id
int64 0
7k
| premises
stringlengths 118
4.1k
| paragraph
stringlengths 111
4.06k
| conclusion
stringlengths 15
240
| question
stringlengths 14
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values | arg
stringlengths 54
2.02k
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stringlengths 51
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int64 1
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3,785 |
['At least one of two things is true: conservatives look to individual character values as a basis for a strong society, or many insurers cover all or some of health care costs.', 'When schnitzels are pork cutlets that are usually breaded and then deep fried is true, it follows that teachers observe ability.', 'Given that teachers observe ability, it can be inferred that it is not true that conservatives look to individual character values as a basis for a strong society.', 'Given that the claim that schnitzels are pork cutlets that are usually breaded and then deep fried does not correspond with reality, it can be inferred that either a religious service is a religious ritual or common milkweed is a robust, erect perennial.', 'The claim that either a religious service is a religious ritual or common milkweed is a robust, erect perennial has no merit.']
|
At least one of two things is true: conservatives look to individual character values as a basis for a strong society, or many insurers cover all or some of health care costs. When schnitzels are pork cutlets that are usually breaded and then deep fried is true, it follows that teachers observe ability. Given that teachers observe ability, it can be inferred that it is not true that conservatives look to individual character values as a basis for a strong society. Given that the claim that schnitzels are pork cutlets that are usually breaded and then deep fried does not correspond with reality, it can be inferred that either a religious service is a religious ritual or common milkweed is a robust, erect perennial. The claim that either a religious service is a religious ritual or common milkweed is a robust, erect perennial has no merit.
|
Many people rightly believe that many insurers cover all or some of health care costs.
|
Many people rightly believe that many insurers cover all or some of health care costs.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [2], then (Not [1].). [SC1-2]
[2] [SC2-2]
Therefore, Not [1]..
[SC1-2]
Hypothetical Syllogism:
If [2], then [5].
If [5], then (Not [1].).
Therefore, If [2], then (Not [1].)..
[SC2-2]
Modus Tonens:
If (Not [2].), then (Either [3] or [4].).
Not (Either [3] or [4].).
Therefore, [2].
|
{0: 'Many insurers cover all or some of health care costs.', 1: 'Conservatives look to individual character values as a basis for a strong society.', 2: 'Schnitzels are pork cutlets that are usually breaded and then deep fried.', 3: 'A religious service is a religious ritual.', 4: 'Common milkweed is a robust, erect perennial.', 5: 'Teachers observe ability.'}
| 4 |
3,873 |
['The claim that most monkeys live in rainforests has no merit.', 'It is rational to believe that either opera singers can also give solo performances or every parent uses some form of punishment with children, like taking away a toy.', 'Assuming every parent uses some form of punishment with children, like taking away a toy, we know that if stalls are located in markets, then most monkeys live in rainforests.', 'The claim that some energy depends on materials holds true.', "Assuming the statement 'if some energy depends on materials, then if opera singers can also give solo performances, then if stalls are located in markets, then most monkeys live in rainforests' can be considered false, we know that humans are animals.", "Assuming the statement 'if some energy depends on materials, then if opera singers can also give solo performances, then if stalls are located in markets, then most monkeys live in rainforests' can be considered false, we know that those that suggest humans are animals are wrong."]
|
The claim that most monkeys live in rainforests has no merit. It is rational to believe that either opera singers can also give solo performances or every parent uses some form of punishment with children, like taking away a toy. Assuming every parent uses some form of punishment with children, like taking away a toy, we know that if stalls are located in markets, then most monkeys live in rainforests. The claim that some energy depends on materials holds true. Assuming the statement 'if some energy depends on materials, then if opera singers can also give solo performances, then if stalls are located in markets, then most monkeys live in rainforests' can be considered false, we know that humans are animals. Assuming the statement 'if some energy depends on materials, then if opera singers can also give solo performances, then if stalls are located in markets, then most monkeys live in rainforests' can be considered false, we know that those that suggest humans are animals are wrong.
|
The claim that stalls are located in markets does not correspond with reality.
|
The claim that stalls are located in markets does not correspond with reality.
|
TRUE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If [0], then [1].). [SC2-2]
If [3], then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC2-2]
Modus Ponens:
If [4], then (If [2], then (If [0], then [1].).). [SC1-3]
[4]
Therefore, If [2], then (If [0], then [1].)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If [4], then (If [2], then (If [0], then [1].).).).), then [5].
If (Not (If [4], then (If [2], then (If [0], then [1].).).).), then (Not [5].).
Therefore, If [4], then (If [2], then (If [0], then [1].).)..
|
{0: 'Stalls are located in markets.', 1: 'Most monkeys live in rainforests.', 2: 'Opera singers can also give solo performances.', 3: 'Every parent uses some form of punishment with children, like taking away a toy.', 4: 'Some energy depends on materials.', 5: 'Humans are animals.'}
| 4 |
3,065 |
['Given that a lodestar is an example, it can be inferred that peas are part of peas.', "When the statement that states if a lodestar is an example, then the statement 'peas are part of peas' can be considered false is false is true, it follows that if batteries contain acid-based liquids, which helps create an electrical charge, then arms control is the opiate of the policy-making class in both parties.", "Whenever it is true that it is a common misconception that if the statement that states if a lodestar is an example, then the statement 'peas are part of peas' can be considered false is false, then those that suggest if batteries contain acid-based liquids, which helps create an electrical charge, then arms control is the opiate of the policy-making class in both parties are wrong, 'some gases cause heat' is true.", "There is good reason to believe that either red foxes have impact or if it is a common misconception that if the statement that states if a lodestar is an example, then the statement 'peas are part of peas' can be considered false is false, then those that suggest if batteries contain acid-based liquids, which helps create an electrical charge, then arms control is the opiate of the policy-making class in both parties are wrong, then the notion that 'some gases cause heat' is untrue.", 'The claim that red foxes have impact has no merit.']
|
Given that a lodestar is an example, it can be inferred that peas are part of peas. When the statement that states if a lodestar is an example, then the statement 'peas are part of peas' can be considered false is false is true, it follows that if batteries contain acid-based liquids, which helps create an electrical charge, then arms control is the opiate of the policy-making class in both parties. Whenever it is true that it is a common misconception that if the statement that states if a lodestar is an example, then the statement 'peas are part of peas' can be considered false is false, then those that suggest if batteries contain acid-based liquids, which helps create an electrical charge, then arms control is the opiate of the policy-making class in both parties are wrong, 'some gases cause heat' is true. There is good reason to believe that either red foxes have impact or if it is a common misconception that if the statement that states if a lodestar is an example, then the statement 'peas are part of peas' can be considered false is false, then those that suggest if batteries contain acid-based liquids, which helps create an electrical charge, then arms control is the opiate of the policy-making class in both parties are wrong, then the notion that 'some gases cause heat' is untrue. The claim that red foxes have impact has no merit.
|
The notion that 'a lodestar is an example' is untrue.
|
The notion that 'a lodestar is an example' is untrue.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then [1].
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [0], then (Not [1].).).), then (If [2], then [3].).
If (Not (If [0], then (Not [1].).).), then (Not (If [2], then [3].).). [SC2-2]
Therefore, If [0], then (Not [1].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (If [0], then (Not [1].).).), then (Not (If [2], then [3].).).).), then [4].
If (Not (If (Not (If [0], then (Not [1].).).), then (Not (If [2], then [3].).).).), then (Not [4].). [SC2-3]
Therefore, If (Not (If [0], then (Not [1].).).), then (Not (If [2], then [3].).)..
[SC2-3]
Disjunctive Syllogism:
Either [5] or (If (Not (If (Not (If [0], then (Not [1].).).), then (Not (If [2], then [3].).).).), then (Not [4].).).
Not [5].
Therefore, If (Not (If (Not (If [0], then (Not [1].).).), then (Not (If [2], then [3].).).).), then (Not [4].)..
|
{0: 'A lodestar is an example.', 1: 'Peas are part of peas.', 2: 'Batteries contain acid-based liquids, which helps create an electrical charge.', 3: 'Arms control is the opiate of the policy-making class in both parties.', 4: 'Some gases cause heat.', 5: 'Red foxes have impact.'}
| 4 |
3,902 |
['We know that either either many homeless people experience mental distress and have high rates of suicide or impalas have (part) heads or whole grains provide more fiber, vitamins and minerals than white bread and refined cereals.', 'One may reasonably assume that if either coughs produce mucuses or bone is moderate in proportion to size, then it is not the case that either many homeless people experience mental distress and have high rates of suicide or impalas have (part) heads.', 'On the condition that ethernet requires special wires to connect computers, it is definitely the case that it is not the case that either many homeless people experience mental distress and have high rates of suicide or impalas have (part) heads.', "On the condition that the statement 'either either coughs produce mucuses or bone is moderate in proportion to size or ethernet requires special wires to connect computers' can be considered false, it is definitely the case that shorthand is simply an online form of acronym or abbreviation.", "Either erosion begins and accelerates, severely altering the physical environment or if the statement 'either either coughs produce mucuses or bone is moderate in proportion to size or ethernet requires special wires to connect computers' can be considered false, then some people mistakenly believe that shorthand is simply an online form of acronym or abbreviation.", 'The statement that states erosion begins and accelerates, severely altering the physical environment is false.']
|
We know that either either many homeless people experience mental distress and have high rates of suicide or impalas have (part) heads or whole grains provide more fiber, vitamins and minerals than white bread and refined cereals. One may reasonably assume that if either coughs produce mucuses or bone is moderate in proportion to size, then it is not the case that either many homeless people experience mental distress and have high rates of suicide or impalas have (part) heads. On the condition that ethernet requires special wires to connect computers, it is definitely the case that it is not the case that either many homeless people experience mental distress and have high rates of suicide or impalas have (part) heads. On the condition that the statement 'either either coughs produce mucuses or bone is moderate in proportion to size or ethernet requires special wires to connect computers' can be considered false, it is definitely the case that shorthand is simply an online form of acronym or abbreviation. Either erosion begins and accelerates, severely altering the physical environment or if the statement 'either either coughs produce mucuses or bone is moderate in proportion to size or ethernet requires special wires to connect computers' can be considered false, then some people mistakenly believe that shorthand is simply an online form of acronym or abbreviation. The statement that states erosion begins and accelerates, severely altering the physical environment is false.
|
It is the case that whole grains provide more fiber, vitamins and minerals than white bread and refined cereals.
|
Whole grains tend to be higher in fat content than refined grains and become rancid sooner.
|
Uncertain
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or [0].
Not (Either [1] or [2].). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either (Either [3] or [4].) or [5]. [SC1-2]
If (Either [3] or [4].), then (Not (Either [1] or [2].).).
If [5], then (Not (Either [1] or [2].).).
Therefore, Not (Either [1] or [2].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either (Either [3] or [4].) or [5].).), then [6].
If (Not (Either (Either [3] or [4].) or [5].).), then (Not [6].). [SC2-3]
Therefore, Either (Either [3] or [4].) or [5]..
[SC2-3]
Disjunctive Syllogism:
Either [7] or (If (Not (Either (Either [3] or [4].) or [5].).), then (Not [6].).).
Not [7].
Therefore, If (Not (Either (Either [3] or [4].) or [5].).), then (Not [6].)..
|
{0: 'Whole grains provide more fiber, vitamins and minerals than white bread and refined cereals.', 1: 'Many homeless people experience mental distress and have high rates of suicide.', 2: 'Impalas have (part) heads.', 3: 'Coughs produce mucuses.', 4: 'Bone is moderate in proportion to size.', 5: 'Ethernet requires special wires to connect computers.', 6: 'Shorthand is simply an online form of acronym or abbreviation.', 7: 'Erosion begins and accelerates, severely altering the physical environment.'}
| 4 |
3,317 |
['The claim that rabbits have sensitive digestive systems has no merit.', 'When some low temperature increases energy is true, it follows that workers work time.', 'Once we know workers work time, we also know that if the statement that states lips are located in mouths is false, then rabbits have sensitive digestive systems.', 'Either familial sarcoidosis is linked to the major histocompatibility complex region or some low temperature increases energy.', "The notion that 'familial sarcoidosis is linked to the major histocompatibility complex region ' is untrue."]
|
The claim that rabbits have sensitive digestive systems has no merit. When some low temperature increases energy is true, it follows that workers work time. Once we know workers work time, we also know that if the statement that states lips are located in mouths is false, then rabbits have sensitive digestive systems. Either familial sarcoidosis is linked to the major histocompatibility complex region or some low temperature increases energy. The notion that 'familial sarcoidosis is linked to the major histocompatibility complex region ' is untrue.
|
Those that suggest lips are located in mouths are right.
|
LIPs occur when continents are converging and diverging.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (If (Not [0].), then [1].). [SC1-2]
[2] [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Hypothetical Syllogism:
If [2], then [3].
If [3], then (If (Not [0].), then [1].).
Therefore, If [2], then (If (Not [0].), then [1].)..
[SC2-2]
Disjunctive Syllogism:
Either [4] or [2].
Not [4].
Therefore, [2].
|
{0: 'Lips are located in mouths.', 1: 'Rabbits have sensitive digestive systems.', 2: 'Some low temperature increases energy.', 3: 'Workers work time.', 4: 'Familial sarcoidosis is linked to the major histocompatibility complex region .'}
| 4 |
3,636 |
["Given that it is a common misconception that either a refining is a processing or the statement that 'pangolins have no teeth. ' is incorrect, it can be inferred that the statement 'if endoparasites live inside a plant or animal, then a hepatotoxin is a toxin' can be considered false.", "Either a tributary is a branch or the statement that 'a refining is a processing' is incorrect.", 'We know that the claim that a tributary is a branch is false.', "Should it be the case that it is a common misconception that either a refining is a processing or the statement that 'pangolins have no teeth. ' is incorrect, it follows that some medications seem to help memory in some people.", 'Given that some medications seem to help memory in some people, it can be inferred that if endoparasites live inside a plant or animal, then a hepatotoxin is a toxin.']
|
Given that it is a common misconception that either a refining is a processing or the statement that 'pangolins have no teeth. ' is incorrect, it can be inferred that the statement 'if endoparasites live inside a plant or animal, then a hepatotoxin is a toxin' can be considered false. Either a tributary is a branch or the statement that 'a refining is a processing' is incorrect. We know that the claim that a tributary is a branch is false. Should it be the case that it is a common misconception that either a refining is a processing or the statement that 'pangolins have no teeth. ' is incorrect, it follows that some medications seem to help memory in some people. Given that some medications seem to help memory in some people, it can be inferred that if endoparasites live inside a plant or animal, then a hepatotoxin is a toxin.
|
The statement that 'pangolins have no teeth. ' is incorrect.
|
The statement that 'pangolins have no teeth. ' is incorrect.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or (Not [0].).).), then (If [2], then [3].). [SC1-2]
If (Not (Either [1] or (Not [0].).).), then (Not (If [2], then [3].).).
Therefore, Either [1] or (Not [0].)..
[SC1-2]
Hypothetical Syllogism:
If (Not (Either [1] or (Not [0].).).), then [5].
If [5], then (If [2], then [3].).
Therefore, If (Not (Either [1] or (Not [0].).).), then (If [2], then [3].)..
[SC2-1]
Disjunctive Syllogism:
Either [4] or (Not [1].).
Not [4].
Therefore, Not [1]..
|
{0: 'Pangolins have no teeth. .', 1: 'A refining is a processing.', 2: 'Endoparasites live inside a plant or animal.', 3: 'A hepatotoxin is a toxin.', 4: 'A tributary is a branch.', 5: 'Some medications seem to help memory in some people.'}
| 4 |
3,666 |
['Provided that soy products are also good for women, we know that several methods are used for congenital hemochromatosis.', "Whenever it is true that osteoporosis is now a preventable disease, 'several methods are used for congenital hemochromatosis' is true.", 'On the condition that the claim that if it is not true that either soy products are also good for women or osteoporosis is now a preventable disease, then cumulus clouds indicate fair weather is false, it is definitely the case that nitric oxide relaxes the arterioles, thus increasing blood flow.', 'The statement, nitric oxide relaxes the arterioles, thus increasing blood flow, does not hold.', 'It is rational to believe that either most wallabies have poor sight or cultivars offer variation in foliage color and form.', 'Once we know most wallabies have poor sight, we also know that the claim that cumulus clouds indicate fair weather has no merit.', 'Should it be the case that cultivars offer variation in foliage color and form, it follows that the claim that cumulus clouds indicate fair weather has no merit.']
|
Provided that soy products are also good for women, we know that several methods are used for congenital hemochromatosis. Whenever it is true that osteoporosis is now a preventable disease, 'several methods are used for congenital hemochromatosis' is true. On the condition that the claim that if it is not true that either soy products are also good for women or osteoporosis is now a preventable disease, then cumulus clouds indicate fair weather is false, it is definitely the case that nitric oxide relaxes the arterioles, thus increasing blood flow. The statement, nitric oxide relaxes the arterioles, thus increasing blood flow, does not hold. It is rational to believe that either most wallabies have poor sight or cultivars offer variation in foliage color and form. Once we know most wallabies have poor sight, we also know that the claim that cumulus clouds indicate fair weather has no merit. Should it be the case that cultivars offer variation in foliage color and form, it follows that the claim that cumulus clouds indicate fair weather has no merit.
|
The claim that several methods are used for congenital hemochromatosis is true.
|
The claim that several methods are used for congenital hemochromatosis is true.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0].
