is the ability of a tag to stay in a fish over a period of time. Assuming either proper names are the names of people, countries, etc, businesses and organisations or most engineers work in industries, we know that if nautical charts are some of the best tools to map routes and determine water depth, then large brooms are relatively warm in winter and cool in summer. When if internet radio is probably one of the most popular forms of streaming media, then retention is the ability of a tag to stay in a fish over a period of time is true, it follows that if nautical charts are some of the best tools to map routes and determine water depth, then large brooms are relatively warm in winter and cool in summer. At least one of two things is true: lead poisoning occurs when lead is inhaled or ingested, or men make up more than half of Internet users, but women are rapidly narrowing the gap. Assuming lead poisoning occurs when lead is inhaled or ingested, we know that it is not true that large brooms are relatively warm in winter and cool in summer. Once we know men make up more than half of Internet users, but women are rapidly narrowing the gap, we also know that it is not true that large brooms are relatively warm in winter and cool in summer.
|
The claim that nautical charts are some of the best tools to map routes and determine water depth does not reflect reality.
|
Those that suggest nautical charts are some of the best tools to map routes and determine water depth are right.
|
FALSE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either (Either [4] or [5].) or (If [6], then [7].).
If (Either [4] or [5].), then (If [0], then [1].).
If (If [6], then [7].), then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (Not [1].).
If [3], then (Not [1].).
Therefore, Not [1]..
|
{0: 'Nautical charts are some of the best tools to map routes and determine water depth.', 1: 'Large brooms are relatively warm in winter and cool in summer.', 2: 'Lead poisoning occurs when lead is inhaled or ingested.', 3: 'Men make up more than half of Internet users, but women are rapidly narrowing the gap.', 4: 'Proper names are the names of people, countries, etc, businesses and organisations.', 5: 'Most engineers work in industries.', 6: 'Internet radio is probably one of the most popular forms of streaming media.', 7: 'Retention is the ability of a tag to stay in a fish over a period of time.'}
| 3 |
2,281 |
['Given that lung tumor is sometimes present, it can be inferred that either most young people get spots around puberty or ornamental grasses are beautiful, inexpensive, easy to find and easy to grow in all types of soil.', 'There is good reason to believe that either either foxes are generally nocturnal but can occasionally be seen during the day or household chemicals are dangerous if ingested in large amounts or if neocortexs have (part) nuclei, then reflexology is recommended for chronic conditions such as asthma, headaches and migraines.', 'On the condition that either foxes are generally nocturnal but can occasionally be seen during the day or household chemicals are dangerous if ingested in large amounts, it is definitely the case that lung tumor is sometimes present.', 'On the condition that if neocortexs have (part) nuclei, then reflexology is recommended for chronic conditions such as asthma, headaches and migraines, it is definitely the case that either bogs are more acidic than swamps, and are low in oxygen, so decomposition takes place slowly or most woodchucks have senses.', 'Should it be the case that either bogs are more acidic than swamps, and are low in oxygen, so decomposition takes place slowly or most woodchucks have senses, it follows that most boars make pheromone.', 'One may reasonably assume that if most boars make pheromone, then either most young people get spots around puberty or ornamental grasses are beautiful, inexpensive, easy to find and easy to grow in all types of soil.']
|
Given that lung tumor is sometimes present, it can be inferred that either most young people get spots around puberty or ornamental grasses are beautiful, inexpensive, easy to find and easy to grow in all types of soil. There is good reason to believe that either either foxes are generally nocturnal but can occasionally be seen during the day or household chemicals are dangerous if ingested in large amounts or if neocortexs have (part) nuclei, then reflexology is recommended for chronic conditions such as asthma, headaches and migraines. On the condition that either foxes are generally nocturnal but can occasionally be seen during the day or household chemicals are dangerous if ingested in large amounts, it is definitely the case that lung tumor is sometimes present. On the condition that if neocortexs have (part) nuclei, then reflexology is recommended for chronic conditions such as asthma, headaches and migraines, it is definitely the case that either bogs are more acidic than swamps, and are low in oxygen, so decomposition takes place slowly or most woodchucks have senses. Should it be the case that either bogs are more acidic than swamps, and are low in oxygen, so decomposition takes place slowly or most woodchucks have senses, it follows that most boars make pheromone. One may reasonably assume that if most boars make pheromone, then either most young people get spots around puberty or ornamental grasses are beautiful, inexpensive, easy to find and easy to grow in all types of soil.
|
We know that either most young people get spots around puberty or ornamental grasses are beautiful, inexpensive, easy to find and easy to grow in all types of soil.
|
We know that either most young people get spots around puberty or ornamental grasses are beautiful, inexpensive, easy to find and easy to grow in all types of soil.
|
TRUE
|
Disjunction Elimination:
Either [2] or (Either [3] or [4].). [SC1-1]
If [2], then (Either [0] or [1].).
If (Either [3] or [4].), then (Either [0] or [1].). [SC3-1]
Therefore, Either [0] or [1]..
[SC1-1]
Constructive Dilemma:
Either (Either [6] or [7].) or (If [8], then [9].).
If (Either [6] or [7].), then [2].
If (If [8], then [9].), then (Either [3] or [4].).
Therefore, Either [2] or (Either [3] or [4].)..
[SC3-1]
Hypothetical Syllogism:
If (Either [3] or [4].), then [5].
If [5], then (Either [0] or [1].).
Therefore, If (Either [3] or [4].), then (Either [0] or [1].)..
|
{0: 'Most young people get spots around puberty.', 1: 'Ornamental grasses are beautiful, inexpensive, easy to find and easy to grow in all types of soil.', 2: 'Lung tumor is sometimes present.', 3: 'Bogs are more acidic than swamps, and are low in oxygen, so decomposition takes place slowly.', 4: 'Most woodchucks have senses.', 5: 'Most boars make pheromone.', 6: 'Foxes are generally nocturnal but can occasionally be seen during the day.', 7: 'Household chemicals are dangerous if ingested in large amounts.', 8: 'Neocortexs have (part) nuclei.', 9: 'Reflexology is recommended for chronic conditions such as asthma, headaches and migraines.'}
| 3 |
2,120 |
["Assuming either agriculture also plays an important role in Wyoming's economy or effacements are withdrawals, we know that marine organisms rely on nitrogen-fixing bacteria to convert nitrogen gas into nitrogen compounds.", 'When cells contain long strands of DNA, which are called chromosomes is true, it follows that marine organisms rely on nitrogen-fixing bacteria to convert nitrogen gas into nitrogen compounds.', "The statement 'irradiation is used to.kill insects and bacteria, and to prevent sprouting and slow ripening' is true.", "Once we know lizards are reptiles which means that lizards are cold blooded, we also know that if irradiation is used to.kill insects and bacteria, and to prevent sprouting and slow ripening, then either either agriculture also plays an important role in Wyoming's economy or effacements are withdrawals or cells contain long strands of DNA, which are called chromosomes.", 'It is rational to agree that lizards are reptiles which means that lizards are cold blooded.']
|
Assuming either agriculture also plays an important role in Wyoming's economy or effacements are withdrawals, we know that marine organisms rely on nitrogen-fixing bacteria to convert nitrogen gas into nitrogen compounds. When cells contain long strands of DNA, which are called chromosomes is true, it follows that marine organisms rely on nitrogen-fixing bacteria to convert nitrogen gas into nitrogen compounds. The statement 'irradiation is used to.kill insects and bacteria, and to prevent sprouting and slow ripening' is true. Once we know lizards are reptiles which means that lizards are cold blooded, we also know that if irradiation is used to.kill insects and bacteria, and to prevent sprouting and slow ripening, then either either agriculture also plays an important role in Wyoming's economy or effacements are withdrawals or cells contain long strands of DNA, which are called chromosomes. It is rational to agree that lizards are reptiles which means that lizards are cold blooded.
|
The statement 'marine organisms rely on nitrogen-fixing bacteria to convert nitrogen gas into nitrogen compounds' is true.
|
Marine organisms are aquatic organisms.
|
Uncertain
|
Disjunction Elimination:
Either (Either [1] or [2].) or [3]. [SC1-1]
If (Either [1] or [2].), then [0].
If [3], then [0].
Therefore, [0].
[SC1-1]
Modus Ponens:
If [4], then (Either (Either [1] or [2].) or [3].). [SC1-2]
[4]
Therefore, Either (Either [1] or [2].) or [3]..
[SC1-2]
Modus Ponens:
If [5], then (If [4], then (Either (Either [1] or [2].) or [3].).).
[5]
Therefore, If [4], then (Either (Either [1] or [2].) or [3].)..
|
{0: 'Marine organisms rely on nitrogen-fixing bacteria to convert nitrogen gas into nitrogen compounds.', 1: "Agriculture also plays an important role in Wyoming's economy.", 2: 'Effacements are withdrawals.', 3: 'Cells contain long strands of DNA, which are called chromosomes.', 4: 'Irradiation is used to.kill insects and bacteria, and to prevent sprouting and slow ripening.', 5: 'Lizards are reptiles which means that lizards are cold blooded.'}
| 3 |
2,593 |
["Assuming the claim that mixed seed attracts many birds is false, we know that it is not true that if bears are opportunists, relying on their intelligence and their senses to find food, then back pain is the UK's leading cause of disability, and can affect people of any age.", 'Some people mistakenly believe that flavonoids are antioxidants.', "It is rational to believe that either weed control is the most critical element of organic soybean production or if the notion that 'if the claim that mixed seed attracts many birds is false, then if bears are opportunists, relying on their intelligence and their senses to find food, then back pain is the UK's leading cause of disability, and can affect people of any age' is untrue, then flavonoids are antioxidants.", 'The statement that states weed control is the most critical element of organic soybean production is false.']
|
Assuming the claim that mixed seed attracts many birds is false, we know that it is not true that if bears are opportunists, relying on their intelligence and their senses to find food, then back pain is the UK's leading cause of disability, and can affect people of any age. Some people mistakenly believe that flavonoids are antioxidants. It is rational to believe that either weed control is the most critical element of organic soybean production or if the notion that 'if the claim that mixed seed attracts many birds is false, then if bears are opportunists, relying on their intelligence and their senses to find food, then back pain is the UK's leading cause of disability, and can affect people of any age' is untrue, then flavonoids are antioxidants. The statement that states weed control is the most critical element of organic soybean production is false.
|
It is the case that mixed seed attracts many birds.
|
It is the case that mixed seed attracts many birds.
|
TRUE
|
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]
Modus Tonens:
If (Not (If (Not [0].), then (If [1], then [2].).).), then [3]. [SC1-2]
Not [3].
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC1-2]
Disjunctive Syllogism:
Either [4] or (If (Not (If (Not [0].), then (If [1], then [2].).).), then [3].).
Not [4].
Therefore, If (Not (If (Not [0].), then (If [1], then [2].).).), then [3]..
|
{0: 'Mixed seed attracts many birds.', 1: 'Bears are opportunists, relying on their intelligence and their senses to find food.', 2: "Back pain is the UK's leading cause of disability, and can affect people of any age.", 3: 'Flavonoids are antioxidants.', 4: 'Weed control is the most critical element of organic soybean production.'}
| 3 |
2,981 |
['It is a fact that either hikes take places or adaptations help polar bears survive in the wild.', 'Provided that hikes take places, we know that the claim that baroques are artistic style has no merit.', 'At least one of two things is true: education is an essential tool for achieving the goals of equality, development and peace, or either male dominance is a political system or government is a growth industry.', 'Should it be the case that either male dominance is a political system or government is a growth industry, it follows that if adaptations help polar bears survive in the wild, then the claim that baroques are artistic style has no merit.', 'Once we know the statement, if education is an essential tool for achieving the goals of equality, development and peace, then if adaptations help polar bears survive in the wild, then the claim that baroques are artistic style has no merit, does not hold, we also know that soils are typically the most misunderstood and undervalued resource in urban landscapes.', 'Should it be the case that the statement, if education is an essential tool for achieving the goals of equality, development and peace, then if adaptations help polar bears survive in the wild, then the claim that baroques are artistic style has no merit, does not hold, it follows that we know that the claim that soils are typically the most misunderstood and undervalued resource in urban landscapes is false.']
|
It is a fact that either hikes take places or adaptations help polar bears survive in the wild. Provided that hikes take places, we know that the claim that baroques are artistic style has no merit. At least one of two things is true: education is an essential tool for achieving the goals of equality, development and peace, or either male dominance is a political system or government is a growth industry. Should it be the case that either male dominance is a political system or government is a growth industry, it follows that if adaptations help polar bears survive in the wild, then the claim that baroques are artistic style has no merit. Once we know the statement, if education is an essential tool for achieving the goals of equality, development and peace, then if adaptations help polar bears survive in the wild, then the claim that baroques are artistic style has no merit, does not hold, we also know that soils are typically the most misunderstood and undervalued resource in urban landscapes. Should it be the case that the statement, if education is an essential tool for achieving the goals of equality, development and peace, then if adaptations help polar bears survive in the wild, then the claim that baroques are artistic style has no merit, does not hold, it follows that we know that the claim that soils are typically the most misunderstood and undervalued resource in urban landscapes is false.
|
The claim that baroques are artistic style has no merit.
|
The claim that baroques are artistic style has no merit.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then (Not [0].).
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC3-1]
Disjunction Elimination:
Either [3] or (Either [4] or [5].).
If [3], then (If [2], then (Not [0].).). [SC2-2]
If (Either [4] or [5].), then (If [2], then (Not [0].).).
Therefore, If [2], then (Not [0].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [3], then (If [2], then (Not [0].).).).), then [6].
If (Not (If [3], then (If [2], then (Not [0].).).).), then (Not [6].).
Therefore, If [3], then (If [2], then (Not [0].).)..
|
{0: 'Baroques are artistic style.', 1: 'Hikes take places.', 2: 'Adaptations help polar bears survive in the wild.', 3: 'Education is an essential tool for achieving the goals of equality, development and peace.', 4: 'Male dominance is a political system.', 5: 'Government is a growth industry.', 6: 'Soils are typically the most misunderstood and undervalued resource in urban landscapes.'}
| 3 |
2,013 |
['On the condition that if lasers emit beams, then death is a punishment for disobedience, it is definitely the case that most turbines produce electricity.', 'Once we know most turbines produce electricity, we also know that some ants invade houses.', "So long as the claim that if lasers emit beams, then death is a punishment for disobedience does not reflect reality, 'many people shop on the Internet to avoid paying the tax they owe on their purchases' is true.", 'It is not true that many people shop on the Internet to avoid paying the tax they owe on their purchases.']
|
On the condition that if lasers emit beams, then death is a punishment for disobedience, it is definitely the case that most turbines produce electricity. Once we know most turbines produce electricity, we also know that some ants invade houses. So long as the claim that if lasers emit beams, then death is a punishment for disobedience does not reflect reality, 'many people shop on the Internet to avoid paying the tax they owe on their purchases' is true. It is not true that many people shop on the Internet to avoid paying the tax they owe on their purchases.
|
It is true that some ants invade houses.
|
Most ants are black, brown, red, or yellow.
|
Uncertain
|
Modus Ponens:
If (If [1], then [2].), then [0]. [SC1-1]
If [1], then [2]. [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (If [1], then [2].), then [4].
If [4], then [0].
Therefore, If (If [1], then [2].), then [0]..
[SC2-1]
Modus Tonens:
If (Not (If [1], then [2].).), then [3].
Not [3].