If [2], then [0].
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either [1] or [2].).), then [3]. [SC1-2]
Not [3]. [SC2-2]
Therefore, Either [1] or [2]..
[SC1-2]
Modus Tonens:
If (Not (If (Not (Either [1] or [2].).), then [3].).), then [4].
Not [4].
Therefore, If (Not (Either [1] or [2].).), then [3]..
[SC2-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (Not [3].).
If [6], then (Not [3].).
Therefore, Not [3]..
|
{0: 'Several methods are used for congenital hemochromatosis.', 1: 'Soy products are also good for women.', 2: 'Osteoporosis is now a preventable disease.', 3: 'Cumulus clouds indicate fair weather.', 4: 'Nitric oxide relaxes the arterioles, thus increasing blood flow.', 5: 'Most wallabies have poor sight.', 6: 'Cultivars offer variation in foliage color and form.'}
| 4 |
3,789 |
['Given that increased pressure allows oxygen to get into tissues better, it can be inferred that the claim that gopher is a service that organizes information into menus does not correspond with reality.', 'If a terrorist is a radical, then the claim that gopher is a service that organizes information into menus does not correspond with reality.', 'We know that either control insects with a mixture of DDT and malathion or most mustard seeds have properties.', 'One may reasonably assume that if control insects with a mixture of DDT and malathion, then increased pressure allows oxygen to get into tissues better.', 'Provided that it is not true that if most mustard seeds have properties, then a terrorist is a radical, we know that many countries face major challenges in managing the impact of pollution, especially in big cities.', 'There is good reason to believe that either some american toads feed at nights or the claim that many countries face major challenges in managing the impact of pollution, especially in big cities does not reflect reality.', 'We know that the claim that some american toads feed at nights is false.']
|
Given that increased pressure allows oxygen to get into tissues better, it can be inferred that the claim that gopher is a service that organizes information into menus does not correspond with reality. If a terrorist is a radical, then the claim that gopher is a service that organizes information into menus does not correspond with reality. We know that either control insects with a mixture of DDT and malathion or most mustard seeds have properties. One may reasonably assume that if control insects with a mixture of DDT and malathion, then increased pressure allows oxygen to get into tissues better. Provided that it is not true that if most mustard seeds have properties, then a terrorist is a radical, we know that many countries face major challenges in managing the impact of pollution, especially in big cities. There is good reason to believe that either some american toads feed at nights or the claim that many countries face major challenges in managing the impact of pollution, especially in big cities does not reflect reality. We know that the claim that some american toads feed at nights is false.
|
The claim that gopher is a service that organizes information into menus does not correspond with reality.
|
The claim that gopher is a service that organizes information into menus does not correspond with reality.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].).
If [2], then (Not [0].).
Therefore, Not [0]..
[SC1-1]
Constructive Dilemma:
Either [3] or [4].
If [3], then [1].
If [4], then [2]. [SC3-2]
Therefore, Either [1] or [2]..
[SC3-2]
Modus Tonens:
If (Not (If [4], then [2].).), then [5].
Not [5]. [SC2-3]
Therefore, If [4], then [2]..
[SC2-3]
Disjunctive Syllogism:
Either [6] or (Not [5].).
Not [6].
Therefore, Not [5]..
|
{0: 'Gopher is a service that organizes information into menus.', 1: 'Increased pressure allows oxygen to get into tissues better.', 2: 'A terrorist is a radical.', 3: 'Control insects with a mixture of DDT and malathion.', 4: 'Most mustard seeds have properties.', 5: 'Many countries face major challenges in managing the impact of pollution, especially in big cities.', 6: 'Some american toads feed at nights.'}
| 4 |
3,958 |
['Should it be the case that print is graphic art, it follows that if we know that the claim that most javan rhinos eat plants is false, then some people protect themselves by using mental blinders and ear plugs.', "Given that the statement 'if we know that the claim that most javan rhinos eat plants is false, then the notion that 'some people protect themselves by using mental blinders and ear plugs' is untrue' can be considered false, it can be inferred that some trees even provide key medicinal ingredients for illness cures and treatments.", 'The claim that some trees even provide key medicinal ingredients for illness cures and treatments does not correspond with reality.', 'Should it be the case that the claim that print is graphic art does not reflect reality, it follows that if pockets are located in pants, then eukaryotic genomes have numerous nucleosomes .', 'The claim that if pockets are located in pants, then eukaryotic genomes have numerous nucleosomes does not reflect reality.']
|
Should it be the case that print is graphic art, it follows that if we know that the claim that most javan rhinos eat plants is false, then some people protect themselves by using mental blinders and ear plugs. Given that the statement 'if we know that the claim that most javan rhinos eat plants is false, then the notion that 'some people protect themselves by using mental blinders and ear plugs' is untrue' can be considered false, it can be inferred that some trees even provide key medicinal ingredients for illness cures and treatments. The claim that some trees even provide key medicinal ingredients for illness cures and treatments does not correspond with reality. Should it be the case that the claim that print is graphic art does not reflect reality, it follows that if pockets are located in pants, then eukaryotic genomes have numerous nucleosomes . The claim that if pockets are located in pants, then eukaryotic genomes have numerous nucleosomes does not reflect reality.
|
It is true that most javan rhinos eat plants.
|
Most javan rhinos have sides.
|
Uncertain
|
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 [2], then (If (Not [0].), then [1].).
[2] [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Modus Tonens:
If (Not [2].), then (If [4], then [5].).
Not (If [4], then [5].).
Therefore, [2].
[SC2-1]
Modus Tonens:
If (Not (If (Not [0].), then (Not [1].).).), then [3].
Not [3].
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Most javan rhinos eat plants.', 1: 'Some people protect themselves by using mental blinders and ear plugs.', 2: 'Print is graphic art.', 3: 'Some trees even provide key medicinal ingredients for illness cures and treatments.', 4: 'Pockets are located in pants.', 5: 'Eukaryotic genomes have numerous nucleosomes .'}
| 4 |
3,214 |
['It is a common misconception that either morality is different for different people or demoiselles have (part) cell membranes.', 'The claim that biologists evaluate factors that affect their distribution, abundance, and survival is false.', "Whenever it is true that a cimetidine is medicine, 'either biologists evaluate factors that affect their distribution, abundance, and survival or if either hotter stars shine with more blue light or clutter is located in desks, then either morality is different for different people or demoiselles have (part) cell membranes' is true.", 'On the condition that it is not the case that a cimetidine is medicine, it is definitely the case that sorption occurs when contaminants attach themselves to soil particles.', 'Given that it is not the case that a cimetidine is medicine, it can be inferred that those that suggest sorption occurs when contaminants attach themselves to soil particles are wrong.']
|
It is a common misconception that either morality is different for different people or demoiselles have (part) cell membranes. The claim that biologists evaluate factors that affect their distribution, abundance, and survival is false. Whenever it is true that a cimetidine is medicine, 'either biologists evaluate factors that affect their distribution, abundance, and survival or if either hotter stars shine with more blue light or clutter is located in desks, then either morality is different for different people or demoiselles have (part) cell membranes' is true. On the condition that it is not the case that a cimetidine is medicine, it is definitely the case that sorption occurs when contaminants attach themselves to soil particles. Given that it is not the case that a cimetidine is medicine, it can be inferred that those that suggest sorption occurs when contaminants attach themselves to soil particles are wrong.
|
The claim that either hotter stars shine with more blue light or clutter is located in desks does not correspond with reality.
|
It is a common misconception that hotter stars have higher peak amplitudes, and peak at shorter wavelengths.
|
Uncertain
|
Modus Tonens:
If (Either [0] or [1].), then (Either [2] or [3].). [SC1-1]
Not (Either [2] or [3].).
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Disjunctive Syllogism:
Either [4] or (If (Either [0] or [1].), then (Either [2] or [3].).). [SC1-2]
Not [4].
Therefore, If (Either [0] or [1].), then (Either [2] or [3].)..
[SC1-2]
Modus Ponens:
If [5], then (Either [4] or (If (Either [0] or [1].), then (Either [2] or [3].).).).
[5] [SC2-3]
Therefore, Either [4] or (If (Either [0] or [1].), then (Either [2] or [3].).)..
[SC2-3]
Reductio Ad Absurdum:
If (Not [5].), then [6].
If (Not [5].), then (Not [6].).
Therefore, [5].
|
{0: 'Hotter stars shine with more blue light.', 1: 'Clutter is located in desks.', 2: 'Morality is different for different people.', 3: 'Demoiselles have (part) cell membranes.', 4: 'Biologists evaluate factors that affect their distribution, abundance, and survival.', 5: 'A cimetidine is medicine.', 6: 'Sorption occurs when contaminants attach themselves to soil particles.'}
| 4 |
3,097 |
['Provided that flamingos are the bird with the longest neck and the longest legs compared with body size, we know that we know that the claim that dairy products may have adverse effects is false.', 'Either stuffed animals can also attract a lot of dust or if flamingos are the bird with the longest neck and the longest legs compared with body size, then dairy products may have adverse effects.', "If yield is the load divided by the stream's drainage area, then the claim that stuffed animals can also attract a lot of dust has no merit.", "Once we know the statement 'yield is the load divided by the stream's drainage area' can be considered false, we also know that some disorders have similar or even the same symptoms.", "The statement 'some disorders have similar or even the same symptoms' can be considered false."]
|
Provided that flamingos are the bird with the longest neck and the longest legs compared with body size, we know that we know that the claim that dairy products may have adverse effects is false. Either stuffed animals can also attract a lot of dust or if flamingos are the bird with the longest neck and the longest legs compared with body size, then dairy products may have adverse effects. If yield is the load divided by the stream's drainage area, then the claim that stuffed animals can also attract a lot of dust has no merit. Once we know the statement 'yield is the load divided by the stream's drainage area' can be considered false, we also know that some disorders have similar or even the same symptoms. The statement 'some disorders have similar or even the same symptoms' can be considered false.
|
We know that the claim that flamingos are the bird with the longest neck and the longest legs compared with body size is false.
|
The statement, some flamingos have individuals, does not hold.
|
Uncertain
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].).
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [0], then [1].).
Not [2]. [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Modus Ponens:
If [3], then (Not [2].).
[3] [SC2-3]
Therefore, Not [2]..
[SC2-3]
Modus Tonens:
If (Not [3].), then [4].
Not [4].
Therefore, [3].
|
{0: 'Flamingos are the bird with the longest neck and the longest legs compared with body size.', 1: 'Dairy products may have adverse effects.', 2: 'Stuffed animals can also attract a lot of dust.', 3: "Yield is the load divided by the stream's drainage area.", 4: 'Some disorders have similar or even the same symptoms.'}
| 4 |
3,583 |
["When the statement that 'female prostitutes are often gang raped by mobs of teenage boys out for a night of fun' is incorrect is true, it follows that a dysphonia is disorder.", 'Given that a dysphonia is disorder, it can be inferred that statistics is the science of collecting and analyzing data.', 'It is a fact that either pap isa message or if dads have (part) cytoplasm, then albatrosses feed on fish.', "Should it be the case that if dads have (part) cytoplasm, then albatrosses feed on fish, it follows that if the statement that 'female prostitutes are often gang raped by mobs of teenage boys out for a night of fun' is incorrect, then the statement 'statistics is the science of collecting and analyzing data' can be considered false.", "It is rational to believe that either songs are classical music or if pap isa message, then if the statement that 'female prostitutes are often gang raped by mobs of teenage boys out for a night of fun' is incorrect, then the statement 'statistics is the science of collecting and analyzing data' can be considered false.", 'The claim that songs are classical music does not reflect reality.']
|
When the statement that 'female prostitutes are often gang raped by mobs of teenage boys out for a night of fun' is incorrect is true, it follows that a dysphonia is disorder. Given that a dysphonia is disorder, it can be inferred that statistics is the science of collecting and analyzing data. It is a fact that either pap isa message or if dads have (part) cytoplasm, then albatrosses feed on fish. Should it be the case that if dads have (part) cytoplasm, then albatrosses feed on fish, it follows that if the statement that 'female prostitutes are often gang raped by mobs of teenage boys out for a night of fun' is incorrect, then the statement 'statistics is the science of collecting and analyzing data' can be considered false. It is rational to believe that either songs are classical music or if pap isa message, then if the statement that 'female prostitutes are often gang raped by mobs of teenage boys out for a night of fun' is incorrect, then the statement 'statistics is the science of collecting and analyzing data' can be considered false. The claim that songs are classical music does not reflect reality.
|
It is fair to say that female prostitutes are often gang raped by mobs of teenage boys out for a night of fun.
|
It is not the case that female prostitutes are often gang raped by mobs of teenage boys out for a night of fun.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [2].
If [2], then [1].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then (If (Not [0].), then (Not [1].).). [SC2-2]
If (If [4], then [5].), then (If (Not [0].), then (Not [1].).).
Therefore, If (Not [0].), then (Not [1].)..
[SC2-2]
Disjunctive Syllogism:
Either [6] or (If [3], then (If (Not [0].), then (Not [1].).).).
Not [6].
Therefore, If [3], then (If (Not [0].), then (Not [1].).)..
|
{0: 'Female prostitutes are often gang raped by mobs of teenage boys out for a night of fun.', 1: 'Statistics is the science of collecting and analyzing data.', 2: 'A dysphonia is disorder.', 3: 'Pap isa message.', 4: 'Dads have (part) cytoplasm.', 5: 'Albatrosses feed on fish.', 6: 'Songs are classical music.'}
| 4 |
3,466 |
["Assuming the statement 'if some saguaros have stamens, then butterflies use early morning sun for basking on warm rocks, bricks or paths' can be considered false, we know that antioxidants seem to deactivate free radicals, and therefore protect cells from damage.", "So long as antioxidants seem to deactivate free radicals, and therefore protect cells from damage, 'historical places are rich sources of information' is true.", 'Either one or both of these statements are true: touch screens employ one of three physics principles for detecting the point of touch, or some guinea pigs have large cecums.', 'One may reasonably assume that if touch screens employ one of three physics principles for detecting the point of touch, then it is not the case that historical places are rich sources of information.', 'Either either women are the major consumers of treatments and services for mental illnesses or some objects are more difficult to photograph than others or salt kills slugs.', 'On the condition that either women are the major consumers of treatments and services for mental illnesses or some objects are more difficult to photograph than others, it is definitely the case that if some guinea pigs have large cecums, then it is not the case that historical places are rich sources of information.', "So long as salt kills slugs, 'if some guinea pigs have large cecums, then it is not the case that historical places are rich sources of information' is true."]
|
Assuming the statement 'if some saguaros have stamens, then butterflies use early morning sun for basking on warm rocks, bricks or paths' can be considered false, we know that antioxidants seem to deactivate free radicals, and therefore protect cells from damage. So long as antioxidants seem to deactivate free radicals, and therefore protect cells from damage, 'historical places are rich sources of information' is true. Either one or both of these statements are true: touch screens employ one of three physics principles for detecting the point of touch, or some guinea pigs have large cecums. One may reasonably assume that if touch screens employ one of three physics principles for detecting the point of touch, then it is not the case that historical places are rich sources of information. Either either women are the major consumers of treatments and services for mental illnesses or some objects are more difficult to photograph than others or salt kills slugs. On the condition that either women are the major consumers of treatments and services for mental illnesses or some objects are more difficult to photograph than others, it is definitely the case that if some guinea pigs have large cecums, then it is not the case that historical places are rich sources of information. So long as salt kills slugs, 'if some guinea pigs have large cecums, then it is not the case that historical places are rich sources of information' is true.
|
When some saguaros have stamens is true, it follows that butterflies use early morning sun for basking on warm rocks, bricks or paths.
|
So long as saguaros are unique cacti, 'butterflies use early morning sun for basking on warm rocks, bricks or paths' is true.
|
Uncertain
|
Modus Tonens:
If (Not (If [0], then [1].).), then [2].
Not [2]. [SC2-1]
Therefore, If [0], then [1]..
[SC2-1]
Modus Tonens:
If [2], then [3].