Therefore, If [1], then [2]..
|
{0: 'Some ants invade houses.', 1: 'Lasers emit beams.', 2: 'Death is a punishment for disobedience.', 3: 'Many people shop on the Internet to avoid paying the tax they owe on their purchases.', 4: 'Most turbines produce electricity.'}
| 3 |
2,655 |
["So long as we know that the claim that if baptism also welcomes the baptized person to Holy Communion, then gifts are located in department stores is false, 'peahens are also very aggressive when it comes to finding a suitable partner' is true.", 'Provided that we know that the claim that if baptism also welcomes the baptized person to Holy Communion, then gifts are located in department stores is false, we know that the statement, peahens are also very aggressive when it comes to finding a suitable partner, does not hold.', 'One may reasonably assume that if gifts are located in department stores, then vectors are tensors.', 'Those that suggest vectors are tensors are wrong.']
|
So long as we know that the claim that if baptism also welcomes the baptized person to Holy Communion, then gifts are located in department stores is false, 'peahens are also very aggressive when it comes to finding a suitable partner' is true. Provided that we know that the claim that if baptism also welcomes the baptized person to Holy Communion, then gifts are located in department stores is false, we know that the statement, peahens are also very aggressive when it comes to finding a suitable partner, does not hold. One may reasonably assume that if gifts are located in department stores, then vectors are tensors. Those that suggest vectors are tensors are wrong.
|
The statement 'baptism also welcomes the baptized person to Holy Communion' can be considered false.
|
It is not true that baptisms take place beside streams, in rivers, lakes, oceans, in backyard pools, even indoors.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then [2].
If (Not (If [0], then [1].).), then (Not [2].).
Therefore, If [0], then [1]..
[SC2-1]
Modus Tonens:
If [1], then [3].
Not [3].
Therefore, Not [1]..
|
{0: 'Baptism also welcomes the baptized person to Holy Communion.', 1: 'Gifts are located in department stores.', 2: 'Peahens are also very aggressive when it comes to finding a suitable partner.', 3: 'Vectors are tensors.'}
| 3 |
2,455 |
['Assuming the claim that chinese food lasts for days has no merit, we know that passage is part of text.', 'Those that suggest summers are warm to hot while winters can be extremely cold are wrong.', 'If it is a common misconception that if passage is part of text, then summers are warm to hot while winters can be extremely cold, then venom has functions.', "So long as it is a common misconception that if passage is part of text, then summers are warm to hot while winters can be extremely cold, 'the statement 'venom has functions' can be considered false' is true."]
|
Assuming the claim that chinese food lasts for days has no merit, we know that passage is part of text. Those that suggest summers are warm to hot while winters can be extremely cold are wrong. If it is a common misconception that if passage is part of text, then summers are warm to hot while winters can be extremely cold, then venom has functions. So long as it is a common misconception that if passage is part of text, then summers are warm to hot while winters can be extremely cold, 'the statement 'venom has functions' can be considered false' is true.
|
The statement 'chinese food lasts for days' can be considered true.
|
The statement 'chinese food lasts for days' can be considered true.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If [1], then [2]. [SC1-2]
Not [2].
Therefore, Not [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [1], then [2].).), then [3].
If (Not (If [1], then [2].).), then (Not [3].).
Therefore, If [1], then [2]..
|
{0: 'Chinese food lasts for days.', 1: 'Passage is part of text.', 2: 'Summers are warm to hot while winters can be extremely cold.', 3: 'Venom has functions.'}
| 3 |
2,584 |
['There is good reason to believe that either agility is the ability to change directions while maintaining balance, body control, and speed or if exercise is as valuable to the mind and psyche as it is to the body, then air pollution comes from both manmade and natural sources.', "Given that agility is the ability to change directions while maintaining balance, body control, and speed, it can be inferred that if the statement 'if uncertainty limits effects, then net debt is gross debt minus cash-like assets' can be considered false, then minerals contain bonds.", "When if exercise is as valuable to the mind and psyche as it is to the body, then air pollution comes from both manmade and natural sources is true, it follows that if the statement 'if uncertainty limits effects, then net debt is gross debt minus cash-like assets' can be considered false, then minerals contain bonds.", "On the condition that the claim that if the statement 'if uncertainty limits effects, then net debt is gross debt minus cash-like assets' can be considered false, then it is not the case that minerals contain bonds has no merit, it is definitely the case that if fear is also a motivator, then most sciatica is due to prolapse of a lumbar intervertebral disc.", 'The claim that if fear is also a motivator, then most sciatica is due to prolapse of a lumbar intervertebral disc is false.']
|
There is good reason to believe that either agility is the ability to change directions while maintaining balance, body control, and speed or if exercise is as valuable to the mind and psyche as it is to the body, then air pollution comes from both manmade and natural sources. Given that agility is the ability to change directions while maintaining balance, body control, and speed, it can be inferred that if the statement 'if uncertainty limits effects, then net debt is gross debt minus cash-like assets' can be considered false, then minerals contain bonds. When if exercise is as valuable to the mind and psyche as it is to the body, then air pollution comes from both manmade and natural sources is true, it follows that if the statement 'if uncertainty limits effects, then net debt is gross debt minus cash-like assets' can be considered false, then minerals contain bonds. On the condition that the claim that if the statement 'if uncertainty limits effects, then net debt is gross debt minus cash-like assets' can be considered false, then it is not the case that minerals contain bonds has no merit, it is definitely the case that if fear is also a motivator, then most sciatica is due to prolapse of a lumbar intervertebral disc. The claim that if fear is also a motivator, then most sciatica is due to prolapse of a lumbar intervertebral disc is false.
|
One may reasonably assume that if uncertainty limits effects, then net debt is gross debt minus cash-like assets.
|
One may reasonably assume that if uncertainty limits effects, then net debt is gross debt minus cash-like assets.
|
TRUE
|
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then [2]. [SC1-1]
If (Not (If [0], then [1].).), then (Not [2].). [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then (If (Not (If [0], then [1].).), then [2].).
If (If [4], then [5].), then (If (Not (If [0], then [1].).), then [2].).
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC2-1]
Modus Tonens:
If (Not (If (Not (If [0], then [1].).), then (Not [2].).).), then (If [6], then [7].).
Not (If [6], then [7].).
Therefore, If (Not (If [0], then [1].).), then (Not [2].)..
|
{0: 'Uncertainty limits effects.', 1: 'Net debt is gross debt minus cash-like assets.', 2: 'Minerals contain bonds.', 3: 'Agility is the ability to change directions while maintaining balance, body control, and speed.', 4: 'Exercise is as valuable to the mind and psyche as it is to the body.', 5: 'Air pollution comes from both manmade and natural sources.', 6: 'Fear is also a motivator.', 7: 'Most sciatica is due to prolapse of a lumbar intervertebral disc.'}
| 3 |
2,955 |
['Given that the claim that ubiquinone is made by the body and is present in many common foods does not correspond with reality, it can be inferred that shuffles have (part) strides.', 'We know that at least one of two things is true: some agronomists routinely take stem samples for aphid counts, or either electronic commerce raises a significant number of legal issues or active Immunity Is Long-Lived a. Develops naturally after person is infected with microbe.', 'On the condition that some agronomists routinely take stem samples for aphid counts, it is definitely the case that the statement that states shuffles have (part) strides is false.', 'One may reasonably assume that if the claim that if either electronic commerce raises a significant number of legal issues or active Immunity Is Long-Lived a. Develops naturally after person is infected with microbe, then the statement that states shuffles have (part) strides is false does not reflect reality, then soil aeration increases water infiltrations.', 'On the condition that the claim that if either electronic commerce raises a significant number of legal issues or active Immunity Is Long-Lived a. Develops naturally after person is infected with microbe, then the statement that states shuffles have (part) strides is false does not reflect reality, it is definitely the case that it is not the case that soil aeration increases water infiltrations.']
|
Given that the claim that ubiquinone is made by the body and is present in many common foods does not correspond with reality, it can be inferred that shuffles have (part) strides. We know that at least one of two things is true: some agronomists routinely take stem samples for aphid counts, or either electronic commerce raises a significant number of legal issues or active Immunity Is Long-Lived a. Develops naturally after person is infected with microbe. On the condition that some agronomists routinely take stem samples for aphid counts, it is definitely the case that the statement that states shuffles have (part) strides is false. One may reasonably assume that if the claim that if either electronic commerce raises a significant number of legal issues or active Immunity Is Long-Lived a. Develops naturally after person is infected with microbe, then the statement that states shuffles have (part) strides is false does not reflect reality, then soil aeration increases water infiltrations. On the condition that the claim that if either electronic commerce raises a significant number of legal issues or active Immunity Is Long-Lived a. Develops naturally after person is infected with microbe, then the statement that states shuffles have (part) strides is false does not reflect reality, it is definitely the case that it is not the case that soil aeration increases water infiltrations.
|
It is reasonable to believe that ubiquinone is made by the body and is present in many common foods.
|
It is reasonable to believe that ubiquinone is made by the body and is present in many common foods.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [2] or (Either [3] or [4].).
If [2], then (Not [1].).
If (Either [3] or [4].), then (Not [1].). [SC3-2]
Therefore, Not [1]..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If (Either [3] or [4].), then (Not [1].).).), then [5].
If (Not (If (Either [3] or [4].), then (Not [1].).).), then (Not [5].).
Therefore, If (Either [3] or [4].), then (Not [1].)..
|
{0: 'Ubiquinone is made by the body and is present in many common foods.', 1: 'Shuffles have (part) strides.', 2: 'Some agronomists routinely take stem samples for aphid counts.', 3: 'Electronic commerce raises a significant number of legal issues.', 4: 'Active Immunity Is Long-Lived a. Develops naturally after person is infected with microbe.', 5: 'Soil aeration increases water infiltrations.'}
| 3 |
2,160 |
['Given that many hunters believe deer kills are up because of the weather, it can be inferred that leafy greens are great sources of folate, orange and yellow veggies provide beta-carotene.', "Whenever it is true that either marriage is the union of a man and a woman or farmers have the highest rate of prostrate cancer, 'leafy greens are great sources of folate, orange and yellow veggies provide beta-carotene' is true.", "Should it be the case that the claim that either many hunters believe deer kills are up because of the weather or either marriage is the union of a man and a woman or farmers have the highest rate of prostrate cancer has no merit, it follows that the statement that 'cultural imperialism is the conquest of one culture by another' is incorrect.", 'There is good reason to believe that either if technology is a part of the natural order of things, then cocaine is the second most popular smuggled drug or either removals have little effects or small businesses drive our economy and create jobs.', 'Provided that if technology is a part of the natural order of things, then cocaine is the second most popular smuggled drug, we know that if the claim that either many hunters believe deer kills are up because of the weather or either marriage is the union of a man and a woman or farmers have the highest rate of prostrate cancer has no merit, then cultural imperialism is the conquest of one culture by another.', 'If either removals have little effects or small businesses drive our economy and create jobs, then if the claim that either many hunters believe deer kills are up because of the weather or either marriage is the union of a man and a woman or farmers have the highest rate of prostrate cancer has no merit, then cultural imperialism is the conquest of one culture by another.']
|
Given that many hunters believe deer kills are up because of the weather, it can be inferred that leafy greens are great sources of folate, orange and yellow veggies provide beta-carotene. Whenever it is true that either marriage is the union of a man and a woman or farmers have the highest rate of prostrate cancer, 'leafy greens are great sources of folate, orange and yellow veggies provide beta-carotene' is true. Should it be the case that the claim that either many hunters believe deer kills are up because of the weather or either marriage is the union of a man and a woman or farmers have the highest rate of prostrate cancer has no merit, it follows that the statement that 'cultural imperialism is the conquest of one culture by another' is incorrect. There is good reason to believe that either if technology is a part of the natural order of things, then cocaine is the second most popular smuggled drug or either removals have little effects or small businesses drive our economy and create jobs. Provided that if technology is a part of the natural order of things, then cocaine is the second most popular smuggled drug, we know that if the claim that either many hunters believe deer kills are up because of the weather or either marriage is the union of a man and a woman or farmers have the highest rate of prostrate cancer has no merit, then cultural imperialism is the conquest of one culture by another. If either removals have little effects or small businesses drive our economy and create jobs, then if the claim that either many hunters believe deer kills are up because of the weather or either marriage is the union of a man and a woman or farmers have the highest rate of prostrate cancer has no merit, then cultural imperialism is the conquest of one culture by another.
|
We can assume that leafy greens are great sources of folate, orange and yellow veggies provide beta-carotene.
|
Leafy greens can tolerate light shade.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].). [SC1-1]
If [1], then [0].
If (Either [2] or [3].), then [0].
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or (Either [2] or [3].).).), then [4]. [SC1-2]
If (Not (Either [1] or (Either [2] or [3].).).), then (Not [4].).
Therefore, Either [1] or (Either [2] or [3].)..
[SC1-2]
Disjunction Elimination:
Either (If [5], then [6].) or (Either [7] or [8].).
If (If [5], then [6].), then (If (Not (Either [1] or (Either [2] or [3].).).), then [4].).
If (Either [7] or [8].), then (If (Not (Either [1] or (Either [2] or [3].).).), then [4].).
Therefore, If (Not (Either [1] or (Either [2] or [3].).).), then [4]..
|
{0: 'Leafy greens are great sources of folate, orange and yellow veggies provide beta-carotene.', 1: 'Many hunters believe deer kills are up because of the weather.', 2: 'Marriage is the union of a man and a woman.', 3: 'Farmers have the highest rate of prostrate cancer.', 4: 'Cultural imperialism is the conquest of one culture by another.', 5: 'Technology is a part of the natural order of things.', 6: 'Cocaine is the second most popular smuggled drug.', 7: 'Removals have little effects.', 8: 'Small businesses drive our economy and create jobs.'}
| 3 |
2,977 |
['We know that either all atoms attempt to achieve the stable configuration of eight electrons in the outer most shell or nociceptive pain is caused by damage to tissue.', "Whenever it is true that all atoms attempt to achieve the stable configuration of eight electrons in the outer most shell, 'either bodily fluid regulates blood pressure or stimulants can bring a feeling of alertness and self confidence' is true.", 'If nociceptive pain is caused by damage to tissue, then hot chocolate is liquid.', "It is rational to believe that either if percussion instruments are acoustic instruments, then oceans supply the world's people with more animal protein than any other source or the statement that 'either bodily fluid regulates blood pressure or stimulants can bring a feeling of alertness and self confidence' is incorrect.", "The claim that if percussion instruments are acoustic instruments, then oceans supply the world's people with more animal protein than any other source is false."]
|
We know that either all atoms attempt to achieve the stable configuration of eight electrons in the outer most shell or nociceptive pain is caused by damage to tissue. Whenever it is true that all atoms attempt to achieve the stable configuration of eight electrons in the outer most shell, 'either bodily fluid regulates blood pressure or stimulants can bring a feeling of alertness and self confidence' is true. If nociceptive pain is caused by damage to tissue, then hot chocolate is liquid. It is rational to believe that either if percussion instruments are acoustic instruments, then oceans supply the world's people with more animal protein than any other source or the statement that 'either bodily fluid regulates blood pressure or stimulants can bring a feeling of alertness and self confidence' is incorrect. The claim that if percussion instruments are acoustic instruments, then oceans supply the world's people with more animal protein than any other source is false.
|
We can assume that hot chocolate is liquid.
|
We can assume that hot chocolate is liquid.
|
TRUE
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or [0]. [SC1-1]
Not (Either [1] or [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either [5] or [6].
If [5], then (Either [1] or [2].).
If [6], then [0].
Therefore, Either (Either [1] or [2].) or [0]..
[SC2-1]
Disjunctive Syllogism:
Either (If [3], then [4].) or (Not (Either [1] or [2].).).
Not (If [3], then [4].).
Therefore, Not (Either [1] or [2].)..
|
{0: 'Hot chocolate is liquid.', 1: 'Bodily fluid regulates blood pressure.', 2: 'Stimulants can bring a feeling of alertness and self confidence.', 3: 'Percussion instruments are acoustic instruments.', 4: "Oceans supply the world's people with more animal protein than any other source.", 5: 'All atoms attempt to achieve the stable configuration of eight electrons in the outer most shell.', 6: 'Nociceptive pain is caused by damage to tissue.'}
| 3 |
2,973 |
['We know that either asbestos fibers can cause asbestosis, a fibrosing interstitial lung disease or poppies are flowers.', "Whenever it is true that asbestos fibers can cause asbestosis, a fibrosing interstitial lung disease, 'fibrin sealants are biological adhesives derived from blood' is true.", 'We know that the claim that lava isa stuff is false.', 'At least one of two things is true: caulk can be difficult to keep in vertical joints and on a variety of substrates, or if the claim that if poppies are flowers, then fibrin sealants are biological adhesives derived from blood is false, then lava isa stuff.', 'It is not true that caulk can be difficult to keep in vertical joints and on a variety of substrates.']
|
We know that either asbestos fibers can cause asbestosis, a fibrosing interstitial lung disease or poppies are flowers. Whenever it is true that asbestos fibers can cause asbestosis, a fibrosing interstitial lung disease, 'fibrin sealants are biological adhesives derived from blood' is true. We know that the claim that lava isa stuff is false. At least one of two things is true: caulk can be difficult to keep in vertical joints and on a variety of substrates, or if the claim that if poppies are flowers, then fibrin sealants are biological adhesives derived from blood is false, then lava isa stuff. It is not true that caulk can be difficult to keep in vertical joints and on a variety of substrates.
|
The claim that fibrin sealants are biological adhesives derived from blood is true.
|
The claim that fibrin sealants are biological adhesives derived from blood 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 [3]. [SC1-2]
Not [3].
Therefore, If [2], then [0]..
[SC1-2]
Disjunctive Syllogism:
Either [4] or (If (Not (If [2], then [0].).), then [3].).
Not [4].
Therefore, If (Not (If [2], then [0].).), then [3]..
|
{0: 'Fibrin sealants are biological adhesives derived from blood.', 1: 'Asbestos fibers can cause asbestosis, a fibrosing interstitial lung disease.', 2: 'Poppies are flowers.', 3: 'Lava isa stuff.', 4: 'Caulk can be difficult to keep in vertical joints and on a variety of substrates.'}
| 3 |
2,715 |
["The notion that 'owls face conditions' is untrue.", 'It is a fact that either wolves live in remote forests or some sticklebacks have active thyroids.', "So long as some sticklebacks have active thyroids, 'if either most amphibians live in dry habitats or some spiders kill children, then owls face conditions' is true.", 'It is rational to believe that either large organisations use petabytes of storage to hold massive amounts of data or spores develop on diseased plant parts and are splashed to other parts of the plant or other plants.', 'Assuming large organisations use petabytes of storage to hold massive amounts of data , we know that if wolves live in remote forests, then if either most amphibians live in dry habitats or some spiders kill children, then owls face conditions.', 'Provided that spores develop on diseased plant parts and are splashed to other parts of the plant or other plants, we know that if wolves live in remote forests, then if either most amphibians live in dry habitats or some spiders kill children, then owls face conditions.']
|
The notion that 'owls face conditions' is untrue. It is a fact that either wolves live in remote forests or some sticklebacks have active thyroids. So long as some sticklebacks have active thyroids, 'if either most amphibians live in dry habitats or some spiders kill children, then owls face conditions' is true. It is rational to believe that either large organisations use petabytes of storage to hold massive amounts of data or spores develop on diseased plant parts and are splashed to other parts of the plant or other plants. Assuming large organisations use petabytes of storage to hold massive amounts of data , we know that if wolves live in remote forests, then if either most amphibians live in dry habitats or some spiders kill children, then owls face conditions. Provided that spores develop on diseased plant parts and are splashed to other parts of the plant or other plants, we know that if wolves live in remote forests, then if either most amphibians live in dry habitats or some spiders kill children, then owls face conditions.
|
We know that the claim that either most amphibians live in dry habitats or some spiders kill children is false.
|
The statement 'most amphibians force air' can be considered false.
|
Uncertain
|
Modus Tonens:
If (Either [0] or [1].), then [2]. [SC1-1]
Not [2].
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If (Either [0] or [1].), then [2].). [SC2-2]
If [4], then (If (Either [0] or [1].), then [2].).
Therefore, If (Either [0] or [1].), then [2]..
[SC2-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [3], then (If (Either [0] or [1].), then [2].).).
If [6], then (If [3], then (If (Either [0] or [1].), then [2].).).
Therefore, If [3], then (If (Either [0] or [1].), then [2].)..
|
{0: 'Most amphibians live in dry habitats.', 1: 'Some spiders kill children.', 2: 'Owls face conditions.', 3: 'Wolves live in remote forests.', 4: 'Some sticklebacks have active thyroids.', 5: 'Large organisations use petabytes of storage to hold massive amounts of data .', 6: 'Spores develop on diseased plant parts and are splashed to other parts of the plant or other plants.'}
| 3 |
2,744 |
['Provided that the claim that higher exports help pay for goods and services that are more cheaply produced abroad does not reflect reality, we know that parents to discuss water conservation.', 'One may reasonably assume that if parents to discuss water conservation, then disturbances are motion.', "There is good reason to believe that either hazardous occupations require safety shoes with reinforced toe caps of steel, fiber, or plastic or if parents to discuss water conservation, then the statement 'disturbances are motion' can be considered false.", 'We know that the claim that hazardous occupations require safety shoes with reinforced toe caps of steel, fiber, or plastic is false.']
|
Provided that the claim that higher exports help pay for goods and services that are more cheaply produced abroad does not reflect reality, we know that parents to discuss water conservation. One may reasonably assume that if parents to discuss water conservation, then disturbances are motion. There is good reason to believe that either hazardous occupations require safety shoes with reinforced toe caps of steel, fiber, or plastic or if parents to discuss water conservation, then the statement 'disturbances are motion' can be considered false. We know that the claim that hazardous occupations require safety shoes with reinforced toe caps of steel, fiber, or plastic is false.
|
Many people rightly believe that higher exports help pay for goods and services that are more cheaply produced abroad.
|
Ignorance becomes empowering because it enable people to live.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2].
If [1], then (Not [2].). [SC2-2]
Therefore, Not [1]..
[SC2-2]
Disjunctive Syllogism:
Either [3] or (If [1], then (Not [2].).).
Not [3].
Therefore, If [1], then (Not [2].)..
|
{0: 'Higher exports help pay for goods and services that are more cheaply produced abroad.', 1: 'Parents to discuss water conservation.', 2: 'Disturbances are motion.', 3: 'Hazardous occupations require safety shoes with reinforced toe caps of steel, fiber, or plastic.'}
| 3 |
2,195 |
['It is not the case that some people carry glasses of wine at a ball.', 'The claim that most bread comes from yeast does not correspond with reality.', 'If the statement that states if the statement that states spiders are very sensitive to vibrations, especially in their webs is false, then some people carry glasses of wine at a ball is false, then sandy soils contain large sized soil particles that are loose and easy to work.', 'Provided that sandy soils contain large sized soil particles that are loose and easy to work, we know that most bread comes from yeast.']
|
It is not the case that some people carry glasses of wine at a ball. The claim that most bread comes from yeast does not correspond with reality. If the statement that states if the statement that states spiders are very sensitive to vibrations, especially in their webs is false, then some people carry glasses of wine at a ball is false, then sandy soils contain large sized soil particles that are loose and easy to work. Provided that sandy soils contain large sized soil particles that are loose and easy to work, we know that most bread comes from yeast.
|
It is the case that spiders are very sensitive to vibrations, especially in their webs.
|
It is the case that spiders are very sensitive to vibrations, especially in their webs.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Not [0].), then [1].).), then [2]. [SC1-2]
Not [2].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Hypothetical Syllogism:
If (Not (If (Not [0].), then [1].).), then [3].
If [3], then [2].
Therefore, If (Not (If (Not [0].), then [1].).), then [2]..
|
{0: 'Spiders are very sensitive to vibrations, especially in their webs.', 1: 'Some people carry glasses of wine at a ball.', 2: 'Most bread comes from yeast.', 3: 'Sandy soils contain large sized soil particles that are loose and easy to work.'}
| 3 |
2,191 |
["Whenever it is true that the notion that 'if cigarette smoking is by far the most important risk factor in the development of lung cancer, then hookworms are a major world parasite, infecting nearly a billion people' is untrue, 'dark matter is transparent and emits no light' is true.", 'The claim that dark matter is transparent and emits no light does not reflect reality.', 'Once we know hookworms are a major world parasite, infecting nearly a billion people, we also know that marriage is a privilege granted by state governments to whoever they choose.', "Whenever it is true that marriage is a privilege granted by state governments to whoever they choose, 'blood tests play an important role in the diagnosis and treatment of many cardiovascular conditions' is true."]
|
Whenever it is true that the notion that 'if cigarette smoking is by far the most important risk factor in the development of lung cancer, then hookworms are a major world parasite, infecting nearly a billion people' is untrue, 'dark matter is transparent and emits no light' is true. The claim that dark matter is transparent and emits no light does not reflect reality. Once we know hookworms are a major world parasite, infecting nearly a billion people, we also know that marriage is a privilege granted by state governments to whoever they choose. Whenever it is true that marriage is a privilege granted by state governments to whoever they choose, 'blood tests play an important role in the diagnosis and treatment of many cardiovascular conditions' is true.
|
When cigarette smoking is by far the most important risk factor in the development of lung cancer is true, it follows that blood tests play an important role in the diagnosis and treatment of many cardiovascular conditions.
|
When cigarette smoking is by far the most important risk factor in the development of lung cancer is true, it follows that blood tests play an important role in the diagnosis and treatment of many cardiovascular conditions.
|
TRUE
|
Hypothetical Syllogism:
If [0], then [2]. [SC1-1]
If [2], then [1]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Modus Tonens:
If (Not (If [0], then [2].).), then [4].
Not [4].
Therefore, If [0], then [2]..
[SC2-1]
Hypothetical Syllogism:
If [2], then [3].
If [3], then [1].
Therefore, If [2], then [1]..
|
{0: 'Cigarette smoking is by far the most important risk factor in the development of lung cancer.', 1: 'Blood tests play an important role in the diagnosis and treatment of many cardiovascular conditions.', 2: 'Hookworms are a major world parasite, infecting nearly a billion people.', 3: 'Marriage is a privilege granted by state governments to whoever they choose.', 4: 'Dark matter is transparent and emits no light.'}
| 3 |
2,628 |
['Given that scallops are surface-dwelling bivalves that can swim by clappng together their valves, it can be inferred that if margays can hang from a branch by one back foot, then passports are given by national governments.', 'Assuming it is not the case that scallops are surface-dwelling bivalves that can swim by clappng together their valves, we know that frogs have more well-developed hind legs than toads do.', 'It is rational to believe that either if public health includes more than just the absence of illness, then some foods are high in fat naturally or if it is not the case that scallops are surface-dwelling bivalves that can swim by clappng together their valves, then the statement that states frogs have more well-developed hind legs than toads do is false.', "The statement 'if public health includes more than just the absence of illness, then some foods are high in fat naturally' can be considered false."]
|
Given that scallops are surface-dwelling bivalves that can swim by clappng together their valves, it can be inferred that if margays can hang from a branch by one back foot, then passports are given by national governments. Assuming it is not the case that scallops are surface-dwelling bivalves that can swim by clappng together their valves, we know that frogs have more well-developed hind legs than toads do. It is rational to believe that either if public health includes more than just the absence of illness, then some foods are high in fat naturally or if it is not the case that scallops are surface-dwelling bivalves that can swim by clappng together their valves, then the statement that states frogs have more well-developed hind legs than toads do is false. The statement 'if public health includes more than just the absence of illness, then some foods are high in fat naturally' can be considered false.
|
Given that margays can hang from a branch by one back foot, it can be inferred that passports are given by national governments.
|
Given that margays can hang from a branch by one back foot, it can be inferred that passports are given by national governments.
|
TRUE
|
Modus Ponens:
If [2], then (If [0], then [1].).
[2] [SC2-1]
Therefore, If [0], then [1]..
[SC2-1]
Reductio Ad Absurdum:
If (Not [2].), then [3].
If (Not [2].), then (Not [3].). [SC2-2]
Therefore, [2].
[SC2-2]
Disjunctive Syllogism:
Either (If [4], then [5].) or (If (Not [2].), then (Not [3].).).
Not (If [4], then [5].).
Therefore, If (Not [2].), then (Not [3].)..
|
{0: 'Margays can hang from a branch by one back foot.', 1: 'Passports are given by national governments.', 2: 'Scallops are surface-dwelling bivalves that can swim by clappng together their valves.', 3: 'Frogs have more well-developed hind legs than toads do.', 4: 'Public health includes more than just the absence of illness.', 5: 'Some foods are high in fat naturally.'}
| 3 |
2,536 |
['It is rational to believe that either evil is that which soils our mind or scientists to develop theories.', 'When the claim that if evil is that which soils our mind, then the claim that aromatherapy is said to provide some answers for mirgraine sufferers as well does not correspond with reality does not reflect reality is true, it follows that some many birds feed on buds.', 'On the condition that the claim that if evil is that which soils our mind, then the claim that aromatherapy is said to provide some answers for mirgraine sufferers as well does not correspond with reality does not reflect reality, it is definitely the case that the claim that some many birds feed on buds does not correspond with reality.', 'Once we know scientists to develop theories, we also know that piles of wood are an ideal hiding place for rattlesnakes.', 'Should it be the case that piles of wood are an ideal hiding place for rattlesnakes, it follows that the claim that aromatherapy is said to provide some answers for mirgraine sufferers as well does not correspond with reality.']
|
It is rational to believe that either evil is that which soils our mind or scientists to develop theories. When the claim that if evil is that which soils our mind, then the claim that aromatherapy is said to provide some answers for mirgraine sufferers as well does not correspond with reality does not reflect reality is true, it follows that some many birds feed on buds. On the condition that the claim that if evil is that which soils our mind, then the claim that aromatherapy is said to provide some answers for mirgraine sufferers as well does not correspond with reality does not reflect reality, it is definitely the case that the claim that some many birds feed on buds does not correspond with reality. Once we know scientists to develop theories, we also know that piles of wood are an ideal hiding place for rattlesnakes. Should it be the case that piles of wood are an ideal hiding place for rattlesnakes, it follows that the claim that aromatherapy is said to provide some answers for mirgraine sufferers as well does not correspond with reality.
|
The claim that aromatherapy is said to provide some answers for mirgraine sufferers as well does not correspond with reality.
|
The claim that aromatherapy is said to provide some answers for mirgraine sufferers as well does not correspond with reality.
|
TRUE
|
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]
Reductio Ad Absurdum:
If (Not (If [1], then (Not [0].).).), then [4].
If (Not (If [1], then (Not [0].).).), then (Not [4].).
Therefore, If [1], then (Not [0].)..
[SC3-1]
Hypothetical Syllogism:
If [2], then [3].
If [3], then (Not [0].).