Not [3]. [SC2-2]
Therefore, Not [2]..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Not [3].).
If [5], then (Not [3].). [SC3-3]
Therefore, Not [3]..
[SC3-3]
Disjunction Elimination:
Either (Either [6] or [7].) or [8].
If (Either [6] or [7].), then (If [5], then (Not [3].).).
If [8], then (If [5], then (Not [3].).).
Therefore, If [5], then (Not [3].)..
|
{0: 'Some saguaros have stamens.', 1: 'Butterflies use early morning sun for basking on warm rocks, bricks or paths.', 2: 'Antioxidants seem to deactivate free radicals, and therefore protect cells from damage.', 3: 'Historical places are rich sources of information.', 4: 'Touch screens employ one of three physics principles for detecting the point of touch.', 5: 'Some guinea pigs have large cecums.', 6: 'Women are the major consumers of treatments and services for mental illnesses.', 7: 'Some objects are more difficult to photograph than others.', 8: 'Salt kills slugs.'}
| 4 |
3,523 |
['Some people mistakenly believe that inactivation occurs early in development due to the presence of mosaics.', 'Once we know a commute is a journey, we also know that if we know that the claim that if the statement that states silkworms are an ideal food source for chameleons of all sizes, and it is also very nutritious is false, then inactivation occurs early in development due to the presence of mosaics is false, then either grebes make their nest from plants found in the water or most soils contain varying amounts of uranium.', 'It is fair to say that a commute is a journey.', 'Should it be the case that some people mistakenly believe that if we know that the claim that if the statement that states silkworms are an ideal food source for chameleons of all sizes, and it is also very nutritious is false, then inactivation occurs early in development due to the presence of mosaics is false, then the claim that either grebes make their nest from plants found in the water or most soils contain varying amounts of uranium has no merit, it follows that neuroglial nuclei surround the neuron.', 'One may reasonably assume that if some people mistakenly believe that if we know that the claim that if the statement that states silkworms are an ideal food source for chameleons of all sizes, and it is also very nutritious is false, then inactivation occurs early in development due to the presence of mosaics is false, then the claim that either grebes make their nest from plants found in the water or most soils contain varying amounts of uranium has no merit, then it is a common misconception that neuroglial nuclei surround the neuron.']
|
Some people mistakenly believe that inactivation occurs early in development due to the presence of mosaics. Once we know a commute is a journey, we also know that if we know that the claim that if the statement that states silkworms are an ideal food source for chameleons of all sizes, and it is also very nutritious is false, then inactivation occurs early in development due to the presence of mosaics is false, then either grebes make their nest from plants found in the water or most soils contain varying amounts of uranium. It is fair to say that a commute is a journey. Should it be the case that some people mistakenly believe that if we know that the claim that if the statement that states silkworms are an ideal food source for chameleons of all sizes, and it is also very nutritious is false, then inactivation occurs early in development due to the presence of mosaics is false, then the claim that either grebes make their nest from plants found in the water or most soils contain varying amounts of uranium has no merit, it follows that neuroglial nuclei surround the neuron. One may reasonably assume that if some people mistakenly believe that if we know that the claim that if the statement that states silkworms are an ideal food source for chameleons of all sizes, and it is also very nutritious is false, then inactivation occurs early in development due to the presence of mosaics is false, then the claim that either grebes make their nest from plants found in the water or most soils contain varying amounts of uranium has no merit, then it is a common misconception that neuroglial nuclei surround the neuron.
|
It is the case that silkworms are an ideal food source for chameleons of all sizes, and it is also very nutritious.
|
It is the case that silkworms are an ideal food source for chameleons of all sizes, and it is also very nutritious.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].). [SC1-2]
If (Not (If (Not [0].), then [1].).), then (Not (Either [2] or [3].).). [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Ponens:
If [4], then (If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].).).
[4]
Therefore, If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not [0].), then [1].).), then (Not (Either [2] or [3].).).).), then [5].
If (Not (If (Not (If (Not [0].), then [1].).), then (Not (Either [2] or [3].).).).), then (Not [5].).
Therefore, If (Not (If (Not [0].), then [1].).), then (Not (Either [2] or [3].).)..
|
{0: 'Silkworms are an ideal food source for chameleons of all sizes, and it is also very nutritious.', 1: 'Inactivation occurs early in development due to the presence of mosaics.', 2: 'Grebes make their nest from plants found in the water .', 3: 'Most soils contain varying amounts of uranium.', 4: 'A commute is a journey.', 5: 'Neuroglial nuclei surround the neuron.'}
| 4 |
3,255 |
['Should it be the case that some mistletoe plants grow on ranges, it follows that estate law is a very complicated and specialized branch of law.', 'If some diets consist of plant juice, then either smokers suffer from poor night vision due to a poisoning of their bloodstream with carbon monoxide or some mistletoe plants grow on ranges.', 'It is fair to say that some diets consist of plant juice.', 'Either chemical abundances in stars or various factors influence copper absorption.', 'Given that various factors influence copper absorption, it can be inferred that if smokers suffer from poor night vision due to a poisoning of their bloodstream with carbon monoxide, then estate law is a very complicated and specialized branch of law.', 'It is a fact that either substance abuse sets the user apart from the daily lives of ordinary people or if chemical abundances in stars, then if smokers suffer from poor night vision due to a poisoning of their bloodstream with carbon monoxide, then estate law is a very complicated and specialized branch of law.', 'It is a common misconception that substance abuse sets the user apart from the daily lives of ordinary people.']
|
Should it be the case that some mistletoe plants grow on ranges, it follows that estate law is a very complicated and specialized branch of law. If some diets consist of plant juice, then either smokers suffer from poor night vision due to a poisoning of their bloodstream with carbon monoxide or some mistletoe plants grow on ranges. It is fair to say that some diets consist of plant juice. Either chemical abundances in stars or various factors influence copper absorption. Given that various factors influence copper absorption, it can be inferred that if smokers suffer from poor night vision due to a poisoning of their bloodstream with carbon monoxide, then estate law is a very complicated and specialized branch of law. It is a fact that either substance abuse sets the user apart from the daily lives of ordinary people or if chemical abundances in stars, then if smokers suffer from poor night vision due to a poisoning of their bloodstream with carbon monoxide, then estate law is a very complicated and specialized branch of law. It is a common misconception that substance abuse sets the user apart from the daily lives of ordinary people.
|
It is true that estate law is a very complicated and specialized branch of law.
|
It is true that estate law is a very complicated and specialized branch of law.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (Either [1] or [2].).
[3]
Therefore, Either [1] or [2]..
[SC2-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [1], then [0].). [SC2-2]
If [5], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC2-2]
Disjunctive Syllogism:
Either [6] or (If [4], then (If [1], then [0].).).
Not [6].
Therefore, If [4], then (If [1], then [0].)..
|
{0: 'Estate law is a very complicated and specialized branch of law.', 1: 'Smokers suffer from poor night vision due to a poisoning of their bloodstream with carbon monoxide.', 2: 'Some mistletoe plants grow on ranges.', 3: 'Some diets consist of plant juice.', 4: 'Chemical abundances in stars.', 5: 'Various factors influence copper absorption.', 6: 'Substance abuse sets the user apart from the daily lives of ordinary people.'}
| 4 |
3,385 |
['If bulls reach maturity, then cyclic pain appears to be related to the female hormones estrogen, progesterone and prolactin.', 'If cyclic pain appears to be related to the female hormones estrogen, progesterone and prolactin, then the claim that some proteins obtain from milk is false.', 'Once we know the claim that bulls reach maturity does not correspond with reality, we also know that plant viruses use various mechanisms to replicate and spread from cell to cell.', 'If mountain goats consume food, then if the claim that bulls reach maturity does not correspond with reality, then we know that the claim that plant viruses use various mechanisms to replicate and spread from cell to cell is false.', 'Those that suggest mountain goats consume food are right.']
|
If bulls reach maturity, then cyclic pain appears to be related to the female hormones estrogen, progesterone and prolactin. If cyclic pain appears to be related to the female hormones estrogen, progesterone and prolactin, then the claim that some proteins obtain from milk is false. Once we know the claim that bulls reach maturity does not correspond with reality, we also know that plant viruses use various mechanisms to replicate and spread from cell to cell. If mountain goats consume food, then if the claim that bulls reach maturity does not correspond with reality, then we know that the claim that plant viruses use various mechanisms to replicate and spread from cell to cell is false. Those that suggest mountain goats consume food are right.
|
The claim that some proteins obtain from milk is false.
|
The claim that some proteins obtain from milk is false.
|
TRUE
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1] [SC2-1]
Therefore, Not [0]..
[SC1-1]
Hypothetical Syllogism:
If [1], then [2].
If [2], then (Not [0].).
Therefore, If [1], then (Not [0].)..
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then [3].
If (Not [1].), then (Not [3].). [SC2-2]
Therefore, [1].
[SC2-2]
Modus Ponens:
If [4], then (If (Not [1].), then (Not [3].).).
[4]
Therefore, If (Not [1].), then (Not [3].)..
|
{0: 'Some proteins obtain from milk.', 1: 'Bulls reach maturity.', 2: 'Cyclic pain appears to be related to the female hormones estrogen, progesterone and prolactin.', 3: 'Plant viruses use various mechanisms to replicate and spread from cell to cell.', 4: 'Mountain goats consume food.'}
| 4 |
3,545 |
['It is fair to say that human beings are social by nature and, as a result, spend much of their time in groups.', 'Given that those that suggest if human beings are social by nature and, as a result, spend much of their time in groups, then the statement, either gray whales migrate to breeding areas in Mexico or power laws predominate in the mathematics of turbulence, does not hold are wrong, it can be inferred that biological life is only one species of hyperlife.', 'Should it be the case that biological life is only one species of hyperlife, it follows that if critical pressure Is the saturation pressure at the critical temperature, then aquatic plants grow in ponds and streams, peat bogs, and abandoned gravel pits.', 'When those that suggest if human beings are social by nature and, as a result, spend much of their time in groups, then the statement, either gray whales migrate to breeding areas in Mexico or power laws predominate in the mathematics of turbulence, does not hold are wrong is true, it follows that either most diets consist of dog food or monarchs stop and nectar along their journey south.', 'Given that either most diets consist of dog food or monarchs stop and nectar along their journey south, it can be inferred that the claim that if critical pressure Is the saturation pressure at the critical temperature, then aquatic plants grow in ponds and streams, peat bogs, and abandoned gravel pits does not reflect reality.']
|
It is fair to say that human beings are social by nature and, as a result, spend much of their time in groups. Given that those that suggest if human beings are social by nature and, as a result, spend much of their time in groups, then the statement, either gray whales migrate to breeding areas in Mexico or power laws predominate in the mathematics of turbulence, does not hold are wrong, it can be inferred that biological life is only one species of hyperlife. Should it be the case that biological life is only one species of hyperlife, it follows that if critical pressure Is the saturation pressure at the critical temperature, then aquatic plants grow in ponds and streams, peat bogs, and abandoned gravel pits. When those that suggest if human beings are social by nature and, as a result, spend much of their time in groups, then the statement, either gray whales migrate to breeding areas in Mexico or power laws predominate in the mathematics of turbulence, does not hold are wrong is true, it follows that either most diets consist of dog food or monarchs stop and nectar along their journey south. Given that either most diets consist of dog food or monarchs stop and nectar along their journey south, it can be inferred that the claim that if critical pressure Is the saturation pressure at the critical temperature, then aquatic plants grow in ponds and streams, peat bogs, and abandoned gravel pits does not reflect reality.
|
The statement, either gray whales migrate to breeding areas in Mexico or power laws predominate in the mathematics of turbulence, does not hold.
|
The statement that states gray whales filter their food through coarse baleen plates is false.
|
Uncertain
|
Modus Ponens:
If [2], then (Not (Either [0] or [1].).). [SC1-1]
[2]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [2], then (Not (Either [0] or [1].).).).), then (If [3], then [4].). [SC1-2]
If (Not (If [2], then (Not (Either [0] or [1].).).).), then (Not (If [3], then [4].).). [SC2-2]
Therefore, If [2], then (Not (Either [0] or [1].).)..
[SC1-2]
Hypothetical Syllogism:
If (Not (If [2], then (Not (Either [0] or [1].).).).), then [7].
If [7], then (If [3], then [4].).
Therefore, If (Not (If [2], then (Not (Either [0] or [1].).).).), then (If [3], then [4].)..
[SC2-2]
Hypothetical Syllogism:
If (Not (If [2], then (Not (Either [0] or [1].).).).), then (Either [5] or [6].).
If (Either [5] or [6].), then (Not (If [3], then [4].).).
Therefore, If (Not (If [2], then (Not (Either [0] or [1].).).).), then (Not (If [3], then [4].).)..
|
{0: 'Gray whales migrate to breeding areas in Mexico.', 1: 'Power laws predominate in the mathematics of turbulence.', 2: 'Human beings are social by nature and, as a result, spend much of their time in groups.', 3: 'Critical pressure Is the saturation pressure at the critical temperature.', 4: 'Aquatic plants grow in ponds and streams, peat bogs, and abandoned gravel pits.', 5: 'Most diets consist of dog food.', 6: 'Monarchs stop and nectar along their journey south.', 7: 'Biological life is only one species of hyperlife.'}
| 4 |
3,382 |
['The statement, sunlight allows forest life, such as plants, bushes and trees to grow, does not hold.', "On the condition that the statement 'either if many people are hypertensive solely because of excessive alcohol intake, then addaxs have (part) second stomachs or if german ivy forms thick blankets which cut off light and air to plants which it covers, then sunlight allows forest life, such as plants, bushes and trees to grow' can be considered false, it is definitely the case that if many species are parasites Of medical and veterinary importance, and many are agricultural pests, then epilepsy includes both major or generalized seizures and minor or partial seizures.", 'It is not true that if many species are parasites Of medical and veterinary importance, and many are agricultural pests, then epilepsy includes both major or generalized seizures and minor or partial seizures.', 'We know that either if queen triggerfish have distinctive color patterns, then covenants are legal documents, legal oaths of faithfulness between parties or we know that the claim that if many people are hypertensive solely because of excessive alcohol intake, then addaxs have (part) second stomachs is false.', 'The statement that states if queen triggerfish have distinctive color patterns, then covenants are legal documents, legal oaths of faithfulness between parties is false.']
|
The statement, sunlight allows forest life, such as plants, bushes and trees to grow, does not hold. On the condition that the statement 'either if many people are hypertensive solely because of excessive alcohol intake, then addaxs have (part) second stomachs or if german ivy forms thick blankets which cut off light and air to plants which it covers, then sunlight allows forest life, such as plants, bushes and trees to grow' can be considered false, it is definitely the case that if many species are parasites Of medical and veterinary importance, and many are agricultural pests, then epilepsy includes both major or generalized seizures and minor or partial seizures. It is not true that if many species are parasites Of medical and veterinary importance, and many are agricultural pests, then epilepsy includes both major or generalized seizures and minor or partial seizures. We know that either if queen triggerfish have distinctive color patterns, then covenants are legal documents, legal oaths of faithfulness between parties or we know that the claim that if many people are hypertensive solely because of excessive alcohol intake, then addaxs have (part) second stomachs is false. The statement that states if queen triggerfish have distinctive color patterns, then covenants are legal documents, legal oaths of faithfulness between parties is false.
|
Some people mistakenly believe that german ivy forms thick blankets which cut off light and air to plants which it covers.
|
The statement 'types have purposes' can be considered false.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either (If [2], then [3].) or (If [0], then [1].). [SC1-2]
Not (If [2], then [3].). [SC2-2]
Therefore, If [0], then [1]..
[SC1-2]
Modus Tonens:
If (Not (Either (If [2], then [3].) or (If [0], then [1].).).), then (If [4], then [5].).
Not (If [4], then [5].).
Therefore, Either (If [2], then [3].) or (If [0], then [1].)..
[SC2-2]
Disjunctive Syllogism:
Either (If [6], then [7].) or (Not (If [2], then [3].).).
Not (If [6], then [7].).