Therefore, If [2], then (Not [0].)..
|
{0: 'Aromatherapy is said to provide some answers for mirgraine sufferers as well.', 1: 'Evil is that which soils our mind.', 2: 'Scientists to develop theories.', 3: 'Piles of wood are an ideal hiding place for rattlesnakes.', 4: 'Some many birds feed on buds.'}
| 3 |
2,880 |
['It is the case that practical godliness is a mysterious paradox, which is incomprehensible to the natural man.', 'The statement, diffusion is the movement of materials from a higher concentration to a lower concentration, does not hold.', 'Either one or both of these statements are true: fords are bodies of water, or if the statement, if practical godliness is a mysterious paradox, which is incomprehensible to the natural man, then most beetles consume other insects, does not hold, then diffusion is the movement of materials from a higher concentration to a lower concentration.', "The statement 'fords are bodies of water' can be considered false."]
|
It is the case that practical godliness is a mysterious paradox, which is incomprehensible to the natural man. The statement, diffusion is the movement of materials from a higher concentration to a lower concentration, does not hold. Either one or both of these statements are true: fords are bodies of water, or if the statement, if practical godliness is a mysterious paradox, which is incomprehensible to the natural man, then most beetles consume other insects, does not hold, then diffusion is the movement of materials from a higher concentration to a lower concentration. The statement 'fords are bodies of water' can be considered false.
|
The statement 'most beetles consume other insects' is true.
|
The statement 'most beetles consume other insects' is true.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If [1], then [0].).), then [2]. [SC1-2]
Not [2].
Therefore, If [1], then [0]..
[SC1-2]
Disjunctive Syllogism:
Either [3] or (If (Not (If [1], then [0].).), then [2].).
Not [3].
Therefore, If (Not (If [1], then [0].).), then [2]..
|
{0: 'Most beetles consume other insects.', 1: 'Practical godliness is a mysterious paradox, which is incomprehensible to the natural man.', 2: 'Diffusion is the movement of materials from a higher concentration to a lower concentration.', 3: 'Fords are bodies of water.'}
| 3 |
2,164 |
['It is not the case that eyelash isa hair.', 'It is a common misconception that either many drug abusers drink alcohol to disguise their use of drugs or love is a marriage of two hearts and two souls.', 'We know that at least one of two things is true: some children can hear and can speak, yet have trouble understanding or producing utterances, or either either many drug abusers drink alcohol to disguise their use of drugs or love is a marriage of two hearts and two souls or if the claim that either binary trees are trees or bananas contain compounds does not correspond with reality, then eyelash isa hair.', 'The statement, some children can hear and can speak, yet have trouble understanding or producing utterances, does not hold.']
|
It is not the case that eyelash isa hair. It is a common misconception that either many drug abusers drink alcohol to disguise their use of drugs or love is a marriage of two hearts and two souls. We know that at least one of two things is true: some children can hear and can speak, yet have trouble understanding or producing utterances, or either either many drug abusers drink alcohol to disguise their use of drugs or love is a marriage of two hearts and two souls or if the claim that either binary trees are trees or bananas contain compounds does not correspond with reality, then eyelash isa hair. The statement, some children can hear and can speak, yet have trouble understanding or producing utterances, does not hold.
|
It is a fact that either binary trees are trees or bananas contain compounds.
|
It is a fact that either binary trees are trees or bananas contain compounds.
|
TRUE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
Not [2].
Therefore, Either [0] or [1]..
[SC1-1]
Disjunctive Syllogism:
Either (Either [3] or [4].) or (If (Not (Either [0] or [1].).), then [2].). [SC1-2]
Not (Either [3] or [4].).
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC1-2]
Disjunctive Syllogism:
Either [5] or (Either (Either [3] or [4].) or (If (Not (Either [0] or [1].).), then [2].).).
Not [5].
Therefore, Either (Either [3] or [4].) or (If (Not (Either [0] or [1].).), then [2].)..
|
{0: 'Binary trees are trees.', 1: 'Bananas contain compounds.', 2: 'Eyelash isa hair.', 3: 'Many drug abusers drink alcohol to disguise their use of drugs.', 4: 'Love is a marriage of two hearts and two souls.', 5: 'Some children can hear and can speak, yet have trouble understanding or producing utterances.'}
| 3 |
2,106 |
['Those that suggest minutes are the official written record of the meetings of an organization or group are right.', "Whenever it is true that blueberries also have a place in the annals of folk medicine, 'if minutes are the official written record of the meetings of an organization or group, then it is not true that ginkgo trees bear fruit' is true.", 'Either one or both of these statements are true: mobility means crossing linguistic and cultural barriers, or crappies are fish.', 'Assuming mobility means crossing linguistic and cultural barriers, we know that blueberries also have a place in the annals of folk medicine.', 'Should it be the case that crappies are fish, it follows that blueberries also have a place in the annals of folk medicine.']
|
Those that suggest minutes are the official written record of the meetings of an organization or group are right. Whenever it is true that blueberries also have a place in the annals of folk medicine, 'if minutes are the official written record of the meetings of an organization or group, then it is not true that ginkgo trees bear fruit' is true. Either one or both of these statements are true: mobility means crossing linguistic and cultural barriers, or crappies are fish. Assuming mobility means crossing linguistic and cultural barriers, we know that blueberries also have a place in the annals of folk medicine. Should it be the case that crappies are fish, it follows that blueberries also have a place in the annals of folk medicine.
|
It is not true that ginkgo trees bear fruit.
|
It is not true that ginkgo trees bear fruit.
|
TRUE
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [2], then (If [1], then (Not [0].).).
[2] [SC2-2]
Therefore, If [1], then (Not [0].)..
[SC2-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then [2].
If [4], then [2].
Therefore, [2].
|
{0: 'Ginkgo trees bear fruit.', 1: 'Minutes are the official written record of the meetings of an organization or group.', 2: 'Blueberries also have a place in the annals of folk medicine.', 3: 'Mobility means crossing linguistic and cultural barriers.', 4: 'Crappies are fish.'}
| 3 |
2,016 |
['We know that at least one of two things is true: spring flowering bulbs are easy to grow and provide years of enjoyment, or most adenoviruses cause serious illnesses.', 'Either one or both of these statements are true: doctors determine overall patterns, or if spring flowering bulbs are easy to grow and provide years of enjoyment, then brazils have (part) sections.', "The statement that 'doctors determine overall patterns' is incorrect.", "So long as the statement that states if most adenoviruses cause serious illnesses, then brazils have (part) sections is false, 'melanocytes are the cells from which melanoma begins to develop' is true.", 'It is not the case that melanocytes are the cells from which melanoma begins to develop.']
|
We know that at least one of two things is true: spring flowering bulbs are easy to grow and provide years of enjoyment, or most adenoviruses cause serious illnesses. Either one or both of these statements are true: doctors determine overall patterns, or if spring flowering bulbs are easy to grow and provide years of enjoyment, then brazils have (part) sections. The statement that 'doctors determine overall patterns' is incorrect. So long as the statement that states if most adenoviruses cause serious illnesses, then brazils have (part) sections is false, 'melanocytes are the cells from which melanoma begins to develop' is true. It is not the case that melanocytes are the cells from which melanoma begins to develop.
|
Those that suggest brazils have (part) sections are right.
|
Brazils have (part) kernels.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [4] or (If [1], then [0].).
Not [4].
Therefore, If [1], then [0]..
[SC3-1]
Modus Tonens:
If (Not (If [2], then [0].).), then [3].
Not [3].
Therefore, If [2], then [0]..
|
{0: 'Brazils have (part) sections.', 1: 'Spring flowering bulbs are easy to grow and provide years of enjoyment.', 2: 'Most adenoviruses cause serious illnesses.', 3: 'Melanocytes are the cells from which melanoma begins to develop.', 4: 'Doctors determine overall patterns.'}
| 3 |
2,575 |
['On the condition that some monkeys live on the ground, while others live in trees, it is definitely the case that most kidneys play roles.', 'Provided that most kidneys play roles, we know that photographers often develop and print their own photographs.', 'There is good reason to believe that either smokers develop problems or biology is the study of all living things.', "So long as smokers develop problems, 'the notion that 'photographers often develop and print their own photographs' is untrue' is true.", "One may reasonably assume that if biology is the study of all living things, then the notion that 'photographers often develop and print their own photographs' is untrue."]
|
On the condition that some monkeys live on the ground, while others live in trees, it is definitely the case that most kidneys play roles. Provided that most kidneys play roles, we know that photographers often develop and print their own photographs. There is good reason to believe that either smokers develop problems or biology is the study of all living things. So long as smokers develop problems, 'the notion that 'photographers often develop and print their own photographs' is untrue' is true. One may reasonably assume that if biology is the study of all living things, then the notion that 'photographers often develop and print their own photographs' is untrue.
|
The claim that some monkeys live on the ground, while others live in trees is false.
|
We can assume that some monkeys live on the ground, while others live in trees.
|
FALSE
|
Modus Tonens:
If [0], then [1].
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC2-1]
Modus Tonens:
If [1], then [2].
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not [2].).
If [4], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Some monkeys live on the ground, while others live in trees.', 1: 'Most kidneys play roles.', 2: 'Photographers often develop and print their own photographs.', 3: 'Smokers develop problems.', 4: 'Biology is the study of all living things.'}
| 3 |
2,925 |
['If collectivism leads to concentration camps, leader worship and war, then if if excretion occurs in the feces, then most caterpillars eat leaves, then tea is rich in tannin, which very efficiently complexes iron ions in solution.', "The statement 'collectivism leads to concentration camps, leader worship and war' can be considered true.", 'If if excretion occurs in the feces, then most caterpillars eat leaves, then if eggs develop by dividing unequally instead of in the spiral pattern of other molluscs, then claymores are swords.', 'Provided that if eggs develop by dividing unequally instead of in the spiral pattern of other molluscs, then claymores are swords, we know that the claim that tea is rich in tannin, which very efficiently complexes iron ions in solution has no merit.']
|
If collectivism leads to concentration camps, leader worship and war, then if if excretion occurs in the feces, then most caterpillars eat leaves, then tea is rich in tannin, which very efficiently complexes iron ions in solution. The statement 'collectivism leads to concentration camps, leader worship and war' can be considered true. If if excretion occurs in the feces, then most caterpillars eat leaves, then if eggs develop by dividing unequally instead of in the spiral pattern of other molluscs, then claymores are swords. Provided that if eggs develop by dividing unequally instead of in the spiral pattern of other molluscs, then claymores are swords, we know that the claim that tea is rich in tannin, which very efficiently complexes iron ions in solution has no merit.
|
The claim that if excretion occurs in the feces, then most caterpillars eat leaves has no merit.
|
The claim that excretion is carried out by paired nephridia that empty into a duct shared with the gonads does not correspond with reality.
|
Uncertain
|
Reductio Ad Absurdum:
If (If [0], then [1].), then [2]. [SC1-1]
If (If [0], then [1].), then (Not [2].). [SC2-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Modus Ponens:
If [5], then (If (If [0], then [1].), then [2].).
[5]
Therefore, If (If [0], then [1].), then [2]..
[SC2-1]
Hypothetical Syllogism:
If (If [0], then [1].), then (If [3], then [4].).
If (If [3], then [4].), then (Not [2].).
Therefore, If (If [0], then [1].), then (Not [2].)..
|
{0: 'Excretion occurs in the feces.', 1: 'Most caterpillars eat leaves.', 2: 'Tea is rich in tannin, which very efficiently complexes iron ions in solution.', 3: 'Eggs develop by dividing unequally instead of in the spiral pattern of other molluscs.', 4: 'Claymores are swords.', 5: 'Collectivism leads to concentration camps, leader worship and war.'}
| 3 |
2,712 |
['At least one of two things is true: cars rust faster in areas with a lot of snow if salt is used on the roads, or detectors measure the rays that pass through and send the measurements to a computer.', 'If most flames affect gases, then the claim that cars rust faster in areas with a lot of snow if salt is used on the roads is false.', "Should it be the case that the statement that 'most flames affect gases' is incorrect, it follows that students express knowledge.", "The statement that 'students express knowledge' is incorrect."]
|
At least one of two things is true: cars rust faster in areas with a lot of snow if salt is used on the roads, or detectors measure the rays that pass through and send the measurements to a computer. If most flames affect gases, then the claim that cars rust faster in areas with a lot of snow if salt is used on the roads is false. Should it be the case that the statement that 'most flames affect gases' is incorrect, it follows that students express knowledge. The statement that 'students express knowledge' is incorrect.
|
The idea that detectors measure the rays that pass through and send the measurements to a computer is true.
|
Some people mistakenly believe that detectors measure the rays that pass through and send the measurements to a computer.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [2], then (Not [1].).
[2] [SC2-2]
Therefore, Not [1]..
[SC2-2]
Modus Tonens:
If (Not [2].), then [3].
Not [3].
Therefore, [2].
|
{0: 'Detectors measure the rays that pass through and send the measurements to a computer.', 1: 'Cars rust faster in areas with a lot of snow if salt is used on the roads.', 2: 'Most flames affect gases.', 3: 'Students express knowledge.'}
| 3 |
2,540 |
["Once we know the notion that 'either roosters have (part) flight feathers or chemical resistance varies between different coatings' is untrue, we also know that red algae use diverse strategies to reproduce, including fragmentation and spore production.", 'When red algae use diverse strategies to reproduce, including fragmentation and spore production is true, it follows that data management supports information and knowledge management, which facilitate decision-making.', 'We know that at least one of two things is true: sodium chlorate is also a potent nephrotoxin and acute tubular necrosis is common, or some wheat has nodes.', 'Assuming sodium chlorate is also a potent nephrotoxin and acute tubular necrosis is common, we know that the statement, data management supports information and knowledge management, which facilitate decision-making, does not hold.', 'Assuming some wheat has nodes, we know that the statement, data management supports information and knowledge management, which facilitate decision-making, does not hold.']
|
Once we know the notion that 'either roosters have (part) flight feathers or chemical resistance varies between different coatings' is untrue, we also know that red algae use diverse strategies to reproduce, including fragmentation and spore production. When red algae use diverse strategies to reproduce, including fragmentation and spore production is true, it follows that data management supports information and knowledge management, which facilitate decision-making. We know that at least one of two things is true: sodium chlorate is also a potent nephrotoxin and acute tubular necrosis is common, or some wheat has nodes. Assuming sodium chlorate is also a potent nephrotoxin and acute tubular necrosis is common, we know that the statement, data management supports information and knowledge management, which facilitate decision-making, does not hold. Assuming some wheat has nodes, we know that the statement, data management supports information and knowledge management, which facilitate decision-making, does not hold.
|
We know that either roosters have (part) flight feathers or chemical resistance varies between different coatings.
|
We know that the claim that either roosters have (part) flight feathers or chemical resistance varies between different coatings is false.
|
FALSE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Hypothetical Syllogism:
If (Not (Either [0] or [1].).), then [5].
If [5], then [2].
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not [2].).
If [4], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Roosters have (part) flight feathers.', 1: 'Chemical resistance varies between different coatings.', 2: 'Data management supports information and knowledge management, which facilitate decision-making.', 3: 'Sodium chlorate is also a potent nephrotoxin and acute tubular necrosis is common.', 4: 'Some wheat has nodes.', 5: 'Red algae use diverse strategies to reproduce, including fragmentation and spore production.'}
| 3 |
2,329 |
['We know that either shrews belong to an entirely different order from rodents like mice or either proteins involve in gamete interaction or computer literacy is important as is the experience of doing casework.', "The statement that 'shrews belong to an entirely different order from rodents like mice' is incorrect.", 'We know that either some raptors nest in hollows or most pathogenic bacteria produce poisons.', 'Once we know some raptors nest in hollows, we also know that the claim that proteins involve in gamete interaction does not correspond with reality.', 'One may reasonably assume that if most pathogenic bacteria produce poisons, then the claim that proteins involve in gamete interaction does not correspond with reality.']
|
We know that either shrews belong to an entirely different order from rodents like mice or either proteins involve in gamete interaction or computer literacy is important as is the experience of doing casework. The statement that 'shrews belong to an entirely different order from rodents like mice' is incorrect. We know that either some raptors nest in hollows or most pathogenic bacteria produce poisons. Once we know some raptors nest in hollows, we also know that the claim that proteins involve in gamete interaction does not correspond with reality. One may reasonably assume that if most pathogenic bacteria produce poisons, then the claim that proteins involve in gamete interaction does not correspond with reality.
|
It is fair to say that computer literacy is important as is the experience of doing casework.
|
Computer literacy is learned through practice, practice, practice.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [4] or (Either [1] or [0].).
Not [4].
Therefore, Either [1] or [0]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (Not [1].).
If [3], then (Not [1].).
Therefore, Not [1]..
|
{0: 'Computer literacy is important as is the experience of doing casework.', 1: 'Proteins involve in gamete interaction.', 2: 'Some raptors nest in hollows.', 3: 'Most pathogenic bacteria produce poisons.', 4: 'Shrews belong to an entirely different order from rodents like mice.'}
| 3 |
2,480 |
['Given that those that suggest if the claim that mandibles have (part) gum ridges has no merit, then frogs are bizarre lissamphibians with dramatically reduced skeletons are wrong, it can be inferred that either gooseberries are thorny or decompression is a period following a major life change.', 'Assuming those that suggest if the claim that mandibles have (part) gum ridges has no merit, then frogs are bizarre lissamphibians with dramatically reduced skeletons are wrong, we know that it is not the case that either gooseberries are thorny or decompression is a period following a major life change.', 'We know that either nitrates are one of the most widespread contaminants threatening Michigan groundwater or some wolverines attack prey.', 'Should it be the case that nitrates are one of the most widespread contaminants threatening Michigan groundwater, it follows that if the claim that mandibles have (part) gum ridges has no merit, then some people mistakenly believe that frogs are bizarre lissamphibians with dramatically reduced skeletons.', "Whenever it is true that some wolverines attack prey, 'if the claim that mandibles have (part) gum ridges has no merit, then some people mistakenly believe that frogs are bizarre lissamphibians with dramatically reduced skeletons' is true."]
|
Given that those that suggest if the claim that mandibles have (part) gum ridges has no merit, then frogs are bizarre lissamphibians with dramatically reduced skeletons are wrong, it can be inferred that either gooseberries are thorny or decompression is a period following a major life change. Assuming those that suggest if the claim that mandibles have (part) gum ridges has no merit, then frogs are bizarre lissamphibians with dramatically reduced skeletons are wrong, we know that it is not the case that either gooseberries are thorny or decompression is a period following a major life change. We know that either nitrates are one of the most widespread contaminants threatening Michigan groundwater or some wolverines attack prey. Should it be the case that nitrates are one of the most widespread contaminants threatening Michigan groundwater, it follows that if the claim that mandibles have (part) gum ridges has no merit, then some people mistakenly believe that frogs are bizarre lissamphibians with dramatically reduced skeletons. Whenever it is true that some wolverines attack prey, 'if the claim that mandibles have (part) gum ridges has no merit, then some people mistakenly believe that frogs are bizarre lissamphibians with dramatically reduced skeletons' is true.
|
Those that suggest mandibles have (part) gum ridges are right.
|
The claim that mandibles have (part) gum ridges does not correspond with reality.
|
FALSE
|
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 (Either [4] or [5].).
If (Not (If (Not [0].), then [1].).), then (Not (Either [4] or [5].).).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If (Not [0].), then (Not [1].).).
If [3], then (If (Not [0].), then (Not [1].).).
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Mandibles have (part) gum ridges.', 1: 'Frogs are bizarre lissamphibians with dramatically reduced skeletons.', 2: 'Nitrates are one of the most widespread contaminants threatening Michigan groundwater.', 3: 'Some wolverines attack prey.', 4: 'Gooseberries are thorny.', 5: 'Decompression is a period following a major life change.'}
| 3 |
2,498 |
['Either adjective clauses modify nouns or pronouns or electromagnetic radiation travels in waves.', 'Given that adjective clauses modify nouns or pronouns , it can be inferred that breathing affects the flow of hormones through the endocrine system.', 'Some people mistakenly believe that students begin experiments.', "So long as the claim that if electromagnetic radiation travels in waves, then breathing affects the flow of hormones through the endocrine system does not correspond with reality, 'natural gas is by far the cleanest-burning of fossil fuels' is true.", 'Assuming natural gas is by far the cleanest-burning of fossil fuels, we know that students begin experiments.']
|
Either adjective clauses modify nouns or pronouns or electromagnetic radiation travels in waves. Given that adjective clauses modify nouns or pronouns , it can be inferred that breathing affects the flow of hormones through the endocrine system. Some people mistakenly believe that students begin experiments. So long as the claim that if electromagnetic radiation travels in waves, then breathing affects the flow of hormones through the endocrine system does not correspond with reality, 'natural gas is by far the cleanest-burning of fossil fuels' is true. Assuming natural gas is by far the cleanest-burning of fossil fuels, we know that students begin experiments.
|
The statement 'breathing affects the flow of hormones through the endocrine system' is true.
|
The statement 'breathing affects the flow of hormones through the endocrine system' 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 [3]. [SC1-2]
Not [3].
Therefore, If [2], then [0]..
[SC1-2]
Hypothetical Syllogism:
If (Not (If [2], then [0].).), then [4].
If [4], then [3].
Therefore, If (Not (If [2], then [0].).), then [3]..
|
{0: 'Breathing affects the flow of hormones through the endocrine system.', 1: 'Adjective clauses modify nouns or pronouns .', 2: 'Electromagnetic radiation travels in waves.', 3: 'Students begin experiments.', 4: 'Natural gas is by far the cleanest-burning of fossil fuels.'}
| 3 |
2,968 |
['It is rational to believe that either most orchids grow during summer or if the claim that animals burrowing or moving through cracks can break rock is false, then other animals have eyes.', 'We know that the claim that most orchids grow during summer is false.', 'Either people can also tolerate fluctuations in relative humidity or if river transportation has a direct impact on the prices consumers pay for the things they buy, then inclusion can benefit children with and without disabilities.', "On the condition that people can also tolerate fluctuations in relative humidity, it is definitely the case that the statement 'other animals have eyes' can be considered false.", "One may reasonably assume that if if river transportation has a direct impact on the prices consumers pay for the things they buy, then inclusion can benefit children with and without disabilities, then the statement 'other animals have eyes' can be considered false."]
|
It is rational to believe that either most orchids grow during summer or if the claim that animals burrowing or moving through cracks can break rock is false, then other animals have eyes. We know that the claim that most orchids grow during summer is false. Either people can also tolerate fluctuations in relative humidity or if river transportation has a direct impact on the prices consumers pay for the things they buy, then inclusion can benefit children with and without disabilities. On the condition that people can also tolerate fluctuations in relative humidity, it is definitely the case that the statement 'other animals have eyes' can be considered false. One may reasonably assume that if if river transportation has a direct impact on the prices consumers pay for the things they buy, then inclusion can benefit children with and without disabilities, then the statement 'other animals have eyes' can be considered false.
|
The claim that animals burrowing or moving through cracks can break rock holds true.
|
Pollen tends to collect on the exposed body surfaces and especially in the hair.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then [1].).
Not [2].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then (Not [1].).
If (If [4], then [5].), then (Not [1].).
Therefore, Not [1]..
|
{0: 'Animals burrowing or moving through cracks can break rock.', 1: 'Other animals have eyes.', 2: 'Most orchids grow during summer.', 3: 'People can also tolerate fluctuations in relative humidity.', 4: 'River transportation has a direct impact on the prices consumers pay for the things they buy.', 5: 'Inclusion can benefit children with and without disabilities.'}
| 3 |
2,405 |
['Assuming if cats usually avoid defecating or urinating in areas where they eat, then humans have fear, we know that if the statement, materials have interest, does not hold, then some archeological sites show the presence of arboriginal people.', 'Given that cats usually avoid defecating or urinating in areas where they eat, it can be inferred that humans have fear.', 'If either honey bees nest in a wide variety of sites or death Valley is a part of the Mojave Desert, then if the statement, materials have interest, does not hold, then it is not true that some archeological sites show the presence of arboriginal people.', 'At least one of two things is true: honey bees nest in a wide variety of sites, or death Valley is a part of the Mojave Desert.']
|
Assuming if cats usually avoid defecating or urinating in areas where they eat, then humans have fear, we know that if the statement, materials have interest, does not hold, then some archeological sites show the presence of arboriginal people. Given that cats usually avoid defecating or urinating in areas where they eat, it can be inferred that humans have fear. If either honey bees nest in a wide variety of sites or death Valley is a part of the Mojave Desert, then if the statement, materials have interest, does not hold, then it is not true that some archeological sites show the presence of arboriginal people. At least one of two things is true: honey bees nest in a wide variety of sites, or death Valley is a part of the Mojave Desert.
|
Those that suggest materials have interest are right.
|
Those that suggest materials have interest are right.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If (If [2], then [3].), then (If (Not [0].), then [1].).
If [2], then [3].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Modus Ponens:
If (Either [4] or [5].), then (If (Not [0].), then (Not [1].).).
Either [4] or [5].
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Materials have interest.', 1: 'Some archeological sites show the presence of arboriginal people.', 2: 'Cats usually avoid defecating or urinating in areas where they eat.', 3: 'Humans have fear.', 4: 'Honey bees nest in a wide variety of sites.', 5: 'Death Valley is a part of the Mojave Desert.'}
| 3 |
2,743 |
['Either pharmacists prepare and dispense the drugs prescribed by physicians or either cardiopulmonary resuscitation is an emergency procedure or ubiquities are software.', 'Should it be the case that pharmacists prepare and dispense the drugs prescribed by physicians, it follows that if chess sets are used for buying, then water going down in rivers, some have half meter.', 'On the condition that if chess sets are used for buying, then water going down in rivers, some have half meter, it is definitely the case that water transport requires regulation, and dynamic control is provided by stomata.', 'Should it be the case that either cardiopulmonary resuscitation is an emergency procedure or ubiquities are software, it follows that death is usually the result of wasting or an opportunistic infection or neoplasm.', 'Should it be the case that death is usually the result of wasting or an opportunistic infection or neoplasm, it follows that whole blood contains all four components and is sometimes used to treat acute hemorrhage patients.']
|
Either pharmacists prepare and dispense the drugs prescribed by physicians or either cardiopulmonary resuscitation is an emergency procedure or ubiquities are software. Should it be the case that pharmacists prepare and dispense the drugs prescribed by physicians, it follows that if chess sets are used for buying, then water going down in rivers, some have half meter. On the condition that if chess sets are used for buying, then water going down in rivers, some have half meter, it is definitely the case that water transport requires regulation, and dynamic control is provided by stomata. Should it be the case that either cardiopulmonary resuscitation is an emergency procedure or ubiquities are software, it follows that death is usually the result of wasting or an opportunistic infection or neoplasm. Should it be the case that death is usually the result of wasting or an opportunistic infection or neoplasm, it follows that whole blood contains all four components and is sometimes used to treat acute hemorrhage patients.
|
Either water transport requires regulation, and dynamic control is provided by stomata or whole blood contains all four components and is sometimes used to treat acute hemorrhage patients.
|
Those that suggest either water transport requires regulation, and dynamic control is provided by stomata or whole blood contains all four components and is sometimes used to treat acute hemorrhage patients are wrong.
|
FALSE
|
Constructive Dilemma:
Either [2] or (Either [3] or [4].).
If [2], then [0]. [SC2-1]
If (Either [3] or [4].), then [1]. [SC3-1]
Therefore, Either [0] or [1]..
[SC2-1]
Hypothetical Syllogism:
If [2], then (If [6], then [7].).
If (If [6], then [7].), then [0].
Therefore, If [2], then [0]..
[SC3-1]
Hypothetical Syllogism:
If (Either [3] or [4].), then [5].
If [5], then [1].
Therefore, If (Either [3] or [4].), then [1]..
|
{0: 'Water transport requires regulation, and dynamic control is provided by stomata.', 1: 'Whole blood contains all four components and is sometimes used to treat acute hemorrhage patients.', 2: 'Pharmacists prepare and dispense the drugs prescribed by physicians.', 3: 'Cardiopulmonary resuscitation is an emergency procedure.', 4: 'Ubiquities are software.', 5: 'Death is usually the result of wasting or an opportunistic infection or neoplasm.', 6: 'Chess sets are used for buying.', 7: 'Water going down in rivers, some have half meter.'}
| 3 |
2,093 |
['Either plants typically develop large patches and are difficult to control or aphids have tailpipes.', 'The claim that twigs have sessile, pointed axillary buds does not reflect reality.', "Whenever it is true that most chickens live in farms, 'either twigs have sessile, pointed axillary buds or it is a common misconception that plants typically develop large patches and are difficult to control' is true.", 'It is reasonable to believe that most chickens live in farms.']
|
Either plants typically develop large patches and are difficult to control or aphids have tailpipes. The claim that twigs have sessile, pointed axillary buds does not reflect reality. Whenever it is true that most chickens live in farms, 'either twigs have sessile, pointed axillary buds or it is a common misconception that plants typically develop large patches and are difficult to control' is true. It is reasonable to believe that most chickens live in farms.
|
It is rational to agree that aphids have tailpipes.
|
Aphids can travel far in the air .
|
Uncertain
|
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]
Modus Ponens:
If [3], then (Either [2] or (Not [1].).).
[3]
Therefore, Either [2] or (Not [1].)..
|
{0: 'Aphids have tailpipes.', 1: 'Plants typically develop large patches and are difficult to control.', 2: 'Twigs have sessile, pointed axillary buds.', 3: 'Most chickens live in farms.'}
| 3 |
2,433 |
["The statement 'bushbucks have (part) rib cages' can be considered false.", 'It is rational to believe that either most anemones have short vase life or meerkats live in groups.', 'Assuming most anemones have short vase life, we know that if it is not true that if biology is also an interdisciplinary subject, then sediment consists of particles of all sizes, including fine clay particles, silt, sand, and gravel, then bushbucks have (part) rib cages.', 'Either one or both of these statements are true: personality traits are normally aspects of a personality, or physical shape has far less to do with backpacking than mental shape does.', 'When personality traits are normally aspects of a personality is true, it follows that if meerkats live in groups, then if it is not true that if biology is also an interdisciplinary subject, then sediment consists of particles of all sizes, including fine clay particles, silt, sand, and gravel, then bushbucks have (part) rib cages.', 'If physical shape has far less to do with backpacking than mental shape does, then if meerkats live in groups, then if it is not true that if biology is also an interdisciplinary subject, then sediment consists of particles of all sizes, including fine clay particles, silt, sand, and gravel, then bushbucks have (part) rib cages.']
|
The statement 'bushbucks have (part) rib cages' can be considered false. It is rational to believe that either most anemones have short vase life or meerkats live in groups. Assuming most anemones have short vase life, we know that if it is not true that if biology is also an interdisciplinary subject, then sediment consists of particles of all sizes, including fine clay particles, silt, sand, and gravel, then bushbucks have (part) rib cages. Either one or both of these statements are true: personality traits are normally aspects of a personality, or physical shape has far less to do with backpacking than mental shape does. When personality traits are normally aspects of a personality is true, it follows that if meerkats live in groups, then if it is not true that if biology is also an interdisciplinary subject, then sediment consists of particles of all sizes, including fine clay particles, silt, sand, and gravel, then bushbucks have (part) rib cages. If physical shape has far less to do with backpacking than mental shape does, then if meerkats live in groups, then if it is not true that if biology is also an interdisciplinary subject, then sediment consists of particles of all sizes, including fine clay particles, silt, sand, and gravel, then bushbucks have (part) rib cages.
|
Provided that biology is also an interdisciplinary subject, we know that sediment consists of particles of all sizes, including fine clay particles, silt, sand, and gravel
|
Provided that biology is also an interdisciplinary subject, we know that sediment consists of particles of all sizes, including fine clay particles, silt, sand, and gravel
|
TRUE
|
Modus Tonens:
If (Not (If [0], then [1].).), then [2]. [SC1-1]
Not [2].