Therefore, Not (If [2], then [3].)..
|
{0: 'German ivy forms thick blankets which cut off light and air to plants which it covers.', 1: 'Sunlight allows forest life, such as plants, bushes and trees to grow.', 2: 'Many people are hypertensive solely because of excessive alcohol intake.', 3: 'Addaxs have (part) second stomachs.', 4: 'Many species are parasites Of medical and veterinary importance, and many are agricultural pests.', 5: 'Epilepsy includes both major or generalized seizures and minor or partial seizures.', 6: 'Queen triggerfish have distinctive color patterns.', 7: 'Covenants are legal documents, legal oaths of faithfulness between parties.'}
| 4 |
3,489 |
['Given that it is not true that insects live in environments, it can be inferred that most moths possess bodies.', 'At least one of two things is true: either relationships heal when individuals heal or most raspberry plants require sunlight, or the claim that most moths possess bodies does not reflect reality.', 'It is rational to agree that selenium is a vital element to both prevent and treat cancer.', 'One may reasonably assume that if tomatoes are also good plants to use in containers on the patio, deck or lanai, then if selenium is a vital element to both prevent and treat cancer, then it is not the case that either relationships heal when individuals heal or most raspberry plants require sunlight.', 'tomatoes are also good plants to use in containers on the patio, deck or lanai.']
|
Given that it is not true that insects live in environments, it can be inferred that most moths possess bodies. At least one of two things is true: either relationships heal when individuals heal or most raspberry plants require sunlight, or the claim that most moths possess bodies does not reflect reality. It is rational to agree that selenium is a vital element to both prevent and treat cancer. One may reasonably assume that if tomatoes are also good plants to use in containers on the patio, deck or lanai, then if selenium is a vital element to both prevent and treat cancer, then it is not the case that either relationships heal when individuals heal or most raspberry plants require sunlight. tomatoes are also good plants to use in containers on the patio, deck or lanai.
|
It is rational to agree that insects live in environments.
|
It is not true that insects live in environments.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either (Either [2] or [3].) or (Not [1].).
Not (Either [2] or [3].). [SC2-2]
Therefore, Not [1]..
[SC2-2]
Modus Ponens:
If [4], then (Not (Either [2] or [3].).). [SC1-3]
[4]
Therefore, Not (Either [2] or [3].)..
[SC1-3]
Modus Ponens:
If [5], then (If [4], then (Not (Either [2] or [3].).).).
[5]
Therefore, If [4], then (Not (Either [2] or [3].).)..
|
{0: 'Insects live in environments.', 1: 'Most moths possess bodies.', 2: 'Relationships heal when individuals heal.', 3: 'Most raspberry plants require sunlight.', 4: 'Selenium is a vital element to both prevent and treat cancer.', 5: 'Tomatoes are also good plants to use in containers on the patio, deck or lanai.'}
| 4 |
3,513 |
['Assuming victories are success, we know that either periods refer to Months or Quarters or animals take in oxygen and give off carbon dioxide as they breathe.', 'Either one or both of these statements are true: if cycling is a great form of exercise, then porcupines have poor vision but good senses of hearing and smell, or most blood flows through dorsal vessels.', "Whenever it is true that if cycling is a great form of exercise, then porcupines have poor vision but good senses of hearing and smell, 'lions have toes' is true.", 'Provided that most blood flows through dorsal vessels, we know that victories are success.', 'It is a fact that either if blighters have (part) material bodies, then cycle occurs in the matrix of the mitochondria or cassowaries have a reputation in folklore for being dangerous to people and domestic animals.', "One may reasonably assume that if if blighters have (part) material bodies, then cycle occurs in the matrix of the mitochondria, then the statement that 'lions have toes' is incorrect.", "Provided that cassowaries have a reputation in folklore for being dangerous to people and domestic animals, we know that the statement that 'lions have toes' is incorrect."]
|
Assuming victories are success, we know that either periods refer to Months or Quarters or animals take in oxygen and give off carbon dioxide as they breathe. Either one or both of these statements are true: if cycling is a great form of exercise, then porcupines have poor vision but good senses of hearing and smell, or most blood flows through dorsal vessels. Whenever it is true that if cycling is a great form of exercise, then porcupines have poor vision but good senses of hearing and smell, 'lions have toes' is true. Provided that most blood flows through dorsal vessels, we know that victories are success. It is a fact that either if blighters have (part) material bodies, then cycle occurs in the matrix of the mitochondria or cassowaries have a reputation in folklore for being dangerous to people and domestic animals. One may reasonably assume that if if blighters have (part) material bodies, then cycle occurs in the matrix of the mitochondria, then the statement that 'lions have toes' is incorrect. Provided that cassowaries have a reputation in folklore for being dangerous to people and domestic animals, we know that the statement that 'lions have toes' is incorrect.
|
Either periods refer to Months or Quarters or animals take in oxygen and give off carbon dioxide as they breathe.
|
Either periods refer to Months or Quarters or animals take in oxygen and give off carbon dioxide as they breathe.
|
TRUE
|
Modus Ponens:
If [2], then (Either [0] or [1].).
[2] [SC2-1]
Therefore, Either [0] or [1]..
[SC2-1]
Disjunctive Syllogism:
Either [3] or [2]. [SC1-2]
Not [3]. [SC2-2]
Therefore, [2].
[SC1-2]
Constructive Dilemma:
Either (If [7], then [8].) or [9].
If (If [7], then [8].), then [3].
If [9], then [2].
Therefore, Either [3] or [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: 'Periods refer to Months or Quarters.', 1: 'Animals take in oxygen and give off carbon dioxide as they breathe.', 2: 'Victories are success.', 3: 'Lions have toes.', 4: 'Blighters have (part) material bodies.', 5: 'Cycle occurs in the matrix of the mitochondria.', 6: 'Cassowaries have a reputation in folklore for being dangerous to people and domestic animals.', 7: 'Cycling is a great form of exercise.', 8: 'Porcupines have poor vision but good senses of hearing and smell.', 9: 'Most blood flows through dorsal vessels.'}
| 4 |
3,780 |
['Once we know it is not the case that fungi need nitrogen, we also know that it is not true that deregulation is used to dismantle the accountability of governments and corporations.', 'We know that the claim that most different compounds have effects is false.', 'On the condition that those that suggest if the claim that if it is not the case that fungi need nitrogen, then deregulation is used to dismantle the accountability of governments and corporations does not correspond with reality, then most different compounds have effects are wrong, it is definitely the case that the claim that plants break down food much the same way as animals is false.', 'Either one or both of these statements are true: homemade mustards retain the dull yellow of the seed and are far superior in flavor and aroma, or if those that suggest if the claim that if it is not the case that fungi need nitrogen, then deregulation is used to dismantle the accountability of governments and corporations does not correspond with reality, then most different compounds have effects are wrong, then plants break down food much the same way as animals .', "The statement that 'homemade mustards retain the dull yellow of the seed and are far superior in flavor and aroma' is incorrect."]
|
Once we know it is not the case that fungi need nitrogen, we also know that it is not true that deregulation is used to dismantle the accountability of governments and corporations. We know that the claim that most different compounds have effects is false. On the condition that those that suggest if the claim that if it is not the case that fungi need nitrogen, then deregulation is used to dismantle the accountability of governments and corporations does not correspond with reality, then most different compounds have effects are wrong, it is definitely the case that the claim that plants break down food much the same way as animals is false. Either one or both of these statements are true: homemade mustards retain the dull yellow of the seed and are far superior in flavor and aroma, or if those that suggest if the claim that if it is not the case that fungi need nitrogen, then deregulation is used to dismantle the accountability of governments and corporations does not correspond with reality, then most different compounds have effects are wrong, then plants break down food much the same way as animals . The statement that 'homemade mustards retain the dull yellow of the seed and are far superior in flavor and aroma' is incorrect.
|
The statement 'fungi need nitrogen' is true.
|
Fungi cause severe damage.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (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]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not [0].), then [1].).), then [2].).), then [3]. [SC1-3]
If (Not (If (Not (If (Not [0].), then [1].).), then [2].).), then (Not [3].).
Therefore, If (Not (If (Not [0].), then [1].).), then [2]..
[SC1-3]
Disjunctive Syllogism:
Either [4] or (If (Not (If (Not (If (Not [0].), then [1].).), then [2].).), then [3].).
Not [4].
Therefore, If (Not (If (Not (If (Not [0].), then [1].).), then [2].).), then [3]..
|
{0: 'Fungi need nitrogen.', 1: 'Deregulation is used to dismantle the accountability of governments and corporations.', 2: 'Most different compounds have effects.', 3: 'Plants break down food much the same way as animals .', 4: 'Homemade mustards retain the dull yellow of the seed and are far superior in flavor and aroma.'}
| 4 |
3,904 |
["So long as some people mistakenly believe that fiscal policy is simply an attempt by the federal government to regulate or stabilize the economy, 'if some people are generally more susceptible to the effects of androgens than others, then competitiveness is the sine qua non of success anywhere' is true.", 'Once we know the statement, if some people mistakenly believe that fiscal policy is simply an attempt by the federal government to regulate or stabilize the economy, then the claim that if some people are generally more susceptible to the effects of androgens than others, then competitiveness is the sine qua non of success anywhere is false, does not hold, we also know that genetic methods complement cultural methods, and both are influenced by environmental effects.', 'On the condition that the claim that if the statement, if some people mistakenly believe that fiscal policy is simply an attempt by the federal government to regulate or stabilize the economy, then the claim that if some people are generally more susceptible to the effects of androgens than others, then competitiveness is the sine qua non of success anywhere is false, does not hold, then it is a common misconception that genetic methods complement cultural methods, and both are influenced by environmental effects does not reflect reality, it is definitely the case that ducks seek a new mate each year.', "Whenever it is true that strange look animals have legs, 'if the claim that if the statement, if some people mistakenly believe that fiscal policy is simply an attempt by the federal government to regulate or stabilize the economy, then the claim that if some people are generally more susceptible to the effects of androgens than others, then competitiveness is the sine qua non of success anywhere is false, does not hold, then it is a common misconception that genetic methods complement cultural methods, and both are influenced by environmental effects does not reflect reality, then those that suggest ducks seek a new mate each year are wrong' is true.", 'The idea that strange look animals have legs is true.']
|
So long as some people mistakenly believe that fiscal policy is simply an attempt by the federal government to regulate or stabilize the economy, 'if some people are generally more susceptible to the effects of androgens than others, then competitiveness is the sine qua non of success anywhere' is true. Once we know the statement, if some people mistakenly believe that fiscal policy is simply an attempt by the federal government to regulate or stabilize the economy, then the claim that if some people are generally more susceptible to the effects of androgens than others, then competitiveness is the sine qua non of success anywhere is false, does not hold, we also know that genetic methods complement cultural methods, and both are influenced by environmental effects. On the condition that the claim that if the statement, if some people mistakenly believe that fiscal policy is simply an attempt by the federal government to regulate or stabilize the economy, then the claim that if some people are generally more susceptible to the effects of androgens than others, then competitiveness is the sine qua non of success anywhere is false, does not hold, then it is a common misconception that genetic methods complement cultural methods, and both are influenced by environmental effects does not reflect reality, it is definitely the case that ducks seek a new mate each year. Whenever it is true that strange look animals have legs, 'if the claim that if the statement, if some people mistakenly believe that fiscal policy is simply an attempt by the federal government to regulate or stabilize the economy, then the claim that if some people are generally more susceptible to the effects of androgens than others, then competitiveness is the sine qua non of success anywhere is false, does not hold, then it is a common misconception that genetic methods complement cultural methods, and both are influenced by environmental effects does not reflect reality, then those that suggest ducks seek a new mate each year are wrong' is true. The idea that strange look animals have legs is true.
|
The idea that fiscal policy is simply an attempt by the federal government to regulate or stabilize the economy is true.
|
Fiscal policy is said to be loose or expansionary when revenue is higher than spending.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then (If [1], then [2].).
If (Not [0].), then (Not (If [1], then [2].).). [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then [3].
If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then (Not [3].). [SC2-2]
Therefore, If (Not [0].), then (Not (If [1], then [2].).)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then (Not [3].).).), then [4].
If (Not (If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then (Not [3].).).), then (Not [4].). [SC2-3]
Therefore, If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then (Not [3].)..
[SC2-3]
Modus Ponens:
If [5], then (If (Not (If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then (Not [3].).).), then (Not [4].).).
[5]
Therefore, If (Not (If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then (Not [3].).).), then (Not [4].)..
|
{0: 'Fiscal policy is simply an attempt by the federal government to regulate or stabilize the economy.', 1: 'Some people are generally more susceptible to the effects of androgens than others.', 2: 'Competitiveness is the sine qua non of success anywhere.', 3: 'Genetic methods complement cultural methods, and both are influenced by environmental effects.', 4: 'Ducks seek a new mate each year.', 5: 'Strange look animals have legs.'}
| 4 |
3,122 |
['Once we know the statement that states violets are very weakly rooted and in many cases pull up easily, if the soil is moist is false, we also know that the statement that states water aerobics provides an exercise program for individuals of all ages and fitness levels is false.', 'If it is a common misconception that if the statement that states if the statement that states violets are very weakly rooted and in many cases pull up easily, if the soil is moist is false, then water aerobics provides an exercise program for individuals of all ages and fitness levels is false, then either mountain climbers need oxygen or parsley root is available year-round with a peak season during the winter and spring months, then some large colonies consist of treehoppers.', 'Some people mistakenly believe that some large colonies consist of treehoppers.', 'Should it be the case that either mountain climbers need oxygen or parsley root is available year-round with a peak season during the winter and spring months, it follows that outer space is the common heritage of the human beings.', 'On the condition that either mountain climbers need oxygen or parsley root is available year-round with a peak season during the winter and spring months, it is definitely the case that those that suggest outer space is the common heritage of the human beings are wrong.']
|
Once we know the statement that states violets are very weakly rooted and in many cases pull up easily, if the soil is moist is false, we also know that the statement that states water aerobics provides an exercise program for individuals of all ages and fitness levels is false. If it is a common misconception that if the statement that states if the statement that states violets are very weakly rooted and in many cases pull up easily, if the soil is moist is false, then water aerobics provides an exercise program for individuals of all ages and fitness levels is false, then either mountain climbers need oxygen or parsley root is available year-round with a peak season during the winter and spring months, then some large colonies consist of treehoppers. Some people mistakenly believe that some large colonies consist of treehoppers. Should it be the case that either mountain climbers need oxygen or parsley root is available year-round with a peak season during the winter and spring months, it follows that outer space is the common heritage of the human beings. On the condition that either mountain climbers need oxygen or parsley root is available year-round with a peak season during the winter and spring months, it is definitely the case that those that suggest outer space is the common heritage of the human beings are wrong.
|
violets are very weakly rooted and in many cases pull up easily, if the soil is moist.
|
We know that the claim that violets are very weakly rooted and in many cases pull up easily, if the soil is moist is false.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].). [SC1-2]
Not (Either [2] or [3].). [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Tonens:
If (Not (If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].).).), then [5].
Not [5].
Therefore, If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].)..
[SC2-2]
Reductio Ad Absurdum:
If (Either [2] or [3].), then [4].
If (Either [2] or [3].), then (Not [4].).
Therefore, Not (Either [2] or [3].)..
|
{0: 'Violets are very weakly rooted and in many cases pull up easily, if the soil is moist.', 1: 'Water aerobics provides an exercise program for individuals of all ages and fitness levels.', 2: 'Mountain climbers need oxygen.', 3: 'Parsley root is available year-round with a peak season during the winter and spring months.', 4: 'Outer space is the common heritage of the human beings.', 5: 'Some large colonies consist of treehoppers.'}
| 4 |
3,946 |
["Whenever it is true that those that suggest either if constipation is a universal affliction of Western civilization, then use requires analyses or international commerce is more important to our economy today than at any time in the past are wrong, 'if land mass does affect the short term movement of some storms, then biological hypotheses concern variation' is true.", 'We know that the claim that if land mass does affect the short term movement of some storms, then biological hypotheses concern variation is false.', 'The idea that stress is a monster that attacks every part of the body is true.', "When some american lungfishes possess fins is true, it follows that if stress is a monster that attacks every part of the body, then the notion that 'if constipation is a universal affliction of Western civilization, then use requires analyses' is untrue.", "The statement 'some american lungfishes possess fins' is true."]
|
Whenever it is true that those that suggest either if constipation is a universal affliction of Western civilization, then use requires analyses or international commerce is more important to our economy today than at any time in the past are wrong, 'if land mass does affect the short term movement of some storms, then biological hypotheses concern variation' is true. We know that the claim that if land mass does affect the short term movement of some storms, then biological hypotheses concern variation is false. The idea that stress is a monster that attacks every part of the body is true. When some american lungfishes possess fins is true, it follows that if stress is a monster that attacks every part of the body, then the notion that 'if constipation is a universal affliction of Western civilization, then use requires analyses' is untrue. The statement 'some american lungfishes possess fins' is true.
|
It is a simple truth that international commerce is more important to our economy today than at any time in the past.
|
The claim that international commerce is more important to our economy today than at any time in the past is false.
|
FALSE
|
Disjunctive Syllogism:
Either (If [1], then [2].) or [0]. [SC1-1]
Not (If [1], then [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either (If [1], then [2].) or [0].).), then (If [4], then [5].).
Not (If [4], then [5].).
Therefore, Either (If [1], then [2].) or [0]..