Therefore, If [0], then [1]..
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If (Not (If [0], then [1].).), then [2].).
If [4], then (If (Not (If [0], then [1].).), then [2].). [SC3-2]
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC3-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [4], then (If (Not (If [0], then [1].).), then [2].).).
If [6], then (If [4], then (If (Not (If [0], then [1].).), then [2].).).
Therefore, If [4], then (If (Not (If [0], then [1].).), then [2].)..
|
{0: 'Biology is also an interdisciplinary subject.', 1: 'Sediment consists of particles of all sizes, including fine clay particles, silt, sand, and gravel.', 2: 'Bushbucks have (part) rib cages.', 3: 'Most anemones have short vase life.', 4: 'Meerkats live in groups.', 5: 'Personality traits are normally aspects of a personality.', 6: 'Physical shape has far less to do with backpacking than mental shape does.'}
| 3 |
2,083 |
['Once we know those that suggest clothing also provides protection from ultraviolet radiation are wrong, we also know that most lower atmospheres create wind.', 'Provided that most lower atmospheres create wind, we know that some herbs have potentially serious side effects.', 'Either most black cobras have habitats or if those that suggest clothing also provides protection from ultraviolet radiation are wrong, then we know that the claim that some herbs have potentially serious side effects is false.', 'Some people mistakenly believe that most black cobras have habitats.']
|
Once we know those that suggest clothing also provides protection from ultraviolet radiation are wrong, we also know that most lower atmospheres create wind. Provided that most lower atmospheres create wind, we know that some herbs have potentially serious side effects. Either most black cobras have habitats or if those that suggest clothing also provides protection from ultraviolet radiation are wrong, then we know that the claim that some herbs have potentially serious side effects is false. Some people mistakenly believe that most black cobras have habitats.
|
The idea that clothing also provides protection from ultraviolet radiation is true.
|
Clothing is subject to availability of fabric.
|
Uncertain
|
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].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then (Not [1].).).
Not [2].
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Clothing also provides protection from ultraviolet radiation .', 1: 'Some herbs have potentially serious side effects.', 2: 'Most black cobras have habitats.', 3: 'Most lower atmospheres create wind.'}
| 3 |
2,843 |
["The statement 'either caterpillars give birth to caterpillars or water contains metabolic waste' can be considered false.", "Whenever it is true that cruxs are constellations, 'asset allocation is the process of selecting the very best mix of competing financial instruments' is true.", 'On the condition that if cruxs are constellations, then asset allocation is the process of selecting the very best mix of competing financial instruments, it is definitely the case that evolutionists say dinosaurs predated man by millions of years.', 'Given that evolutionists say dinosaurs predated man by millions of years, it can be inferred that either either caterpillars give birth to caterpillars or water contains metabolic waste or many herbalists divide herbs into groups, depending on what they do.']
|
The statement 'either caterpillars give birth to caterpillars or water contains metabolic waste' can be considered false. Whenever it is true that cruxs are constellations, 'asset allocation is the process of selecting the very best mix of competing financial instruments' is true. On the condition that if cruxs are constellations, then asset allocation is the process of selecting the very best mix of competing financial instruments, it is definitely the case that evolutionists say dinosaurs predated man by millions of years. Given that evolutionists say dinosaurs predated man by millions of years, it can be inferred that either either caterpillars give birth to caterpillars or water contains metabolic waste or many herbalists divide herbs into groups, depending on what they do.
|
many herbalists divide herbs into groups, depending on what they do.
|
Many herbalists divide herbs into groups, depending on what they do.
|
TRUE
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or [0]. [SC1-1]
Not (Either [1] or [2].).
Therefore, [0].
[SC1-1]
Modus Ponens:
If (If [3], then [4].), then (Either (Either [1] or [2].) or [0].). [SC1-2]
If [3], then [4].
Therefore, Either (Either [1] or [2].) or [0]..
[SC1-2]
Hypothetical Syllogism:
If (If [3], then [4].), then [5].
If [5], then (Either (Either [1] or [2].) or [0].).
Therefore, If (If [3], then [4].), then (Either (Either [1] or [2].) or [0].)..
|
{0: 'Many herbalists divide herbs into groups, depending on what they do.', 1: 'Caterpillars give birth to caterpillars.', 2: 'Water contains metabolic waste.', 3: 'Cruxs are constellations.', 4: 'Asset allocation is the process of selecting the very best mix of competing financial instruments.', 5: 'Evolutionists say dinosaurs predated man by millions of years.'}
| 3 |
2,914 |
["So long as we know that the claim that condoms come in a wide variety of styles, colors, thicknesses and flavors is false, 'either copper is found in most foods or modern agriculture uses a vast array of poisons' is true.", "Whenever it is true that if young foxes tend to have a paler but thicker dorsal fur coat compared to adults, then socialism says the state owns the property and people just use it, 'we know that the claim that either copper is found in most foods or modern agriculture uses a vast array of poisons is false' is true.", 'One may reasonably assume that if analyses reveal levels, then if we know that the claim that condoms come in a wide variety of styles, colors, thicknesses and flavors is false, then if young foxes tend to have a paler but thicker dorsal fur coat compared to adults, then socialism says the state owns the property and people just use it.', 'The claim that analyses reveal levels holds true.']
|
So long as we know that the claim that condoms come in a wide variety of styles, colors, thicknesses and flavors is false, 'either copper is found in most foods or modern agriculture uses a vast array of poisons' is true. Whenever it is true that if young foxes tend to have a paler but thicker dorsal fur coat compared to adults, then socialism says the state owns the property and people just use it, 'we know that the claim that either copper is found in most foods or modern agriculture uses a vast array of poisons is false' is true. One may reasonably assume that if analyses reveal levels, then if we know that the claim that condoms come in a wide variety of styles, colors, thicknesses and flavors is false, then if young foxes tend to have a paler but thicker dorsal fur coat compared to adults, then socialism says the state owns the property and people just use it. The claim that analyses reveal levels holds true.
|
Those that suggest condoms come in a wide variety of styles, colors, thicknesses and flavors are right.
|
Condoms come in a variety of styles.
|
Uncertain
|
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]
Hypothetical Syllogism:
If (Not [0].), then (If [3], then [4].). [SC1-2]
If (If [3], then [4].), then (Not (Either [1] or [2].).).
Therefore, If (Not [0].), then (Not (Either [1] or [2].).)..
[SC1-2]
Modus Ponens:
If [5], then (If (Not [0].), then (If [3], then [4].).).
[5]
Therefore, If (Not [0].), then (If [3], then [4].)..
|
{0: 'Condoms come in a wide variety of styles, colors, thicknesses and flavors.', 1: 'Copper is found in most foods.', 2: 'Modern agriculture uses a vast array of poisons.', 3: 'Young foxes tend to have a paler but thicker dorsal fur coat compared to adults.', 4: 'Socialism says the state owns the property and people just use it.', 5: 'Analyses reveal levels.'}
| 3 |
2,657 |
['Given that other scientists use techniques, it can be inferred that menadione mimics the infarct-limiting effect of preconditioning in isolated rat hearts.', 'There is good reason to believe that either most zooplankton contains enzymes or layers protect pansy plants.', "Whenever it is true that most zooplankton contains enzymes, 'most herbs take two to three days to dry except in sand, where they can take as long as three weeks' is true.", 'Given that layers protect pansy plants, it can be inferred that other scientists use techniques.', "So long as mud is located in waterfalls, 'if most herbs take two to three days to dry except in sand, where they can take as long as three weeks, then menadione mimics the infarct-limiting effect of preconditioning in isolated rat hearts' is true.", 'The idea that mud is located in waterfalls is true.']
|
Given that other scientists use techniques, it can be inferred that menadione mimics the infarct-limiting effect of preconditioning in isolated rat hearts. There is good reason to believe that either most zooplankton contains enzymes or layers protect pansy plants. Whenever it is true that most zooplankton contains enzymes, 'most herbs take two to three days to dry except in sand, where they can take as long as three weeks' is true. Given that layers protect pansy plants, it can be inferred that other scientists use techniques. So long as mud is located in waterfalls, 'if most herbs take two to three days to dry except in sand, where they can take as long as three weeks, then menadione mimics the infarct-limiting effect of preconditioning in isolated rat hearts' is true. The idea that mud is located in waterfalls is true.
|
It is reasonable to believe that menadione mimics the infarct-limiting effect of preconditioning in isolated rat hearts.
|
It is reasonable to believe that menadione mimics the infarct-limiting effect of preconditioning in isolated rat hearts.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either [4] or [5].
If [4], then [1].
If [5], then [2].
Therefore, Either [1] or [2]..
[SC2-1]
Modus Ponens:
If [3], then (If [1], then [0].).
[3]
Therefore, If [1], then [0]..
|
{0: 'Menadione mimics the infarct-limiting effect of preconditioning in isolated rat hearts.', 1: 'Most herbs take two to three days to dry except in sand, where they can take as long as three weeks.', 2: 'Other scientists use techniques.', 3: 'Mud is located in waterfalls.', 4: 'Most zooplankton contains enzymes.', 5: 'Layers protect pansy plants.'}
| 3 |
2,414 |
["The notion that 'most astronomers use optical telescopes' is untrue.", 'Given that human beings live in caves and grunt a lot, it can be inferred that if if drunk drivers have urine testeds, then oxygen diffuses into the capillaries while the carbon dioxide diffuses the other way, then most astronomers use optical telescopes.', "So long as depression has far-reaching consequences for the person suffering from it, 'if if drunk drivers have urine testeds, then oxygen diffuses into the capillaries while the carbon dioxide diffuses the other way, then most astronomers use optical telescopes' is true.", 'We know that either socialization is an important aspect of police dog training or startings are running.', "Whenever it is true that socialization is an important aspect of police dog training, 'either human beings live in caves and grunt a lot or depression has far-reaching consequences for the person suffering from it' is true.", "Whenever it is true that startings are running, 'either human beings live in caves and grunt a lot or depression has far-reaching consequences for the person suffering from it' is true."]
|
The notion that 'most astronomers use optical telescopes' is untrue. Given that human beings live in caves and grunt a lot, it can be inferred that if if drunk drivers have urine testeds, then oxygen diffuses into the capillaries while the carbon dioxide diffuses the other way, then most astronomers use optical telescopes. So long as depression has far-reaching consequences for the person suffering from it, 'if if drunk drivers have urine testeds, then oxygen diffuses into the capillaries while the carbon dioxide diffuses the other way, then most astronomers use optical telescopes' is true. We know that either socialization is an important aspect of police dog training or startings are running. Whenever it is true that socialization is an important aspect of police dog training, 'either human beings live in caves and grunt a lot or depression has far-reaching consequences for the person suffering from it' is true. Whenever it is true that startings are running, 'either human beings live in caves and grunt a lot or depression has far-reaching consequences for the person suffering from it' is true.
|
The claim that if drunk drivers have urine testeds, then oxygen diffuses into the capillaries while the carbon dioxide diffuses the other way is false.
|
Provided that drunk drivers have urine testeds, we know that oxygen diffuses into the capillaries while the carbon dioxide diffuses the other way
|
FALSE
|
Modus Tonens:
If (If [0], then [1].), then [2]. [SC1-1]
Not [2].
Therefore, Not (If [0], then [1].)..
[SC1-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (If (If [0], then [1].), then [2].).
If [4], then (If (If [0], then [1].), then [2].).
Therefore, If (If [0], then [1].), then [2]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (Either [3] or [4].).
If [6], then (Either [3] or [4].).
Therefore, Either [3] or [4]..
|
{0: 'Drunk drivers have urine testeds.', 1: 'Oxygen diffuses into the capillaries while the carbon dioxide diffuses the other way.', 2: 'Most astronomers use optical telescopes.', 3: 'Human beings live in caves and grunt a lot.', 4: 'Depression has far-reaching consequences for the person suffering from it.', 5: 'Socialization is an important aspect of police dog training.', 6: 'Startings are running.'}
| 3 |
2,662 |
["One may reasonably assume that if the notion that 'if we know that the claim that some animals are sufficiently sensitive that the collars can cause systemic effects, e.g., miosis is false, then either scientists say animals' thoughts and feelings also affect their actions or swimming cause propulsion' is untrue, then either road rage is a criminal offense or spanish ibexs live in mountains.", "Provided that the notion that 'if we know that the claim that some animals are sufficiently sensitive that the collars can cause systemic effects, e.g., miosis is false, then either scientists say animals' thoughts and feelings also affect their actions or swimming cause propulsion' is untrue, we know that the notion that 'either road rage is a criminal offense or spanish ibexs live in mountains' is untrue.", "If environmental technology is any technology that's designed to benefit the environment, then those that suggest either scientists say animals' thoughts and feelings also affect their actions or swimming cause propulsion are wrong.", "It is the case that environmental technology is any technology that's designed to benefit the environment."]
|
One may reasonably assume that if the notion that 'if we know that the claim that some animals are sufficiently sensitive that the collars can cause systemic effects, e.g., miosis is false, then either scientists say animals' thoughts and feelings also affect their actions or swimming cause propulsion' is untrue, then either road rage is a criminal offense or spanish ibexs live in mountains. Provided that the notion that 'if we know that the claim that some animals are sufficiently sensitive that the collars can cause systemic effects, e.g., miosis is false, then either scientists say animals' thoughts and feelings also affect their actions or swimming cause propulsion' is untrue, we know that the notion that 'either road rage is a criminal offense or spanish ibexs live in mountains' is untrue. If environmental technology is any technology that's designed to benefit the environment, then those that suggest either scientists say animals' thoughts and feelings also affect their actions or swimming cause propulsion are wrong. It is the case that environmental technology is any technology that's designed to benefit the environment.
|
It is rational to agree that some animals are sufficiently sensitive that the collars can cause systemic effects, e.g., miosis.
|
We know that the claim that some animals are sufficiently sensitive that the collars can cause systemic effects, e.g., miosis is false.
|
FALSE
|
Modus Tonens:
If (Not [0].), then (Either [1] or [2].). [SC1-1]
Not (Either [1] or [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then (Either [1] or [2].).).), then (Either [4] or [5].).
If (Not (If (Not [0].), then (Either [1] or [2].).).), then (Not (Either [4] or [5].).).
Therefore, If (Not [0].), then (Either [1] or [2].)..
[SC2-1]
Modus Ponens:
If [3], then (Not (Either [1] or [2].).).
[3]
Therefore, Not (Either [1] or [2].)..
|
{0: 'Some animals are sufficiently sensitive that the collars can cause systemic effects, e.g., miosis.', 1: "Scientists say animals' thoughts and feelings also affect their actions.", 2: 'Swimming cause propulsion.', 3: "Environmental technology is any technology that's designed to benefit the environment.", 4: 'Road rage is a criminal offense.', 5: 'Spanish ibexs live in mountains.'}
| 3 |
2,978 |
["Should it be the case that those that suggest if if most salamanders occur within deciduous forest habitats, then china is the world's largest barite producer, accounting for about a third of total production, then sea slugs leave slime trails, just as slugs and snails do on land are wrong, it follows that either doves have (part) ears or animal life is impacted by the lack of food, too, more than climatic changes.", 'It is not the case that either doves have (part) ears or animal life is impacted by the lack of food, too, more than climatic changes.', "Either one or both of these statements are true: underclassmans are films, or the notion that 'sea slugs leave slime trails, just as slugs and snails do on land' is untrue.", 'It is not true that underclassmans are films.']
|
Should it be the case that those that suggest if if most salamanders occur within deciduous forest habitats, then china is the world's largest barite producer, accounting for about a third of total production, then sea slugs leave slime trails, just as slugs and snails do on land are wrong, it follows that either doves have (part) ears or animal life is impacted by the lack of food, too, more than climatic changes. It is not the case that either doves have (part) ears or animal life is impacted by the lack of food, too, more than climatic changes. Either one or both of these statements are true: underclassmans are films, or the notion that 'sea slugs leave slime trails, just as slugs and snails do on land' is untrue. It is not true that underclassmans are films.
|
The claim that if most salamanders occur within deciduous forest habitats, then china is the world's largest barite producer, accounting for about a third of total production does not reflect reality.
|
The claim that salamanders prefer habitats does not reflect reality.
|
Uncertain
|
Modus Tonens:
If (If [0], then [1].), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Modus Tonens:
If (Not (If (If [0], then [1].), then [2].).), then (Either [3] or [4].).
Not (Either [3] or [4].).
Therefore, If (If [0], then [1].), then [2]..
[SC2-1]
Disjunctive Syllogism:
Either [5] or (Not [2].).
Not [5].
Therefore, Not [2]..
|
{0: 'Most salamanders occur within deciduous forest habitats.', 1: "China is the world's largest barite producer, accounting for about a third of total production.", 2: 'Sea slugs leave slime trails, just as slugs and snails do on land.', 3: 'Doves have (part) ears.', 4: 'Animal life is impacted by the lack of food, too, more than climatic changes.', 5: 'Underclassmans are films.'}
| 3 |
2,771 |
['On the condition that some howler monkeys eat leaves, it is definitely the case that either burrows are most extensive in the northern part of the range where winter temperatures are coldest or buffalo also have specific behavioral adaptations geared to conserving energy.', 'Those that suggest some howler monkeys eat leaves are right.', 'If halophiles are bacteria that are adapted to live in high salt environments, then it is a common misconception that burrows are most extensive in the northern part of the range where winter temperatures are coldest.', 'halophiles are bacteria that are adapted to live in high salt environments.']
|
On the condition that some howler monkeys eat leaves, it is definitely the case that either burrows are most extensive in the northern part of the range where winter temperatures are coldest or buffalo also have specific behavioral adaptations geared to conserving energy. Those that suggest some howler monkeys eat leaves are right. If halophiles are bacteria that are adapted to live in high salt environments, then it is a common misconception that burrows are most extensive in the northern part of the range where winter temperatures are coldest. halophiles are bacteria that are adapted to live in high salt environments.
|
It is a simple truth that buffalo also have specific behavioral adaptations geared to conserving energy.
|
It is a simple truth that buffalo also have specific behavioral adaptations geared to conserving energy.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (Either [1] or [0].).
[3]
Therefore, Either [1] or [0]..
[SC2-1]
Modus Ponens:
If [2], then (Not [1].).
[2]
Therefore, Not [1]..
|
{0: 'Buffalo also have specific behavioral adaptations geared to conserving energy.', 1: 'Burrows are most extensive in the northern part of the range where winter temperatures are coldest.', 2: 'Halophiles are bacteria that are adapted to live in high salt environments.', 3: 'Some howler monkeys eat leaves.'}
| 3 |
2,728 |
['It is rational to believe that either all birds have a cloaca, which is a slit which contains genitals and the end s of excretory tubes or rabbits has-part teeth.', 'Should it be the case that all birds have a cloaca, which is a slit which contains genitals and the end s of excretory tubes, it follows that if it is a common misconception that a zamia is a cycad, then plant bugs frequently cause spotting on leaves, or the death and loss of buds.', "So long as rabbits has-part teeth, 'if it is a common misconception that a zamia is a cycad, then plant bugs frequently cause spotting on leaves, or the death and loss of buds' is true.", 'One may reasonably assume that if it is a common misconception that a zamia is a cycad, then joiners are woodworkers.', 'Provided that joiners are woodworkers, we know that those that suggest plant bugs frequently cause spotting on leaves, or the death and loss of buds are wrong.']
|
It is rational to believe that either all birds have a cloaca, which is a slit which contains genitals and the end s of excretory tubes or rabbits has-part teeth. Should it be the case that all birds have a cloaca, which is a slit which contains genitals and the end s of excretory tubes, it follows that if it is a common misconception that a zamia is a cycad, then plant bugs frequently cause spotting on leaves, or the death and loss of buds. So long as rabbits has-part teeth, 'if it is a common misconception that a zamia is a cycad, then plant bugs frequently cause spotting on leaves, or the death and loss of buds' is true. One may reasonably assume that if it is a common misconception that a zamia is a cycad, then joiners are woodworkers. Provided that joiners are woodworkers, we know that those that suggest plant bugs frequently cause spotting on leaves, or the death and loss of buds are wrong.
|
We can assume that a zamia is a cycad.
|
A zamia is a cycad.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If (Not [0].), then [1].).
If [3], then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Hypothetical Syllogism:
If (Not [0].), then [4].
If [4], then (Not [1].).
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'A zamia is a cycad.', 1: 'Plant bugs frequently cause spotting on leaves, or the death and loss of buds.', 2: 'All birds have a cloaca, which is a slit which contains genitals and the end s of excretory tubes.', 3: 'Rabbits has-part teeth.', 4: 'Joiners are woodworkers.'}
| 3 |
2,911 |
['Once we know some bands say things that never ring true or really ever happen, we also know that we know that the claim that some examples are amoeba, paramecium, bacteria, and cyanobacteria is false.', 'Either one or both of these statements are true: men commit suicide three times more frequently than women do, or either some bands say things that never ring true or really ever happen or curfews are signals.', 'We know that the claim that men commit suicide three times more frequently than women do is false.', 'Either evidence comes to light or if curfews are signals, then we know that the claim that some examples are amoeba, paramecium, bacteria, and cyanobacteria is false.', 'The claim that evidence comes to light does not correspond with reality.']
|
Once we know some bands say things that never ring true or really ever happen, we also know that we know that the claim that some examples are amoeba, paramecium, bacteria, and cyanobacteria is false. Either one or both of these statements are true: men commit suicide three times more frequently than women do, or either some bands say things that never ring true or really ever happen or curfews are signals. We know that the claim that men commit suicide three times more frequently than women do is false. Either evidence comes to light or if curfews are signals, then we know that the claim that some examples are amoeba, paramecium, bacteria, and cyanobacteria is false. The claim that evidence comes to light does not correspond with reality.
|
We know that the claim that some examples are amoeba, paramecium, bacteria, and cyanobacteria is false.
|
We can assume that some examples are amoeba, paramecium, bacteria, and cyanobacteria.
|
FALSE
|
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]
Disjunctive Syllogism:
Either [4] or (Either [1] or [2].).
Not [4].
Therefore, Either [1] or [2]..
[SC3-1]
Disjunctive Syllogism:
Either [3] or (If [2], then (Not [0].).).
Not [3].
Therefore, If [2], then (Not [0].)..
|
{0: 'Some examples are amoeba, paramecium, bacteria, and cyanobacteria.', 1: 'Some bands say things that never ring true or really ever happen.', 2: 'Curfews are signals.', 3: 'Evidence comes to light.', 4: 'Men commit suicide three times more frequently than women do.'}
| 3 |
2,807 |
['When it is not the case that some plants grow in zones is true, it follows that conscious breathing leads to realizing the link between breathing patterns and mental activity.', "When different glands secrete different pheromones which affect a number of behaviors is true, it follows that the statement that 'conscious breathing leads to realizing the link between breathing patterns and mental activity' is incorrect.", 'Given that bombs are part of militaries, it can be inferred that different glands secrete different pheromones which affect a number of behaviors.', 'It is rational to agree that bombs are part of militaries.']
|
When it is not the case that some plants grow in zones is true, it follows that conscious breathing leads to realizing the link between breathing patterns and mental activity. When different glands secrete different pheromones which affect a number of behaviors is true, it follows that the statement that 'conscious breathing leads to realizing the link between breathing patterns and mental activity' is incorrect. Given that bombs are part of militaries, it can be inferred that different glands secrete different pheromones which affect a number of behaviors. It is rational to agree that bombs are part of militaries.
|
It is rational to agree that some plants grow in zones.
|
It is rational to agree that some plants grow in zones.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [2], then (Not [1].).
[2] [SC2-2]
Therefore, Not [1]..
[SC2-2]
Modus Ponens:
If [3], then [2].
[3]
Therefore, [2].
|
{0: 'Some plants grow in zones.', 1: 'Conscious breathing leads to realizing the link between breathing patterns and mental activity.', 2: 'Different glands secrete different pheromones which affect a number of behaviors.', 3: 'Bombs are part of militaries.'}
| 3 |
2,322 |
["So long as the claim that saponins are bitter and reduce the palatability of livestock feeds has no merit, 'chronic endometritis is likely to be a cause in longstanding infertility' is true.", 'If chronic endometritis is likely to be a cause in longstanding infertility, then virtual reality is a new and effective tool for studies and researches in science.', 'It is rational to believe that either intimidation is the use of threatening words or conduct, such as angry shouting and fist-waving or if the claim that saponins are bitter and reduce the palatability of livestock feeds has no merit, then some people mistakenly believe that virtual reality is a new and effective tool for studies and researches in science.', 'The claim that intimidation is the use of threatening words or conduct, such as angry shouting and fist-waving has no merit.']
|
So long as the claim that saponins are bitter and reduce the palatability of livestock feeds has no merit, 'chronic endometritis is likely to be a cause in longstanding infertility' is true. If chronic endometritis is likely to be a cause in longstanding infertility, then virtual reality is a new and effective tool for studies and researches in science. It is rational to believe that either intimidation is the use of threatening words or conduct, such as angry shouting and fist-waving or if the claim that saponins are bitter and reduce the palatability of livestock feeds has no merit, then some people mistakenly believe that virtual reality is a new and effective tool for studies and researches in science. The claim that intimidation is the use of threatening words or conduct, such as angry shouting and fist-waving has no merit.
|
The statement that states saponins are bitter and reduce the palatability of livestock feeds is right.
|
Zinc chloride is an irritant gas which can cause severe pulmonary damage including pulmonary oedema.
|
Uncertain
|
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].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then (Not [1].).).
Not [2].
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Saponins are bitter and reduce the palatability of livestock feeds.', 1: 'Virtual reality is a new and effective tool for studies and researches in science.', 2: 'Intimidation is the use of threatening words or conduct, such as angry shouting and fist-waving.', 3: 'Chronic endometritis is likely to be a cause in longstanding infertility.'}
| 3 |
2,556 |
['It is a fact that either if elephants copulate many times over a few days, then wolves mate for life, and are gentle towards one another or marine iguanas are herbivorous.', 'On the condition that marine iguanas are herbivorous, it is definitely the case that some masts have reproductive output.', 'We know that at least one of two things is true: catchers have (part) human bodies, or either some insects show large variability both temporal and spatial or safeguards are essential for protecting workers from needless and preventable injuries.', 'Once we know catchers have (part) human bodies, we also know that if if elephants copulate many times over a few days, then wolves mate for life, and are gentle towards one another, then some masts have reproductive output.', "So long as the claim that if either some insects show large variability both temporal and spatial or safeguards are essential for protecting workers from needless and preventable injuries, then if if elephants copulate many times over a few days, then wolves mate for life, and are gentle towards one another, then some masts have reproductive output does not reflect reality, 'fire ants are social insects consisting of a queen, workers, eggs and larvae' is true.", "So long as the claim that if either some insects show large variability both temporal and spatial or safeguards are essential for protecting workers from needless and preventable injuries, then if if elephants copulate many times over a few days, then wolves mate for life, and are gentle towards one another, then some masts have reproductive output does not reflect reality, 'it is a common misconception that fire ants are social insects consisting of a queen, workers, eggs and larvae' is true."]
|
It is a fact that either if elephants copulate many times over a few days, then wolves mate for life, and are gentle towards one another or marine iguanas are herbivorous. On the condition that marine iguanas are herbivorous, it is definitely the case that some masts have reproductive output. We know that at least one of two things is true: catchers have (part) human bodies, or either some insects show large variability both temporal and spatial or safeguards are essential for protecting workers from needless and preventable injuries. Once we know catchers have (part) human bodies, we also know that if if elephants copulate many times over a few days, then wolves mate for life, and are gentle towards one another, then some masts have reproductive output. So long as the claim that if either some insects show large variability both temporal and spatial or safeguards are essential for protecting workers from needless and preventable injuries, then if if elephants copulate many times over a few days, then wolves mate for life, and are gentle towards one another, then some masts have reproductive output does not reflect reality, 'fire ants are social insects consisting of a queen, workers, eggs and larvae' is true. So long as the claim that if either some insects show large variability both temporal and spatial or safeguards are essential for protecting workers from needless and preventable injuries, then if if elephants copulate many times over a few days, then wolves mate for life, and are gentle towards one another, then some masts have reproductive output does not reflect reality, 'it is a common misconception that fire ants are social insects consisting of a queen, workers, eggs and larvae' is true.
|
The idea that some masts have reproductive output is true.
|
The idea that some masts have reproductive output is true.
|
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]
Disjunction Elimination:
Either [4] or (Either [5] or [6].).
If [4], then (If (If [1], then [2].), then [0].).
If (Either [5] or [6].), then (If (If [1], then [2].), then [0].). [SC3-2]
Therefore, If (If [1], then [2].), then [0]..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If (Either [5] or [6].), then (If (If [1], then [2].), then [0].).).), then [7].
If (Not (If (Either [5] or [6].), then (If (If [1], then [2].), then [0].).).), then (Not [7].).
Therefore, If (Either [5] or [6].), then (If (If [1], then [2].), then [0].)..
|
{0: 'Some masts have reproductive output.', 1: 'Elephants copulate many times over a few days.', 2: 'Wolves mate for life, and are gentle towards one another.', 3: 'Marine iguanas are herbivorous.', 4: 'Catchers have (part) human bodies.', 5: 'Some insects show large variability both temporal and spatial.', 6: 'Safeguards are essential for protecting workers from needless and preventable injuries.', 7: 'Fire ants are social insects consisting of a queen, workers, eggs and larvae.'}
| 3 |
2,357 |
["So long as free radicals attempt to gain an electron from natural proteins in the skin to acquire stability, 'if those that suggest either chromosomes are present in every cell nucleus with very few and special exceptions or uranium dioxide is oxidized in contact with oxygen to the triuranium octaoxide are wrong, then organisms obtain nutrients' is true.", 'It is the case that free radicals attempt to gain an electron from natural proteins in the skin to acquire stability.', 'We know that either epidemiological evidence is statistical evidence connecting the disease to a particular exposure or the claim that organisms obtain nutrients does not correspond with reality.', 'We know that the claim that epidemiological evidence is statistical evidence connecting the disease to a particular exposure is false.']
|
So long as free radicals attempt to gain an electron from natural proteins in the skin to acquire stability, 'if those that suggest either chromosomes are present in every cell nucleus with very few and special exceptions or uranium dioxide is oxidized in contact with oxygen to the triuranium octaoxide are wrong, then organisms obtain nutrients' is true. It is the case that free radicals attempt to gain an electron from natural proteins in the skin to acquire stability. We know that either epidemiological evidence is statistical evidence connecting the disease to a particular exposure or the claim that organisms obtain nutrients does not correspond with reality. We know that the claim that epidemiological evidence is statistical evidence connecting the disease to a particular exposure is false.
|
We know that at least one of two things is true: chromosomes are present in every cell nucleus with very few and special exceptions, or uranium dioxide is oxidized in contact with oxygen to the triuranium octaoxide .
|
Some people mistakenly believe that either chromosomes are present in every cell nucleus with very few and special exceptions or uranium dioxide is oxidized in contact with oxygen to the triuranium octaoxide .
|
FALSE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Modus Ponens:
If [4], then (If (Not (Either [0] or [1].).), then [2].).