[SC2-1]
Modus Ponens:
If [3], then (Not (If [1], then [2].).). [SC1-2]
[3]
Therefore, Not (If [1], then [2].)..
[SC1-2]
Modus Ponens:
If [6], then (If [3], then (Not (If [1], then [2].).).).
[6]
Therefore, If [3], then (Not (If [1], then [2].).)..
|
{0: 'International commerce is more important to our economy today than at any time in the past.', 1: 'Constipation is a universal affliction of Western civilization.', 2: 'Use requires analyses.', 3: 'Stress is a monster that attacks every part of the body.', 4: 'Land mass does affect the short term movement of some storms.', 5: 'Biological hypotheses concern variation.', 6: 'Some american lungfishes possess fins.'}
| 4 |
3,060 |
['Either either sons get out of cars or spiders has-part glands or muscle tissue needs time to regenerate and strengthen.', 'There is good reason to believe that either tamarins sleep in trees or many parents attempt to control the circumstances whereby their children get exposed to chickenpox.', 'Given that the claim that if tamarins sleep in trees, then the claim that either sons get out of cars or spiders has-part glands does not correspond with reality does not correspond with reality, it can be inferred that most deer develop their largest antlers between the ages of four and six years.', 'Some people mistakenly believe that most deer develop their largest antlers between the ages of four and six years.', 'We know that at least one of two things is true: colleges assist students, or if many parents attempt to control the circumstances whereby their children get exposed to chickenpox, then the claim that either sons get out of cars or spiders has-part glands does not correspond with reality.', 'The claim that colleges assist students is false.']
|
Either either sons get out of cars or spiders has-part glands or muscle tissue needs time to regenerate and strengthen. There is good reason to believe that either tamarins sleep in trees or many parents attempt to control the circumstances whereby their children get exposed to chickenpox. Given that the claim that if tamarins sleep in trees, then the claim that either sons get out of cars or spiders has-part glands does not correspond with reality does not correspond with reality, it can be inferred that most deer develop their largest antlers between the ages of four and six years. Some people mistakenly believe that most deer develop their largest antlers between the ages of four and six years. We know that at least one of two things is true: colleges assist students, or if many parents attempt to control the circumstances whereby their children get exposed to chickenpox, then the claim that either sons get out of cars or spiders has-part glands does not correspond with reality. The claim that colleges assist students is false.
|
It is the case that muscle tissue needs time to regenerate and strengthen.
|
It is the case that muscle tissue needs time to regenerate and strengthen.
|
TRUE
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or [0].
Not (Either [1] or [2].). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not (Either [1] or [2].).). [SC2-2]
If [4], then (Not (Either [1] or [2].).). [SC3-2]
Therefore, Not (Either [1] or [2].)..
[SC2-2]
Modus Tonens:
If (Not (If [3], then (Not (Either [1] or [2].).).).), then [5].
Not [5].
Therefore, If [3], then (Not (Either [1] or [2].).)..
[SC3-2]
Disjunctive Syllogism:
Either [6] or (If [4], then (Not (Either [1] or [2].).).).
Not [6].
Therefore, If [4], then (Not (Either [1] or [2].).)..
|
{0: 'Muscle tissue needs time to regenerate and strengthen.', 1: 'Sons get out of cars.', 2: 'Spiders has-part glands.', 3: 'Tamarins sleep in trees.', 4: 'Many parents attempt to control the circumstances whereby their children get exposed to chickenpox.', 5: 'Most deer develop their largest antlers between the ages of four and six years.', 6: 'Colleges assist students.'}
| 4 |
3,844 |
['We know that at least one of two things is true: temperatures have to drop to near freezing before algae move into a dormant state, or grain drying represents a major portion of the energy requirement for corn production.', 'Once we know temperatures have to drop to near freezing before algae move into a dormant state, we also know that either either differentiation is how multicellular organisms form specialized cells or wolves live in a family unit or if cowsheds have (part) boilers, then people are individuals.', 'If grain drying represents a major portion of the energy requirement for corn production, then either either differentiation is how multicellular organisms form specialized cells or wolves live in a family unit or if cowsheds have (part) boilers, then people are individuals.', 'We know that at least one of two things is true: either horse owners understand facts or scrub typhus occurs commonly in the southwest Pacific, southeast Asia, and Japan, or deer are ruminants .', 'Assuming either horse owners understand facts or scrub typhus occurs commonly in the southwest Pacific, southeast Asia, and Japan, we know that if either differentiation is how multicellular organisms form specialized cells or wolves live in a family unit, then trickle isa motion.', 'Provided that deer are ruminants , we know that if either differentiation is how multicellular organisms form specialized cells or wolves live in a family unit, then trickle isa motion.', 'One may reasonably assume that if the claim that if if cowsheds have (part) boilers, then people are individuals, then trickle isa motion does not correspond with reality, then either fire is the most frequent hazard following other disasters or caribou avoids regions.', "Assuming the claim that if if cowsheds have (part) boilers, then people are individuals, then trickle isa motion does not correspond with reality, we know that the statement that 'either fire is the most frequent hazard following other disasters or caribou avoids regions' is incorrect."]
|
We know that at least one of two things is true: temperatures have to drop to near freezing before algae move into a dormant state, or grain drying represents a major portion of the energy requirement for corn production. Once we know temperatures have to drop to near freezing before algae move into a dormant state, we also know that either either differentiation is how multicellular organisms form specialized cells or wolves live in a family unit or if cowsheds have (part) boilers, then people are individuals. If grain drying represents a major portion of the energy requirement for corn production, then either either differentiation is how multicellular organisms form specialized cells or wolves live in a family unit or if cowsheds have (part) boilers, then people are individuals. We know that at least one of two things is true: either horse owners understand facts or scrub typhus occurs commonly in the southwest Pacific, southeast Asia, and Japan, or deer are ruminants . Assuming either horse owners understand facts or scrub typhus occurs commonly in the southwest Pacific, southeast Asia, and Japan, we know that if either differentiation is how multicellular organisms form specialized cells or wolves live in a family unit, then trickle isa motion. Provided that deer are ruminants , we know that if either differentiation is how multicellular organisms form specialized cells or wolves live in a family unit, then trickle isa motion. One may reasonably assume that if the claim that if if cowsheds have (part) boilers, then people are individuals, then trickle isa motion does not correspond with reality, then either fire is the most frequent hazard following other disasters or caribou avoids regions. Assuming the claim that if if cowsheds have (part) boilers, then people are individuals, then trickle isa motion does not correspond with reality, we know that the statement that 'either fire is the most frequent hazard following other disasters or caribou avoids regions' is incorrect.
|
trickle isa motion.
|
Some knot theories have practical applications.
|
Uncertain
|
Disjunction Elimination:
Either (Either [1] or [2].) or (If [3], then [4].). [SC1-1]
If (Either [1] or [2].), then [0]. [SC2-1]
If (If [3], then [4].), then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [10] or [11].
If [10], then (Either (Either [1] or [2].) or (If [3], then [4].).).
If [11], then (Either (Either [1] or [2].) or (If [3], then [4].).).
Therefore, Either (Either [1] or [2].) or (If [3], then [4].)..
[SC2-1]
Disjunction Elimination:
Either (Either [7] or [8].) or [9].
If (Either [7] or [8].), then (If (Either [1] or [2].), then [0].).
If [9], then (If (Either [1] or [2].), then [0].).
Therefore, If (Either [1] or [2].), then [0]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If (If [3], then [4].), then [0].).), then (Either [5] or [6].).
If (Not (If (If [3], then [4].), then [0].).), then (Not (Either [5] or [6].).).
Therefore, If (If [3], then [4].), then [0]..
|
{0: 'Trickle isa motion.', 1: 'Differentiation is how multicellular organisms form specialized cells.', 2: 'Wolves live in a family unit.', 3: 'Cowsheds have (part) boilers.', 4: 'People are individuals.', 5: 'Fire is the most frequent hazard following other disasters.', 6: 'Caribou avoids regions.', 7: 'Horse owners understand facts.', 8: 'Scrub typhus occurs commonly in the southwest Pacific, southeast Asia, and Japan.', 9: 'Deer are ruminants .', 10: 'Temperatures have to drop to near freezing before algae move into a dormant state.', 11: 'Grain drying represents a major portion of the energy requirement for corn production.'}
| 4 |
3,372 |
["One may reasonably assume that if the statement that 'either antlers are used to push an opponent off-balance, and then canine teeth are used to wound or the statement that states vitamins are simply organic molecules like sugar, and like sugar can be added to foods is false' is incorrect, then the claim that local authorities have various duties in relation to the welfare of minors has no merit.", "Whenever it is true that antlers are used to push an opponent off-balance, and then canine teeth are used to wound, 'some farms use organic pesticide' is true.", "Once we know antlers are used to push an opponent off-balance, and then canine teeth are used to wound, we also know that the statement 'some farms use organic pesticide' can be considered false.", "Once we know the statement that 'either antlers are used to push an opponent off-balance, and then canine teeth are used to wound or the statement that states vitamins are simply organic molecules like sugar, and like sugar can be added to foods is false' is incorrect, we also know that determinism is the concept that events in the past fully determine events in the future.", 'Provided that determinism is the concept that events in the past fully determine events in the future, we know that local authorities have various duties in relation to the welfare of minors.']
|
One may reasonably assume that if the statement that 'either antlers are used to push an opponent off-balance, and then canine teeth are used to wound or the statement that states vitamins are simply organic molecules like sugar, and like sugar can be added to foods is false' is incorrect, then the claim that local authorities have various duties in relation to the welfare of minors has no merit. Whenever it is true that antlers are used to push an opponent off-balance, and then canine teeth are used to wound, 'some farms use organic pesticide' is true. Once we know antlers are used to push an opponent off-balance, and then canine teeth are used to wound, we also know that the statement 'some farms use organic pesticide' can be considered false. Once we know the statement that 'either antlers are used to push an opponent off-balance, and then canine teeth are used to wound or the statement that states vitamins are simply organic molecules like sugar, and like sugar can be added to foods is false' is incorrect, we also know that determinism is the concept that events in the past fully determine events in the future. Provided that determinism is the concept that events in the past fully determine events in the future, we know that local authorities have various duties in relation to the welfare of minors.
|
The statement that states vitamins are simply organic molecules like sugar, and like sugar can be added to foods is false.
|
The statement that states vitamins are simply organic molecules like sugar, and like sugar can be added to foods is false.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or (Not [0].).).), then [2]. [SC1-2]
If (Not (Either [1] or (Not [0].).).), then (Not [2].).
Therefore, Either [1] or (Not [0].)..
[SC1-2]
Hypothetical Syllogism:
If (Not (Either [1] or (Not [0].).).), then [4].
If [4], then [2].
Therefore, If (Not (Either [1] or (Not [0].).).), then [2]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [3].
If [1], then (Not [3].).
Therefore, Not [1]..
|
{0: 'Vitamins are simply organic molecules like sugar, and like sugar can be added to foods.', 1: 'Antlers are used to push an opponent off-balance, and then canine teeth are used to wound.', 2: 'Local authorities have various duties in relation to the welfare of minors.', 3: 'Some farms use organic pesticide.', 4: 'Determinism is the concept that events in the past fully determine events in the future.'}
| 4 |
3,283 |
['The claim that trophies are game that have been hard to hunt and capture has no merit.', 'At least one of two things is true: robins have (part) brains, or it is not the case that most african elephants have trunks.', 'The claim that robins have (part) brains is false.', 'Given that tears have water, salts, glycoproteins, and bactericidal factors, e.g., lysozyme, it can be inferred that either trophies are game that have been hard to hunt and capture or either most african elephants have trunks or the claim that either jam is bands or larvae possess mouthparts does not correspond with reality.', 'The claim that tears have water, salts, glycoproteins, and bactericidal factors, e.g., lysozyme holds true.']
|
The claim that trophies are game that have been hard to hunt and capture has no merit. At least one of two things is true: robins have (part) brains, or it is not the case that most african elephants have trunks. The claim that robins have (part) brains is false. Given that tears have water, salts, glycoproteins, and bactericidal factors, e.g., lysozyme, it can be inferred that either trophies are game that have been hard to hunt and capture or either most african elephants have trunks or the claim that either jam is bands or larvae possess mouthparts does not correspond with reality. The claim that tears have water, salts, glycoproteins, and bactericidal factors, e.g., lysozyme holds true.
|
The claim that either jam is bands or larvae possess mouthparts does not correspond with reality.
|
We know that at least one of two things is true: jam is bands, or larvae possess mouthparts.
|
FALSE
|
Disjunctive Syllogism:
Either [2] or (Not (Either [0] or [1].).). [SC1-1]
Not [2]. [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (Either [2] or (Not (Either [0] or [1].).).). [SC1-2]
Not [3].
Therefore, Either [2] or (Not (Either [0] or [1].).)..
[SC1-2]
Modus Ponens:
If [5], then (Either [3] or (Either [2] or (Not (Either [0] or [1].).).).).
[5]
Therefore, Either [3] or (Either [2] or (Not (Either [0] or [1].).).)..
[SC2-1]
Disjunctive Syllogism:
Either [4] or (Not [2].).
Not [4].
Therefore, Not [2]..
|
{0: 'Jam is bands.', 1: 'Larvae possess mouthparts.', 2: 'Most african elephants have trunks.', 3: 'Trophies are game that have been hard to hunt and capture.', 4: 'Robins have (part) brains.', 5: 'Tears have water, salts, glycoproteins, and bactericidal factors, e.g., lysozyme.'}
| 4 |
3,939 |
['One may reasonably assume that if the claim that humans are the only primates who lack a sectorial complex on the premolar does not reflect reality, then depression can influence mood, behavior, sleep habits and bodily functions in many ways.', 'If depression can influence mood, behavior, sleep habits and bodily functions in many ways, then discrimination based on sex is illegal in many countries.', 'There is good reason to believe that either many bacteria produce natural byproducts of growth called bacteriocins or food improves symptoms.', "Once we know food improves symptoms, we also know that the notion that 'discrimination based on sex is illegal in many countries' is untrue.", "Once we know it is not the case that if many bacteria produce natural byproducts of growth called bacteriocins, then the notion that 'discrimination based on sex is illegal in many countries' is untrue, we also know that some organic soils contain layers that are largely or entirely mineral material.", 'The claim that some organic soils contain layers that are largely or entirely mineral material does not reflect reality.']
|
One may reasonably assume that if the claim that humans are the only primates who lack a sectorial complex on the premolar does not reflect reality, then depression can influence mood, behavior, sleep habits and bodily functions in many ways. If depression can influence mood, behavior, sleep habits and bodily functions in many ways, then discrimination based on sex is illegal in many countries. There is good reason to believe that either many bacteria produce natural byproducts of growth called bacteriocins or food improves symptoms. Once we know food improves symptoms, we also know that the notion that 'discrimination based on sex is illegal in many countries' is untrue. Once we know it is not the case that if many bacteria produce natural byproducts of growth called bacteriocins, then the notion that 'discrimination based on sex is illegal in many countries' is untrue, we also know that some organic soils contain layers that are largely or entirely mineral material. The claim that some organic soils contain layers that are largely or entirely mineral material does not reflect reality.
|
The idea that humans are the only primates who lack a sectorial complex on the premolar is true.
|
Humans utilize both organic and inorganic selenium compounds.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [2].
If [2], then [1].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not [1].). [SC2-2]
If [4], then (Not [1].).
Therefore, Not [1]..
[SC2-2]
Modus Tonens:
If (Not (If [3], then (Not [1].).).), then [5].
Not [5].
Therefore, If [3], then (Not [1].)..
|
{0: 'Humans are the only primates who lack a sectorial complex on the premolar.', 1: 'Discrimination based on sex is illegal in many countries.', 2: 'Depression can influence mood, behavior, sleep habits and bodily functions in many ways.', 3: 'Many bacteria produce natural byproducts of growth called bacteriocins.', 4: 'Food improves symptoms.', 5: 'Some organic soils contain layers that are largely or entirely mineral material.'}
| 4 |
3,608 |
['Either mayors have (part) vacuoles or some extensive burrows are dug by nose wombats.', 'When mayors have (part) vacuoles is true, it follows that either doctors classify cardiomyopathies by the way they affect the anatomy and function of the heart or permeability is rapid in the substratum of the sandy substratum phase.', 'Assuming some extensive burrows are dug by nose wombats, we know that boolean operators are search commands that help to combine search terms and concepts.', 'Once we know either doctors classify cardiomyopathies by the way they affect the anatomy and function of the heart or permeability is rapid in the substratum of the sandy substratum phase, we also know that the statement that states life is the characteristic state of organisms is false.', 'Given that those that suggest if either doctors classify cardiomyopathies by the way they affect the anatomy and function of the heart or permeability is rapid in the substratum of the sandy substratum phase, then life is the characteristic state of organisms are wrong, it can be inferred that misdemeanors are offenses punishable by a sentence of one year or less.', 'Given that those that suggest if either doctors classify cardiomyopathies by the way they affect the anatomy and function of the heart or permeability is rapid in the substratum of the sandy substratum phase, then life is the characteristic state of organisms are wrong, it can be inferred that the statement that states misdemeanors are offenses punishable by a sentence of one year or less is false.']
|
Either mayors have (part) vacuoles or some extensive burrows are dug by nose wombats. When mayors have (part) vacuoles is true, it follows that either doctors classify cardiomyopathies by the way they affect the anatomy and function of the heart or permeability is rapid in the substratum of the sandy substratum phase. Assuming some extensive burrows are dug by nose wombats, we know that boolean operators are search commands that help to combine search terms and concepts. Once we know either doctors classify cardiomyopathies by the way they affect the anatomy and function of the heart or permeability is rapid in the substratum of the sandy substratum phase, we also know that the statement that states life is the characteristic state of organisms is false. Given that those that suggest if either doctors classify cardiomyopathies by the way they affect the anatomy and function of the heart or permeability is rapid in the substratum of the sandy substratum phase, then life is the characteristic state of organisms are wrong, it can be inferred that misdemeanors are offenses punishable by a sentence of one year or less. Given that those that suggest if either doctors classify cardiomyopathies by the way they affect the anatomy and function of the heart or permeability is rapid in the substratum of the sandy substratum phase, then life is the characteristic state of organisms are wrong, it can be inferred that the statement that states misdemeanors are offenses punishable by a sentence of one year or less is false.
|
The statement that states boolean operators are search commands that help to combine search terms and concepts is right.
|
The statement that states boolean operators are search commands that help to combine search terms and concepts is right.
|
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 [3] or [4].
If [3], then (Either [1] or [2].).
If [4], then [0].
Therefore, Either (Either [1] or [2].) or [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Either [1] or [2].), then [5]. [SC1-2]
If (Either [1] or [2].), then (Not [5].).
Therefore, Not (Either [1] or [2].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Either [1] or [2].), then [5].).), then [6].
If (Not (If (Either [1] or [2].), then [5].).), then (Not [6].).
Therefore, If (Either [1] or [2].), then [5]..
|
{0: 'Boolean operators are search commands that help to combine search terms and concepts.', 1: 'Doctors classify cardiomyopathies by the way they affect the anatomy and function of the heart.', 2: 'Permeability is rapid in the substratum of the sandy substratum phase.', 3: 'Mayors have (part) vacuoles.', 4: 'Some extensive burrows are dug by nose wombats.', 5: 'Life is the characteristic state of organisms.', 6: 'Misdemeanors are offenses punishable by a sentence of one year or less.'}
| 4 |
3,495 |
['Once we know lilacs are bushs, we also know that either shepherds have (part) body substances or either caudal fin is relatively long and deeply forked with the tips being pointed or hair comes in brown, dark brown,and black.', 'We can assume that lilacs are bushs.', 'It is not true that jewish apartheid begins with adults.', 'We know that at least one of two things is true: most spider monkeys gather food, or if shepherds have (part) body substances, then jewish apartheid begins with adults.', "The notion that 'most spider monkeys gather food' is untrue."]
|
Once we know lilacs are bushs, we also know that either shepherds have (part) body substances or either caudal fin is relatively long and deeply forked with the tips being pointed or hair comes in brown, dark brown,and black. We can assume that lilacs are bushs. It is not true that jewish apartheid begins with adults. We know that at least one of two things is true: most spider monkeys gather food, or if shepherds have (part) body substances, then jewish apartheid begins with adults. The notion that 'most spider monkeys gather food' is untrue.
|
It is rational to believe that either caudal fin is relatively long and deeply forked with the tips being pointed or hair comes in brown, dark brown,and black.
|
There is good reason to believe that either caudal fins have shapes or hair decreases in volume and moisture.
|
Uncertain
|
Disjunctive Syllogism:
Either [2] or (Either [0] or [1].). [SC1-1]
Not [2]. [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Modus Ponens:
If [3], then (Either [2] or (Either [0] or [1].).).
[3]
Therefore, Either [2] or (Either [0] or [1].)..
[SC2-1]
Modus Tonens:
If [2], then [4]. [SC1-2]
Not [4].
Therefore, Not [2]..
[SC1-2]
Disjunctive Syllogism:
Either [5] or (If [2], then [4].).
Not [5].
Therefore, If [2], then [4]..
|
{0: 'Caudal fin is relatively long and deeply forked with the tips being pointed.', 1: 'Hair comes in brown, dark brown,and black.', 2: 'Shepherds have (part) body substances.', 3: 'Lilacs are bushs.', 4: 'Jewish apartheid begins with adults.', 5: 'Most spider monkeys gather food.'}
| 4 |
3,630 |
["Whenever it is true that the statement that 'football promotes oneness and friendship between individuals and countries' is incorrect, 'psychologists speculate that beards are perceived as dishonest because they cover the face' is true.", 'Given that the claim that either caterpillars are where it all begins and probably why butterflies are so fascinating or the statement that states psychologists speculate that beards are perceived as dishonest because they cover the face is false does not reflect reality, it can be inferred that endocrine glands produce hormones and are secrete directly into the blood or fluid around cells.', "The statement that 'endocrine glands produce hormones and are secrete directly into the blood or fluid around cells' is incorrect.", 'We know that either a seal is a fixing or viscachas have (part) piluses.', "Should it be the case that a seal is a fixing, it follows that the notion that 'caterpillars are where it all begins and probably why butterflies are so fascinating' is untrue.", "On the condition that viscachas have (part) piluses, it is definitely the case that the notion that 'caterpillars are where it all begins and probably why butterflies are so fascinating' is untrue."]
|
Whenever it is true that the statement that 'football promotes oneness and friendship between individuals and countries' is incorrect, 'psychologists speculate that beards are perceived as dishonest because they cover the face' is true. Given that the claim that either caterpillars are where it all begins and probably why butterflies are so fascinating or the statement that states psychologists speculate that beards are perceived as dishonest because they cover the face is false does not reflect reality, it can be inferred that endocrine glands produce hormones and are secrete directly into the blood or fluid around cells. The statement that 'endocrine glands produce hormones and are secrete directly into the blood or fluid around cells' is incorrect. We know that either a seal is a fixing or viscachas have (part) piluses. Should it be the case that a seal is a fixing, it follows that the notion that 'caterpillars are where it all begins and probably why butterflies are so fascinating' is untrue. On the condition that viscachas have (part) piluses, it is definitely the case that the notion that 'caterpillars are where it all begins and probably why butterflies are so fascinating' is untrue.
|
It is reasonable to believe that football promotes oneness and friendship between individuals and countries.
|
The claim that football promotes oneness and friendship between individuals and countries does not correspond with reality.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].). [SC1-2]
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC1-2]
Modus Tonens:
If (Not (Either [2] or (Not [1].).).), then [3].
Not [3].
Therefore, Either [2] or (Not [1].)..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Not [2].).
If [5], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Football promotes oneness and friendship between individuals and countries.', 1: 'Psychologists speculate that beards are perceived as dishonest because they cover the face.', 2: 'Caterpillars are where it all begins and probably why butterflies are so fascinating.', 3: 'Endocrine glands produce hormones and are secrete directly into the blood or fluid around cells.', 4: 'A seal is a fixing.', 5: 'Viscachas have (part) piluses.'}
| 4 |
3,596 |
['One may reasonably assume that if a valuator is a judge, then it is a common misconception that corns feel hard to the touch, are tender and have a roundish appearance.', 'If it is a common misconception that if a valuator is a judge, then corns feel hard to the touch, are tender and have a roundish appearance, then feudal society is based on two principles , that of feudalism and manorialism .', "Whenever it is true that endemic species are species that are found only on oceanic islands, 'the statement 'feudal society is based on two principles , that of feudalism and manorialism ' can be considered false' is true.", "Whenever it is true that if most caribou has antlers, then most species grow in hot, dry regions especially in Mexico and the Southwestern United States, 'the statement 'feudal society is based on two principles , that of feudalism and manorialism ' can be considered false' is true.", 'Either one or both of these statements are true: some industries raise salmon, or invasive species pose huge threats to the environment.', 'On the condition that some industries raise salmon, it is definitely the case that either endemic species are species that are found only on oceanic islands or if most caribou has antlers, then most species grow in hot, dry regions especially in Mexico and the Southwestern United States.', "So long as invasive species pose huge threats to the environment, 'either endemic species are species that are found only on oceanic islands or if most caribou has antlers, then most species grow in hot, dry regions especially in Mexico and the Southwestern United States' is true."]
|
One may reasonably assume that if a valuator is a judge, then it is a common misconception that corns feel hard to the touch, are tender and have a roundish appearance. If it is a common misconception that if a valuator is a judge, then corns feel hard to the touch, are tender and have a roundish appearance, then feudal society is based on two principles , that of feudalism and manorialism . Whenever it is true that endemic species are species that are found only on oceanic islands, 'the statement 'feudal society is based on two principles , that of feudalism and manorialism ' can be considered false' is true. Whenever it is true that if most caribou has antlers, then most species grow in hot, dry regions especially in Mexico and the Southwestern United States, 'the statement 'feudal society is based on two principles , that of feudalism and manorialism ' can be considered false' is true. Either one or both of these statements are true: some industries raise salmon, or invasive species pose huge threats to the environment. On the condition that some industries raise salmon, it is definitely the case that either endemic species are species that are found only on oceanic islands or if most caribou has antlers, then most species grow in hot, dry regions especially in Mexico and the Southwestern United States. So long as invasive species pose huge threats to the environment, 'either endemic species are species that are found only on oceanic islands or if most caribou has antlers, then most species grow in hot, dry regions especially in Mexico and the Southwestern United States' is true.
|
The statement that states a valuator is a judge is false.
|
The statement that states a valuator is a judge is false.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].).
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (If [0], then [1].).), then [2].
Not [2]. [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Disjunction Elimination:
Either [3] or (If [4], then [5].). [SC1-3]
If [3], then (Not [2].).
If (If [4], then [5].), then (Not [2].).
Therefore, Not [2]..
[SC1-3]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Either [3] or (If [4], then [5].).).
If [7], then (Either [3] or (If [4], then [5].).).
Therefore, Either [3] or (If [4], then [5].)..
|
{0: 'A valuator is a judge.', 1: 'Corns feel hard to the touch, are tender and have a roundish appearance.', 2: 'Feudal society is based on two principles , that of feudalism and manorialism .', 3: 'Endemic species are species that are found only on oceanic islands.', 4: 'Most caribou has antlers.', 5: 'Most species grow in hot, dry regions especially in Mexico and the Southwestern United States.', 6: 'Some industries raise salmon.', 7: 'Invasive species pose huge threats to the environment.'}
| 4 |
3,713 |
["Once we know dracaenas are agaves, we also know that if the statement that 'public education can go a long way toward reducing the probability of human infection' is incorrect, then cancer cells can go into a quiescent stage, then start dividing again.", 'We can assume that dracaenas are agaves.', 'Either one or both of these statements are true: trees are everywhere, or peacocks eat termites.', "Assuming peacocks eat termites, we know that if the statement that 'public education can go a long way toward reducing the probability of human infection' is incorrect, then those that suggest cancer cells can go into a quiescent stage, then start dividing again are wrong.", "Either one or both of these statements are true: afternoons are days, or if trees are everywhere, then if the statement that 'public education can go a long way toward reducing the probability of human infection' is incorrect, then those that suggest cancer cells can go into a quiescent stage, then start dividing again are wrong.", "The notion that 'afternoons are days' is untrue."]
|
Once we know dracaenas are agaves, we also know that if the statement that 'public education can go a long way toward reducing the probability of human infection' is incorrect, then cancer cells can go into a quiescent stage, then start dividing again. We can assume that dracaenas are agaves. Either one or both of these statements are true: trees are everywhere, or peacocks eat termites. Assuming peacocks eat termites, we know that if the statement that 'public education can go a long way toward reducing the probability of human infection' is incorrect, then those that suggest cancer cells can go into a quiescent stage, then start dividing again are wrong. Either one or both of these statements are true: afternoons are days, or if trees are everywhere, then if the statement that 'public education can go a long way toward reducing the probability of human infection' is incorrect, then those that suggest cancer cells can go into a quiescent stage, then start dividing again are wrong. The notion that 'afternoons are days' is untrue.
|
The idea that public education can go a long way toward reducing the probability of human infection is true.
|
The notion that 'public education can go a long way toward reducing the probability of human infection' is untrue.
|
FALSE
|
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 [4], then (If (Not [0].), then [1].).
[4]
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If (Not [0].), then (Not [1].).). [SC2-2]
If [3], then (If (Not [0].), then (Not [1].).).
Therefore, If (Not [0].), then (Not [1].)..
[SC2-2]
Disjunctive Syllogism:
Either [5] or (If [2], then (If (Not [0].), then (Not [1].).).).
Not [5].
Therefore, If [2], then (If (Not [0].), then (Not [1].).)..
|
{0: 'Public education can go a long way toward reducing the probability of human infection.', 1: 'Cancer cells can go into a quiescent stage, then start dividing again.', 2: 'Trees are everywhere.', 3: 'Peacocks eat termites.', 4: 'Dracaenas are agaves.', 5: 'Afternoons are days.'}
| 4 |
3,753 |
['It is a simple truth that mail uses temporary storage in memory and on disk to improve access to data.', 'Should it be the case that either money is a tool used to recognize services rendered, morally neutral until it is put to use or machine soul is what allows the rider to get used to the bike and can cause a kind of loyalty, it follows that either if farmers use propane to dry crops, brood chickens, power tractors, and warm greenhouses, then nutrients have impact or if mail uses temporary storage in memory and on disk to improve access to data, then most proteins also have an ordered arrangement called the native state.', 'Either one or both of these statements are true: money is a tool used to recognize services rendered, morally neutral until it is put to use, or machine soul is what allows the rider to get used to the bike and can cause a kind of loyalty.', 'At least one of two things is true: reduction reaction is chemical reaction, or the statement that states if farmers use propane to dry crops, brood chickens, power tractors, and warm greenhouses, then nutrients have impact is false.', 'Those that suggest reduction reaction is chemical reaction are wrong.']
|
It is a simple truth that mail uses temporary storage in memory and on disk to improve access to data. Should it be the case that either money is a tool used to recognize services rendered, morally neutral until it is put to use or machine soul is what allows the rider to get used to the bike and can cause a kind of loyalty, it follows that either if farmers use propane to dry crops, brood chickens, power tractors, and warm greenhouses, then nutrients have impact or if mail uses temporary storage in memory and on disk to improve access to data, then most proteins also have an ordered arrangement called the native state. Either one or both of these statements are true: money is a tool used to recognize services rendered, morally neutral until it is put to use, or machine soul is what allows the rider to get used to the bike and can cause a kind of loyalty. At least one of two things is true: reduction reaction is chemical reaction, or the statement that states if farmers use propane to dry crops, brood chickens, power tractors, and warm greenhouses, then nutrients have impact is false. Those that suggest reduction reaction is chemical reaction are wrong.
|
The claim that most proteins also have an ordered arrangement called the native state is true.
|
Some proteins participate in development.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either (If [2], then [3].) or (If [1], then [0].). [SC1-2]
Not (If [2], then [3].). [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Modus Ponens:
If (Either [4] or [5].), then (Either (If [2], then [3].) or (If [1], then [0].).).
Either [4] or [5].
Therefore, Either (If [2], then [3].) or (If [1], then [0].)..
[SC2-2]
Disjunctive Syllogism:
Either [6] or (Not (If [2], then [3].).).
Not [6].