[4]
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (Not [2].).
Not [3].
Therefore, Not [2]..
|
{0: 'Chromosomes are present in every cell nucleus with very few and special exceptions.', 1: 'Uranium dioxide is oxidized in contact with oxygen to the triuranium octaoxide .', 2: 'Organisms obtain nutrients.', 3: 'Epidemiological evidence is statistical evidence connecting the disease to a particular exposure.', 4: 'Free radicals attempt to gain an electron from natural proteins in the skin to acquire stability.'}
| 3 |
2,069 |
['Either electromagnetic waves are a form of energy or if a mental state is a condition, then if some insects have the most unusual methods of home-building, then anemones require bright light in order to survive.', 'Those that suggest electromagnetic waves are a form of energy are wrong.', 'Provided that the statement, a mental state is a condition, does not hold, we know that tropical forests absorb much of carbon dioxide that is released in the atmosphere.', 'It is not true that tropical forests absorb much of carbon dioxide that is released in the atmosphere.']
|
Either electromagnetic waves are a form of energy or if a mental state is a condition, then if some insects have the most unusual methods of home-building, then anemones require bright light in order to survive. Those that suggest electromagnetic waves are a form of energy are wrong. Provided that the statement, a mental state is a condition, does not hold, we know that tropical forests absorb much of carbon dioxide that is released in the atmosphere. It is not true that tropical forests absorb much of carbon dioxide that is released in the atmosphere.
|
If some insects have the most unusual methods of home-building, then anemones require bright light in order to survive.
|
The claim that if some insects have the most unusual methods of home-building, then anemones require bright light in order to survive does not reflect reality.
|
FALSE
|
Modus Ponens:
If [2], then (If [0], then [1].). [SC1-1]
[2] [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If [2], then (If [0], then [1].).).
Not [3].
Therefore, If [2], then (If [0], then [1].)..
[SC2-1]
Modus Tonens:
If (Not [2].), then [4].
Not [4].
Therefore, [2].
|
{0: 'Some insects have the most unusual methods of home-building.', 1: 'Anemones require bright light in order to survive.', 2: 'A mental state is a condition.', 3: 'Electromagnetic waves are a form of energy.', 4: 'Tropical forests absorb much of carbon dioxide that is released in the atmosphere.'}
| 3 |
2,514 |
['On the condition that molds grow year-round, it is definitely the case that substance abuse puts a strain on relationships.', 'Should it be the case that molds grow year-round, it follows that existential guilt is to be punished only roughly by living along.', "Given that the notion that 'if existential guilt is to be punished only roughly by living along, then the notion that 'substance abuse puts a strain on relationships' is untrue' is untrue, it can be inferred that influenza is a common and frequently debilitating condition.", "Whenever it is true that the notion that 'if existential guilt is to be punished only roughly by living along, then the notion that 'substance abuse puts a strain on relationships' is untrue' is untrue, 'it is not the case that influenza is a common and frequently debilitating condition' is true."]
|
On the condition that molds grow year-round, it is definitely the case that substance abuse puts a strain on relationships. Should it be the case that molds grow year-round, it follows that existential guilt is to be punished only roughly by living along. Given that the notion that 'if existential guilt is to be punished only roughly by living along, then the notion that 'substance abuse puts a strain on relationships' is untrue' is untrue, it can be inferred that influenza is a common and frequently debilitating condition. Whenever it is true that the notion that 'if existential guilt is to be punished only roughly by living along, then the notion that 'substance abuse puts a strain on relationships' is untrue' is untrue, 'it is not the case that influenza is a common and frequently debilitating condition' is true.
|
The claim that molds grow year-round does not reflect reality.
|
We know that the claim that molds are larger than bacteria is false.
|
Uncertain
|
Reductio Ad Absurdum:
If [0], then [1].
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC2-1]
Hypothetical Syllogism:
If [0], then [2].
If [2], then (Not [1].). [SC2-2]
Therefore, If [0], then (Not [1].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [2], then (Not [1].).).), then [3].
If (Not (If [2], then (Not [1].).).), then (Not [3].).
Therefore, If [2], then (Not [1].)..
|
{0: 'Molds grow year-round.', 1: 'Substance abuse puts a strain on relationships.', 2: 'Existential guilt is to be punished only roughly by living along.', 3: 'Influenza is a common and frequently debilitating condition.'}
| 3 |
2,509 |
["If some people mistakenly believe that either either hamsters are very noctural and spend most of the day in a very deep sleep or kings have (part) cell membranes or the statement that 'some mushrooms can be deadly if eaten' is incorrect, then prism is many things.", 'It is not the case that prism is many things.', 'There is good reason to believe that either wood rot is caused by extensive exposure to moisture or either complex carbohydrates are many molecules of simple sugars linked together like beads on a string or tellers have (part) vacuoles.', 'Should it be the case that wood rot is caused by extensive exposure to moisture, it follows that it is not the case that either hamsters are very noctural and spend most of the day in a very deep sleep or kings have (part) cell membranes.', 'Given that either complex carbohydrates are many molecules of simple sugars linked together like beads on a string or tellers have (part) vacuoles, it can be inferred that it is not the case that either hamsters are very noctural and spend most of the day in a very deep sleep or kings have (part) cell membranes.']
|
If some people mistakenly believe that either either hamsters are very noctural and spend most of the day in a very deep sleep or kings have (part) cell membranes or the statement that 'some mushrooms can be deadly if eaten' is incorrect, then prism is many things. It is not the case that prism is many things. There is good reason to believe that either wood rot is caused by extensive exposure to moisture or either complex carbohydrates are many molecules of simple sugars linked together like beads on a string or tellers have (part) vacuoles. Should it be the case that wood rot is caused by extensive exposure to moisture, it follows that it is not the case that either hamsters are very noctural and spend most of the day in a very deep sleep or kings have (part) cell membranes. Given that either complex carbohydrates are many molecules of simple sugars linked together like beads on a string or tellers have (part) vacuoles, it can be inferred that it is not the case that either hamsters are very noctural and spend most of the day in a very deep sleep or kings have (part) cell membranes.
|
The statement that 'some mushrooms can be deadly if eaten' is incorrect.
|
The statement that 'some mushrooms can be deadly if eaten' is incorrect.
|
TRUE
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or (Not [0].). [SC1-1]
Not (Either [1] or [2].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (Either (Either [1] or [2].) or (Not [0].).).), then [6].
Not [6].
Therefore, Either (Either [1] or [2].) or (Not [0].)..
[SC2-1]
Disjunction Elimination:
Either [3] or (Either [4] or [5].).
If [3], then (Not (Either [1] or [2].).).
If (Either [4] or [5].), then (Not (Either [1] or [2].).).
Therefore, Not (Either [1] or [2].)..
|
{0: 'Some mushrooms can be deadly if eaten.', 1: 'Hamsters are very noctural and spend most of the day in a very deep sleep.', 2: 'Kings have (part) cell membranes.', 3: 'Wood rot is caused by extensive exposure to moisture.', 4: 'Complex carbohydrates are many molecules of simple sugars linked together like beads on a string.', 5: 'Tellers have (part) vacuoles.', 6: 'Prism is many things.'}
| 3 |
2,340 |
['Assuming dominant inheritance means one copy of the abnormal gene is sufficient to cause disease, we know that it is not true that if old news has low values, then city halls are halls.', 'Either one or both of these statements are true: vibration also damages nerves, muscles, bones and joints of the hand and arm, or dominant inheritance means one copy of the abnormal gene is sufficient to cause disease.', 'Either if cheese is made using milk, then forgery is an important issue for security printers and banks or scratching is one behaviour that causes many cat owners some grief.', 'Provided that if cheese is made using milk, then forgery is an important issue for security printers and banks, we know that the claim that vibration also damages nerves, muscles, bones and joints of the hand and arm does not correspond with reality.', 'Given that scratching is one behaviour that causes many cat owners some grief, it can be inferred that the claim that vibration also damages nerves, muscles, bones and joints of the hand and arm does not correspond with reality.']
|
Assuming dominant inheritance means one copy of the abnormal gene is sufficient to cause disease, we know that it is not true that if old news has low values, then city halls are halls. Either one or both of these statements are true: vibration also damages nerves, muscles, bones and joints of the hand and arm, or dominant inheritance means one copy of the abnormal gene is sufficient to cause disease. Either if cheese is made using milk, then forgery is an important issue for security printers and banks or scratching is one behaviour that causes many cat owners some grief. Provided that if cheese is made using milk, then forgery is an important issue for security printers and banks, we know that the claim that vibration also damages nerves, muscles, bones and joints of the hand and arm does not correspond with reality. Given that scratching is one behaviour that causes many cat owners some grief, it can be inferred that the claim that vibration also damages nerves, muscles, bones and joints of the hand and arm does not correspond with reality.
|
It is not true that if old news has low values, then city halls are halls.
|
It is not true that if old news has low values, then city halls are halls.
|
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 (If [4], then [5].) or [6].
If (If [4], then [5].), then (Not [3].).
If [6], then (Not [3].).
Therefore, Not [3]..
|
{0: 'Old news has low values.', 1: 'City halls are halls.', 2: 'Dominant inheritance means one copy of the abnormal gene is sufficient to cause disease.', 3: 'Vibration also damages nerves, muscles, bones and joints of the hand and arm.', 4: 'Cheese is made using milk.', 5: 'Forgery is an important issue for security printers and banks.', 6: 'Scratching is one behaviour that causes many cat owners some grief.'}
| 3 |
2,221 |
['Provided that the claim that if every microorganism has a very short life, then the statement, hawksbills have (part) nuclei, does not hold does not reflect reality, we know that acupressure is the stimulation of specific points to promote therapeutic results.', 'The statement that states acupressure is the stimulation of specific points to promote therapeutic results is false.', 'Assuming it is a common misconception that every microorganism has a very short life, we know that crosses mark the centers of the two galaxies.', 'It is not true that crosses mark the centers of the two galaxies.']
|
Provided that the claim that if every microorganism has a very short life, then the statement, hawksbills have (part) nuclei, does not hold does not reflect reality, we know that acupressure is the stimulation of specific points to promote therapeutic results. The statement that states acupressure is the stimulation of specific points to promote therapeutic results is false. Assuming it is a common misconception that every microorganism has a very short life, we know that crosses mark the centers of the two galaxies. It is not true that crosses mark the centers of the two galaxies.
|
The statement, hawksbills have (part) nuclei, does not hold.
|
The claim that hawksbills have (part) nuclei is true.
|
FALSE
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1] [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (If [1], then (Not [0].).).), then [3].
Not [3].
Therefore, If [1], then (Not [0].)..
[SC2-1]
Modus Tonens:
If (Not [1].), then [2].
Not [2].
Therefore, [1].
|
{0: 'Hawksbills have (part) nuclei.', 1: 'Every microorganism has a very short life.', 2: 'Crosses mark the centers of the two galaxies.', 3: 'Acupressure is the stimulation of specific points to promote therapeutic results.'}
| 3 |
2,928 |
['Those that suggest ignorance belongs to uninstructed human brains are wrong.', "On the condition that either some avocados contain poison or all migratory birds require tags with hunter's name and address and dates of kills, it is definitely the case that if the claim that scorpions to conserve venom is false, then ignorance belongs to uninstructed human brains.", 'One may reasonably assume that if if uniforms have details, then scientific research is more than just data collection and analyses, then if the claim that scorpions to conserve venom is false, then ignorance belongs to uninstructed human brains.', 'Either one or both of these statements are true: experience is the food that feeds brain connections, or bristles are hair.', "Provided that experience is the food that feeds brain connections, we know that either some avocados contain poison or all migratory birds require tags with hunter's name and address and dates of kills.", 'On the condition that bristles are hair, it is definitely the case that if uniforms have details, then scientific research is more than just data collection and analyses.']
|
Those that suggest ignorance belongs to uninstructed human brains are wrong. On the condition that either some avocados contain poison or all migratory birds require tags with hunter's name and address and dates of kills, it is definitely the case that if the claim that scorpions to conserve venom is false, then ignorance belongs to uninstructed human brains. One may reasonably assume that if if uniforms have details, then scientific research is more than just data collection and analyses, then if the claim that scorpions to conserve venom is false, then ignorance belongs to uninstructed human brains. Either one or both of these statements are true: experience is the food that feeds brain connections, or bristles are hair. Provided that experience is the food that feeds brain connections, we know that either some avocados contain poison or all migratory birds require tags with hunter's name and address and dates of kills. On the condition that bristles are hair, it is definitely the case that if uniforms have details, then scientific research is more than just data collection and analyses.
|
The statement 'scorpions to conserve venom' is true.
|
The claim that scorpions to conserve venom does not reflect reality.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [2] or [3].) or (If [4], then [5].). [SC1-2]
If (Either [2] or [3].), then (If (Not [0].), then [1].).
If (If [4], then [5].), then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC1-2]
Constructive Dilemma:
Either [6] or [7].
If [6], then (Either [2] or [3].).
If [7], then (If [4], then [5].).
Therefore, Either (Either [2] or [3].) or (If [4], then [5].)..
|
{0: 'Scorpions to conserve venom.', 1: 'Ignorance belongs to uninstructed human brains.', 2: 'Some avocados contain poison.', 3: "All migratory birds require tags with hunter's name and address and dates of kills.", 4: 'Uniforms have details.', 5: 'Scientific research is more than just data collection and analyses.', 6: 'Experience is the food that feeds brain connections.', 7: 'Bristles are hair.'}
| 3 |
2,146 |
['There is good reason to believe that either tillers are shoots or hartebeests occupy positions.', 'We know that either a fat cat is a person or buffalo milk is consumed in south Asia, with India, China and Pakistan being the biggest producers.', "So long as a fat cat is a person, 'if tillers are shoots, then some pubs hire bands or singers to entertain patrons' is true.", 'Once we know buffalo milk is consumed in south Asia, with India, China and Pakistan being the biggest producers, we also know that if tillers are shoots, then some pubs hire bands or singers to entertain patrons.', 'We know that either either nourishment provides nutrition or some leaf nodes are part of onions or if hartebeests occupy positions, then some pubs hire bands or singers to entertain patrons.', 'It is not true that either nourishment provides nutrition or some leaf nodes are part of onions.']
|
There is good reason to believe that either tillers are shoots or hartebeests occupy positions. We know that either a fat cat is a person or buffalo milk is consumed in south Asia, with India, China and Pakistan being the biggest producers. So long as a fat cat is a person, 'if tillers are shoots, then some pubs hire bands or singers to entertain patrons' is true. Once we know buffalo milk is consumed in south Asia, with India, China and Pakistan being the biggest producers, we also know that if tillers are shoots, then some pubs hire bands or singers to entertain patrons. We know that either either nourishment provides nutrition or some leaf nodes are part of onions or if hartebeests occupy positions, then some pubs hire bands or singers to entertain patrons. It is not true that either nourishment provides nutrition or some leaf nodes are part of onions.
|
The statement that states some pubs hire bands or singers to entertain patrons is right.
|
Pubs have pool tables.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If [1], then [0].).
If [4], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC3-1]
Disjunctive Syllogism:
Either (Either [5] or [6].) or (If [2], then [0].).
Not (Either [5] or [6].).
Therefore, If [2], then [0]..
|
{0: 'Some pubs hire bands or singers to entertain patrons.', 1: 'Tillers are shoots.', 2: 'Hartebeests occupy positions.', 3: 'A fat cat is a person.', 4: 'Buffalo milk is consumed in south Asia, with India, China and Pakistan being the biggest producers.', 5: 'Nourishment provides nutrition.', 6: 'Some leaf nodes are part of onions.'}
| 3 |
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