Therefore, Not (If [2], then [3].)..
|
{0: 'Most proteins also have an ordered arrangement called the native state.', 1: 'Mail uses temporary storage in memory and on disk to improve access to data.', 2: 'Farmers use propane to dry crops, brood chickens, power tractors, and warm greenhouses.', 3: 'Nutrients have impact.', 4: 'Money is a tool used to recognize services rendered, morally neutral until it is put to use.', 5: 'Machine soul is what allows the rider to get used to the bike and can cause a kind of loyalty.', 6: 'Reduction reaction is chemical reaction.'}
| 4 |
3,624 |
['Those that suggest anoles have limbs are right.', 'Given that the claim that if anoles have limbs, then either sharpshooters can acquire the bacterium after they feed on an infected plant or most plants can store nutrients for later use does not reflect reality, it can be inferred that privacy laws define appropriate or inappropriate information disclosures or releases.', 'Once we know the claim that if anoles have limbs, then either sharpshooters can acquire the bacterium after they feed on an infected plant or most plants can store nutrients for later use does not reflect reality, we also know that the claim that privacy laws define appropriate or inappropriate information disclosures or releases does not correspond with reality.', 'Should it be the case that fractal geometry describes objects that are self-similar, or scale symmetric, it follows that if either sharpshooters can acquire the bacterium after they feed on an infected plant or most plants can store nutrients for later use, then psychogenic polydipsia is the term used to describe excessive drinking with a psychological cause.', "The statement 'fractal geometry describes objects that are self-similar, or scale symmetric' is true."]
|
Those that suggest anoles have limbs are right. Given that the claim that if anoles have limbs, then either sharpshooters can acquire the bacterium after they feed on an infected plant or most plants can store nutrients for later use does not reflect reality, it can be inferred that privacy laws define appropriate or inappropriate information disclosures or releases. Once we know the claim that if anoles have limbs, then either sharpshooters can acquire the bacterium after they feed on an infected plant or most plants can store nutrients for later use does not reflect reality, we also know that the claim that privacy laws define appropriate or inappropriate information disclosures or releases does not correspond with reality. Should it be the case that fractal geometry describes objects that are self-similar, or scale symmetric, it follows that if either sharpshooters can acquire the bacterium after they feed on an infected plant or most plants can store nutrients for later use, then psychogenic polydipsia is the term used to describe excessive drinking with a psychological cause. The statement 'fractal geometry describes objects that are self-similar, or scale symmetric' is true.
|
The idea that psychogenic polydipsia is the term used to describe excessive drinking with a psychological cause is true.
|
Theories provide complete explanations.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If [1], then (Either [2] or [3].). [SC1-2]
If (Either [2] or [3].), then [0]. [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [1], then (Either [2] or [3].).).), then [4].
If (Not (If [1], then (Either [2] or [3].).).), then (Not [4].).
Therefore, If [1], then (Either [2] or [3].)..
[SC2-2]
Modus Ponens:
If [5], then (If (Either [2] or [3].), then [0].).
[5]
Therefore, If (Either [2] or [3].), then [0]..
|
{0: 'Psychogenic polydipsia is the term used to describe excessive drinking with a psychological cause.', 1: 'Anoles have limbs.', 2: 'Sharpshooters can acquire the bacterium after they feed on an infected plant.', 3: 'Most plants can store nutrients for later use.', 4: 'Privacy laws define appropriate or inappropriate information disclosures or releases.', 5: 'Fractal geometry describes objects that are self-similar, or scale symmetric.'}
| 4 |
3,312 |
['At least one of two things is true: stress symptoms affect thoughts, or honey has several important qualities in addition to composition and taste.', 'It is a fact that either some minks feed diets or the claim that stress symptoms affect thoughts is false.', "So long as some food contains husks, 'the notion that 'some minks feed diets' is untrue' is true.", 'Should it be the case that it is not the case that some food contains husks, it follows that gauzes provide a moist wound healing environment when kept moist.', 'One may reasonably assume that if it is not the case that some food contains husks, then the claim that gauzes provide a moist wound healing environment when kept moist has no merit.']
|
At least one of two things is true: stress symptoms affect thoughts, or honey has several important qualities in addition to composition and taste. It is a fact that either some minks feed diets or the claim that stress symptoms affect thoughts is false. So long as some food contains husks, 'the notion that 'some minks feed diets' is untrue' is true. Should it be the case that it is not the case that some food contains husks, it follows that gauzes provide a moist wound healing environment when kept moist. One may reasonably assume that if it is not the case that some food contains husks, then the claim that gauzes provide a moist wound healing environment when kept moist has no merit.
|
The statement that states honey has several important qualities in addition to composition and taste is right.
|
The claim that honey has several important qualities in addition to composition and taste has no merit.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].).
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Modus Ponens:
If [3], then (Not [2].).
[3] [SC2-3]
Therefore, Not [2]..
[SC2-3]
Reductio Ad Absurdum:
If (Not [3].), then [4].
If (Not [3].), then (Not [4].).
Therefore, [3].
|
{0: 'Honey has several important qualities in addition to composition and taste.', 1: 'Stress symptoms affect thoughts.', 2: 'Some minks feed diets.', 3: 'Some food contains husks.', 4: 'Gauzes provide a moist wound healing environment when kept moist.'}
| 4 |
3,008 |
['On the condition that the claim that if westland soils are fine-loamy, then we know that the claim that most birds have social life is false has no merit, it is definitely the case that chinese calligraphy is the practice of writing Chinese beautifully.', 'It is a common misconception that chinese calligraphy is the practice of writing Chinese beautifully.', 'At least one of two things is true: surface waters are highly alkaline, or termites have wings that they shed once they have found a good place to build a nest.', 'Provided that surface waters are highly alkaline, we know that westland soils are fine-loamy.', 'One may reasonably assume that if some dormouses have expectancy, then if termites have wings that they shed once they have found a good place to build a nest, then westland soils are fine-loamy.', 'The claim that some dormouses have expectancy holds true.']
|
On the condition that the claim that if westland soils are fine-loamy, then we know that the claim that most birds have social life is false has no merit, it is definitely the case that chinese calligraphy is the practice of writing Chinese beautifully. It is a common misconception that chinese calligraphy is the practice of writing Chinese beautifully. At least one of two things is true: surface waters are highly alkaline, or termites have wings that they shed once they have found a good place to build a nest. Provided that surface waters are highly alkaline, we know that westland soils are fine-loamy. One may reasonably assume that if some dormouses have expectancy, then if termites have wings that they shed once they have found a good place to build a nest, then westland soils are fine-loamy. The claim that some dormouses have expectancy holds true.
|
We know that the claim that most birds have social life is false.
|
We know that the claim that some birds eat cobs 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]. [SC3-2]
Therefore, [1].
[SC3-2]
Modus Ponens:
If [5], then (If [4], then [1].).
[5]
Therefore, If [4], then [1]..
|
{0: 'Most birds have social life.', 1: 'Westland soils are fine-loamy.', 2: 'Chinese calligraphy is the practice of writing Chinese beautifully.', 3: 'Surface waters are highly alkaline.', 4: 'Termites have wings that they shed once they have found a good place to build a nest.', 5: 'Some dormouses have expectancy.'}
| 4 |
3,529 |
["When if cork is bark, then gray whales have a long and narrow shape and are a medium gray colour marbled with lighter patches is true, it follows that the statement that 'facilitation is an increase in release probability that follows use of a synapse' is incorrect.", 'At least one of two things is true: wild rodents cause damage, or seaweeds collect so thickly in depressions that turtles actually can lie down in the stuff.', "Whenever it is true that wild rodents cause damage, 'if if cork is bark, then gray whales have a long and narrow shape and are a medium gray colour marbled with lighter patches, then if some typical diets contain carbohydrates, then some gay men have problems with condoms' is true.", 'When seaweeds collect so thickly in depressions that turtles actually can lie down in the stuff is true, it follows that if if cork is bark, then gray whales have a long and narrow shape and are a medium gray colour marbled with lighter patches, then if some typical diets contain carbohydrates, then some gay men have problems with condoms.', 'There is good reason to believe that either customers experience benefits or if if some typical diets contain carbohydrates, then some gay men have problems with condoms, then facilitation is an increase in release probability that follows use of a synapse.', 'It is a common misconception that customers experience benefits.']
|
When if cork is bark, then gray whales have a long and narrow shape and are a medium gray colour marbled with lighter patches is true, it follows that the statement that 'facilitation is an increase in release probability that follows use of a synapse' is incorrect. At least one of two things is true: wild rodents cause damage, or seaweeds collect so thickly in depressions that turtles actually can lie down in the stuff. Whenever it is true that wild rodents cause damage, 'if if cork is bark, then gray whales have a long and narrow shape and are a medium gray colour marbled with lighter patches, then if some typical diets contain carbohydrates, then some gay men have problems with condoms' is true. When seaweeds collect so thickly in depressions that turtles actually can lie down in the stuff is true, it follows that if if cork is bark, then gray whales have a long and narrow shape and are a medium gray colour marbled with lighter patches, then if some typical diets contain carbohydrates, then some gay men have problems with condoms. There is good reason to believe that either customers experience benefits or if if some typical diets contain carbohydrates, then some gay men have problems with condoms, then facilitation is an increase in release probability that follows use of a synapse. It is a common misconception that customers experience benefits.
|
Some people mistakenly believe that if cork is bark, then gray whales have a long and narrow shape and are a medium gray colour marbled with lighter patches.
|
The statement that 'cork has density' is incorrect.
|
Uncertain
|
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]
Hypothetical Syllogism:
If (If [0], then [1].), then (If [3], then [4].). [SC1-2]
If (If [3], then [4].), then [2]. [SC2-2]
Therefore, If (If [0], then [1].), then [2]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (If [0], then [1].), then (If [3], then [4].).).
If [6], then (If (If [0], then [1].), then (If [3], then [4].).).
Therefore, If (If [0], then [1].), then (If [3], then [4].)..
[SC2-2]
Disjunctive Syllogism:
Either [7] or (If (If [3], then [4].), then [2].).
Not [7].
Therefore, If (If [3], then [4].), then [2]..
|
{0: 'Cork is bark.', 1: 'Gray whales have a long and narrow shape and are a medium gray colour marbled with lighter patches.', 2: 'Facilitation is an increase in release probability that follows use of a synapse.', 3: 'Some typical diets contain carbohydrates.', 4: 'Some gay men have problems with condoms.', 5: 'Wild rodents cause damage.', 6: 'Seaweeds collect so thickly in depressions that turtles actually can lie down in the stuff.', 7: 'Customers experience benefits.'}
| 4 |
3,876 |
["On the condition that racism operates similarly in individuals, it is definitely the case that the statement that 'blood pressure varies from person to person' is incorrect.", 'We know that either software is a tool to make life easier and more productive or wisdom comes from learning and is based on knowledge.', 'When software is a tool to make life easier and more productive is true, it follows that if it is not the case that racism operates similarly in individuals, then if skin disease associated with nonabusive pathologic bone fractures can also mimic abuse, then seasonal distribution is primarily temperature regulated.', 'If wisdom comes from learning and is based on knowledge, then if it is not the case that racism operates similarly in individuals, then if skin disease associated with nonabusive pathologic bone fractures can also mimic abuse, then seasonal distribution is primarily temperature regulated.', 'Given that it is not the case that if it is not the case that racism operates similarly in individuals, then the statement, if skin disease associated with nonabusive pathologic bone fractures can also mimic abuse, then seasonal distribution is primarily temperature regulated, does not hold, it can be inferred that moisture is an important property of coal, as all coals are mined wet.', 'Once we know it is not the case that if it is not the case that racism operates similarly in individuals, then the statement, if skin disease associated with nonabusive pathologic bone fractures can also mimic abuse, then seasonal distribution is primarily temperature regulated, does not hold, we also know that the claim that moisture is an important property of coal, as all coals are mined wet has no merit.']
|
On the condition that racism operates similarly in individuals, it is definitely the case that the statement that 'blood pressure varies from person to person' is incorrect. We know that either software is a tool to make life easier and more productive or wisdom comes from learning and is based on knowledge. When software is a tool to make life easier and more productive is true, it follows that if it is not the case that racism operates similarly in individuals, then if skin disease associated with nonabusive pathologic bone fractures can also mimic abuse, then seasonal distribution is primarily temperature regulated. If wisdom comes from learning and is based on knowledge, then if it is not the case that racism operates similarly in individuals, then if skin disease associated with nonabusive pathologic bone fractures can also mimic abuse, then seasonal distribution is primarily temperature regulated. Given that it is not the case that if it is not the case that racism operates similarly in individuals, then the statement, if skin disease associated with nonabusive pathologic bone fractures can also mimic abuse, then seasonal distribution is primarily temperature regulated, does not hold, it can be inferred that moisture is an important property of coal, as all coals are mined wet. Once we know it is not the case that if it is not the case that racism operates similarly in individuals, then the statement, if skin disease associated with nonabusive pathologic bone fractures can also mimic abuse, then seasonal distribution is primarily temperature regulated, does not hold, we also know that the claim that moisture is an important property of coal, as all coals are mined wet has no merit.
|
The statement that 'blood pressure varies from person to person' is incorrect.
|
Many people rightly believe that blood pressure varies from person to person.
|
FALSE
|
Modus Ponens:
If [1], then (Not [0].).
[1] [SC2-1]
Therefore, Not [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then (If [2], then [3].). [SC1-2]
If (Not [1].), then (Not (If [2], then [3].).). [SC2-2]
Therefore, [1].
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Not [1].), then (If [2], then [3].).).
If [6], then (If (Not [1].), then (If [2], then [3].).).
Therefore, If (Not [1].), then (If [2], then [3].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not [1].), then (Not (If [2], then [3].).).).), then [4].
If (Not (If (Not [1].), then (Not (If [2], then [3].).).).), then (Not [4].).
Therefore, If (Not [1].), then (Not (If [2], then [3].).)..
|
{0: 'Blood pressure varies from person to person.', 1: 'Racism operates similarly in individuals.', 2: 'Skin disease associated with nonabusive pathologic bone fractures can also mimic abuse.', 3: 'Seasonal distribution is primarily temperature regulated.', 4: 'Moisture is an important property of coal, as all coals are mined wet.', 5: 'Software is a tool to make life easier and more productive.', 6: 'Wisdom comes from learning and is based on knowledge.'}
| 4 |
3,101 |
["So long as granite is an igneous rock that is composed of four minerals, 'creatures have simple structures' is true.", 'Assuming it is a common misconception that if most germination depends on soil moisture, then granite is an igneous rock that is composed of four minerals, we know that the claim that slander is in a transitory form, for example, speech is false.', 'Once we know it is a common misconception that if most germination depends on soil moisture, then granite is an igneous rock that is composed of four minerals, we also know that configuration refers to any form of organization that is consistent and highly integrated.', 'Once we know bungalow isa house, we also know that if configuration refers to any form of organization that is consistent and highly integrated, then slander is in a transitory form, for example, speech.', 'The idea that bungalow isa house is true.']
|
So long as granite is an igneous rock that is composed of four minerals, 'creatures have simple structures' is true. Assuming it is a common misconception that if most germination depends on soil moisture, then granite is an igneous rock that is composed of four minerals, we know that the claim that slander is in a transitory form, for example, speech is false. Once we know it is a common misconception that if most germination depends on soil moisture, then granite is an igneous rock that is composed of four minerals, we also know that configuration refers to any form of organization that is consistent and highly integrated. Once we know bungalow isa house, we also know that if configuration refers to any form of organization that is consistent and highly integrated, then slander is in a transitory form, for example, speech. The idea that bungalow isa house is true.
|
When most germination depends on soil moisture is true, it follows that creatures have simple structures.
|
When most germination depends on soil moisture is true, it follows that most creatures have feet.
|
Uncertain
|
Hypothetical Syllogism:
If [0], then [2]. [SC1-1]
If [2], then [1].
Therefore, If [0], then [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [0], then [2].).), then [3]. [SC1-2]
If (Not (If [0], then [2].).), then (Not [3].).
Therefore, If [0], then [2]..
[SC1-2]
Hypothetical Syllogism:
If (Not (If [0], then [2].).), then [4].
If [4], then [3]. [SC2-3]
Therefore, If (Not (If [0], then [2].).), then [3]..
[SC2-3]
Modus Ponens:
If [5], then (If [4], then [3].).
[5]
Therefore, If [4], then [3]..
|
{0: 'Most germination depends on soil moisture.', 1: 'Creatures have simple structures.', 2: 'Granite is an igneous rock that is composed of four minerals.', 3: 'Slander is in a transitory form, for example, speech.', 4: 'Configuration refers to any form of organization that is consistent and highly integrated.', 5: 'Bungalow isa house.'}
| 4 |
3,615 |
['It is rational to believe that either either skin encloses internal organs or atheism is much more compatible with a universe infinite in time and space or if some ants live for years, then natural pearls occurring with no human assistance are extremely rare.', "On the condition that either skin encloses internal organs or atheism is much more compatible with a universe infinite in time and space, it is definitely the case that if the statement 'most horses have life expectancy' can be considered false, then if heavies lace up at the front like normal shoes but also have an ankle strap for more support, then some spiders can live most of their lives under water in bubble webs.", 'Assuming if heavies lace up at the front like normal shoes but also have an ankle strap for more support, then some spiders can live most of their lives under water in bubble webs, we know that good roots are roots of the sort that promote the flourishing of a plant.', "Provided that if heavies lace up at the front like normal shoes but also have an ankle strap for more support, then some spiders can live most of their lives under water in bubble webs, we know that the statement that 'good roots are roots of the sort that promote the flourishing of a plant' is incorrect.", "Whenever it is true that the claim that if if some ants live for years, then natural pearls occurring with no human assistance are extremely rare, then if the statement 'most horses have life expectancy' can be considered false, then if heavies lace up at the front like normal shoes but also have an ankle strap for more support, then some spiders can live most of their lives under water in bubble webs is false, 'mangroves thrive in saltwater environments' is true.", "If the claim that if if some ants live for years, then natural pearls occurring with no human assistance are extremely rare, then if the statement 'most horses have life expectancy' can be considered false, then if heavies lace up at the front like normal shoes but also have an ankle strap for more support, then some spiders can live most of their lives under water in bubble webs is false, then some people mistakenly believe that mangroves thrive in saltwater environments."]
|
It is rational to believe that either either skin encloses internal organs or atheism is much more compatible with a universe infinite in time and space or if some ants live for years, then natural pearls occurring with no human assistance are extremely rare. On the condition that either skin encloses internal organs or atheism is much more compatible with a universe infinite in time and space, it is definitely the case that if the statement 'most horses have life expectancy' can be considered false, then if heavies lace up at the front like normal shoes but also have an ankle strap for more support, then some spiders can live most of their lives under water in bubble webs. Assuming if heavies lace up at the front like normal shoes but also have an ankle strap for more support, then some spiders can live most of their lives under water in bubble webs, we know that good roots are roots of the sort that promote the flourishing of a plant. Provided that if heavies lace up at the front like normal shoes but also have an ankle strap for more support, then some spiders can live most of their lives under water in bubble webs, we know that the statement that 'good roots are roots of the sort that promote the flourishing of a plant' is incorrect. Whenever it is true that the claim that if if some ants live for years, then natural pearls occurring with no human assistance are extremely rare, then if the statement 'most horses have life expectancy' can be considered false, then if heavies lace up at the front like normal shoes but also have an ankle strap for more support, then some spiders can live most of their lives under water in bubble webs is false, 'mangroves thrive in saltwater environments' is true. If the claim that if if some ants live for years, then natural pearls occurring with no human assistance are extremely rare, then if the statement 'most horses have life expectancy' can be considered false, then if heavies lace up at the front like normal shoes but also have an ankle strap for more support, then some spiders can live most of their lives under water in bubble webs is false, then some people mistakenly believe that mangroves thrive in saltwater environments.
|
It is fair to say that most horses have life expectancy.
|
The statement, most horses have life expectancy, does not hold.
|
FALSE
|
Modus Tonens:
If (Not [0].), then (If [1], then [2].). [SC1-1]
Not (If [1], then [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [4] or [5].) or (If [6], then [7].).
If (Either [4] or [5].), then (If (Not [0].), then (If [1], then [2].).).
If (If [6], then [7].), then (If (Not [0].), then (If [1], then [2].).). [SC3-2]
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If (If [6], then [7].), then (If (Not [0].), then (If [1], then [2].).).).), then [8].
If (Not (If (If [6], then [7].), then (If (Not [0].), then (If [1], then [2].).).).), then (Not [8].).
Therefore, If (If [6], then [7].), then (If (Not [0].), then (If [1], then [2].).)..
[SC2-1]
Reductio Ad Absurdum:
If (If [1], then [2].), then [3].
If (If [1], then [2].), then (Not [3].).
Therefore, Not (If [1], then [2].)..
|
{0: 'Most horses have life expectancy.', 1: 'Heavies lace up at the front like normal shoes but also have an ankle strap for more support.', 2: 'Some spiders can live most of their lives under water in bubble webs.', 3: 'Good roots are roots of the sort that promote the flourishing of a plant.', 4: 'Skin encloses internal organs.', 5: 'Atheism is much more compatible with a universe infinite in time and space.', 6: 'Some ants live for years.', 7: 'Natural pearls occurring with no human assistance are extremely rare.', 8: 'Mangroves thrive in saltwater environments.'}
| 4 |
3,520 |
['If either whales have holes or some green plants utilize nitrogen gases, then infidelity is primarily a matter of the heart, and an issue of behaviour.', 'Assuming paramecium is a genus in the class of ciliates, we know that the statement that states infidelity is primarily a matter of the heart, and an issue of behaviour is false.', "The statement 'paramecium is a genus in the class of ciliates' can be considered true.", 'Either one or both of these statements are true: if stingrays eat small fish, then architecture has (part) readsides, or notable scientists argue ideas.', "So long as if stingrays eat small fish, then architecture has (part) readsides, 'if it is a common misconception that identities are operators, then either whales have holes or some green plants utilize nitrogen gases' is true.", 'On the condition that notable scientists argue ideas, it is definitely the case that if it is a common misconception that identities are operators, then either whales have holes or some green plants utilize nitrogen gases.']
|
If either whales have holes or some green plants utilize nitrogen gases, then infidelity is primarily a matter of the heart, and an issue of behaviour. Assuming paramecium is a genus in the class of ciliates, we know that the statement that states infidelity is primarily a matter of the heart, and an issue of behaviour is false. The statement 'paramecium is a genus in the class of ciliates' can be considered true. Either one or both of these statements are true: if stingrays eat small fish, then architecture has (part) readsides, or notable scientists argue ideas. So long as if stingrays eat small fish, then architecture has (part) readsides, 'if it is a common misconception that identities are operators, then either whales have holes or some green plants utilize nitrogen gases' is true. On the condition that notable scientists argue ideas, it is definitely the case that if it is a common misconception that identities are operators, then either whales have holes or some green plants utilize nitrogen gases.
|
It is the case that identities are operators.
|
It is the case that identities are operators.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then (Either [2] or [3].). [SC1-2]
If (Either [2] or [3].), then [1].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunction Elimination:
Either (If [5], then [6].) or [7].
If (If [5], then [6].), then (If (Not [0].), then (Either [2] or [3].).).
If [7], then (If (Not [0].), then (Either [2] or [3].).).
Therefore, If (Not [0].), then (Either [2] or [3].)..
[SC2-1]
Modus Ponens:
If [4], then (Not [1].).
[4]
Therefore, Not [1]..
|
{0: 'Identities are operators.', 1: 'Infidelity is primarily a matter of the heart, and an issue of behaviour.', 2: 'Whales have holes.', 3: 'Some green plants utilize nitrogen gases.', 4: 'Paramecium is a genus in the class of ciliates.', 5: 'Stingrays eat small fish.', 6: 'Architecture has (part) readsides.', 7: 'Notable scientists argue ideas.'}
| 4 |
3,249 |
['Given that if particulates are minute separate particles, then all young children handle their genitals, it can be inferred that stem cells are essentially unformed spare parts the body keeps around various organs.', 'Provided that the statement that states either if particulates are minute separate particles, then all young children handle their genitals or volatility is the average movement in any given period of time is false, we know that either color is used to distinguish different atoms or women often start wearing scarves or hats to hide their thin hair.', 'One may reasonably assume that if those that suggest if volatility is the average movement in any given period of time, then stem cells are essentially unformed spare parts the body keeps around various organs are wrong, then natural gas is primarily methane with small amount of ethane , propane , and butane .', "Given that those that suggest if volatility is the average movement in any given period of time, then stem cells are essentially unformed spare parts the body keeps around various organs are wrong, it can be inferred that the statement that 'natural gas is primarily methane with small amount of ethane , propane , and butane ' is incorrect.", 'Once we know it is not the case that if the statement that states either if particulates are minute separate particles, then all young children handle their genitals or volatility is the average movement in any given period of time is false, then the claim that either color is used to distinguish different atoms or women often start wearing scarves or hats to hide their thin hair has no merit, we also know that grandads have (part) cells.', 'If it is not the case that if the statement that states either if particulates are minute separate particles, then all young children handle their genitals or volatility is the average movement in any given period of time is false, then the claim that either color is used to distinguish different atoms or women often start wearing scarves or hats to hide their thin hair has no merit, then it is not true that grandads have (part) cells.']
|
Given that if particulates are minute separate particles, then all young children handle their genitals, it can be inferred that stem cells are essentially unformed spare parts the body keeps around various organs. Provided that the statement that states either if particulates are minute separate particles, then all young children handle their genitals or volatility is the average movement in any given period of time is false, we know that either color is used to distinguish different atoms or women often start wearing scarves or hats to hide their thin hair. One may reasonably assume that if those that suggest if volatility is the average movement in any given period of time, then stem cells are essentially unformed spare parts the body keeps around various organs are wrong, then natural gas is primarily methane with small amount of ethane , propane , and butane . Given that those that suggest if volatility is the average movement in any given period of time, then stem cells are essentially unformed spare parts the body keeps around various organs are wrong, it can be inferred that the statement that 'natural gas is primarily methane with small amount of ethane , propane , and butane ' is incorrect. Once we know it is not the case that if the statement that states either if particulates are minute separate particles, then all young children handle their genitals or volatility is the average movement in any given period of time is false, then the claim that either color is used to distinguish different atoms or women often start wearing scarves or hats to hide their thin hair has no merit, we also know that grandads have (part) cells. If it is not the case that if the statement that states either if particulates are minute separate particles, then all young children handle their genitals or volatility is the average movement in any given period of time is false, then the claim that either color is used to distinguish different atoms or women often start wearing scarves or hats to hide their thin hair has no merit, then it is not true that grandads have (part) cells.
|
stem cells are essentially unformed spare parts the body keeps around various organs.
|
Stem cells are essentially unformed spare parts the body keeps around various organs.
|
TRUE
|
Disjunction Elimination:
Either (If [1], then [2].) or [3]. [SC1-1]
If (If [1], then [2].), then [0].
If [3], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either (If [1], then [2].) or [3].).), then (Either [5] or [6].).
If (Not (Either (If [1], then [2].) or [3].).), then (Not (Either [5] or [6].).). [SC2-2]
Therefore, Either (If [1], then [2].) or [3]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (Either (If [1], then [2].) or [3].).), then (Not (Either [5] or [6].).).).), then [7].
If (Not (If (Not (Either (If [1], then [2].) or [3].).), then (Not (Either [5] or [6].).).).), then (Not [7].).
Therefore, If (Not (Either (If [1], then [2].) or [3].).), then (Not (Either [5] or [6].).)..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [3], then [0].).), then [4].
If (Not (If [3], then [0].).), then (Not [4].).
Therefore, If [3], then [0]..
|
{0: 'Stem cells are essentially unformed spare parts the body keeps around various organs.', 1: 'Particulates are minute separate particles.', 2: 'All young children handle their genitals.', 3: 'Volatility is the average movement in any given period of time.', 4: 'Natural gas is primarily methane with small amount of ethane , propane , and butane .', 5: 'Color is used to distinguish different atoms.', 6: 'Women often start wearing scarves or hats to hide their thin hair.', 7: 'Grandads have (part) cells.'}
| 4 |
3,278 |
['Once we know we know that the claim that wines vary dramatically in their alcoholic content is false, we also know that hockey is a game of tradition.', "It is rational to believe that either scientists agree that estrogen therapy lowers women's risk of heart disease after menopause or if we know that the claim that wines vary dramatically in their alcoholic content is false, then either blood cells look and work differently, but they repair and reproduce themselves in the same way or barbadian water is some of the purest in the world.", "It is not the case that scientists agree that estrogen therapy lowers women's risk of heart disease after menopause.", "At least one of two things is true: personal growth is result of several factors, or if either blood cells look and work differently, but they repair and reproduce themselves in the same way or barbadian water is some of the purest in the world, then the notion that 'hockey is a game of tradition' is untrue.", "The statement 'personal growth is result of several factors' can be considered false."]
|
Once we know we know that the claim that wines vary dramatically in their alcoholic content is false, we also know that hockey is a game of tradition. It is rational to believe that either scientists agree that estrogen therapy lowers women's risk of heart disease after menopause or if we know that the claim that wines vary dramatically in their alcoholic content is false, then either blood cells look and work differently, but they repair and reproduce themselves in the same way or barbadian water is some of the purest in the world. It is not the case that scientists agree that estrogen therapy lowers women's risk of heart disease after menopause. At least one of two things is true: personal growth is result of several factors, or if either blood cells look and work differently, but they repair and reproduce themselves in the same way or barbadian water is some of the purest in the world, then the notion that 'hockey is a game of tradition' is untrue. The statement 'personal growth is result of several factors' can be considered false.
|
It is a simple truth that wines vary dramatically in their alcoholic content.
|
Wine warms the veins, and sun heats the skin while passion destroys caution.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Hypothetical Syllogism:
If (Not [0].), then (Either [2] or [3].). [SC1-2]
If (Either [2] or [3].), then (Not [1].). [SC2-2]
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Disjunctive Syllogism:
Either [5] or (If (Not [0].), then (Either [2] or [3].).).
Not [5].
Therefore, If (Not [0].), then (Either [2] or [3].)..
[SC2-2]
Disjunctive Syllogism:
Either [4] or (If (Either [2] or [3].), then (Not [1].).).
Not [4].
Therefore, If (Either [2] or [3].), then (Not [1].)..
|
{0: 'Wines vary dramatically in their alcoholic content.', 1: 'Hockey is a game of tradition.', 2: 'Blood cells look and work differently, but they repair and reproduce themselves in the same way.', 3: 'Barbadian water is some of the purest in the world.', 4: 'Personal growth is result of several factors.', 5: "Scientists agree that estrogen therapy lowers women's risk of heart disease after menopause."}
| 4 |
3,424 |
['There is good reason to believe that either heart conditions have few different causes or if symbols are key battlefields where the Culture War is being fought, then if gear ratios are infinitely variable from full speed reverse to full speed forward, then some roots have flesh.', "The notion that 'heart conditions have few different causes' is untrue.", "So long as the claim that if symbols are key battlefields where the Culture War is being fought, then the statement that 'if gear ratios are infinitely variable from full speed reverse to full speed forward, then some roots have flesh' is incorrect has no merit, 'titan triggerfish can accelerate for short distances at a fairly surprising speeds' is true.", "Should it be the case that the claim that if symbols are key battlefields where the Culture War is being fought, then the statement that 'if gear ratios are infinitely variable from full speed reverse to full speed forward, then some roots have flesh' is incorrect has no merit, it follows that either fonts are sets of typographic characters, typically used to write documents on word processors or some mealworms have exoskeletons.", 'Provided that either fonts are sets of typographic characters, typically used to write documents on word processors or some mealworms have exoskeletons, we know that the statement that states titan triggerfish can accelerate for short distances at a fairly surprising speeds is false.']
|
There is good reason to believe that either heart conditions have few different causes or if symbols are key battlefields where the Culture War is being fought, then if gear ratios are infinitely variable from full speed reverse to full speed forward, then some roots have flesh. The notion that 'heart conditions have few different causes' is untrue. So long as the claim that if symbols are key battlefields where the Culture War is being fought, then the statement that 'if gear ratios are infinitely variable from full speed reverse to full speed forward, then some roots have flesh' is incorrect has no merit, 'titan triggerfish can accelerate for short distances at a fairly surprising speeds' is true. Should it be the case that the claim that if symbols are key battlefields where the Culture War is being fought, then the statement that 'if gear ratios are infinitely variable from full speed reverse to full speed forward, then some roots have flesh' is incorrect has no merit, it follows that either fonts are sets of typographic characters, typically used to write documents on word processors or some mealworms have exoskeletons. Provided that either fonts are sets of typographic characters, typically used to write documents on word processors or some mealworms have exoskeletons, we know that the statement that states titan triggerfish can accelerate for short distances at a fairly surprising speeds is false.
|
The claim that symbols are key battlefields where the Culture War is being fought does not reflect reality.
|
The statement that 'symbols are much more powerful when they can be touched, felt, occasionally spoken to' is incorrect.
|
Uncertain
|
Reductio Ad Absurdum:
If [0], then (If [1], then [2].). [SC1-1]
If [0], then (Not (If [1], then [2].).). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [4] or (If [0], then (If [1], then [2].).).
Not [4].
Therefore, If [0], then (If [1], then [2].)..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [0], then (Not (If [1], then [2].).).).), then [3].
If (Not (If [0], then (Not (If [1], then [2].).).).), then (Not [3].). [SC2-2]
Therefore, If [0], then (Not (If [1], then [2].).)..
[SC2-2]
Hypothetical Syllogism:
If (Not (If [0], then (Not (If [1], then [2].).).).), then (Either [5] or [6].).
If (Either [5] or [6].), then (Not [3].).
Therefore, If (Not (If [0], then (Not (If [1], then [2].).).).), then (Not [3].)..
|
{0: 'Symbols are key battlefields where the Culture War is being fought.', 1: 'Gear ratios are infinitely variable from full speed reverse to full speed forward.', 2: 'Some roots have flesh.', 3: 'Titan triggerfish can accelerate for short distances at a fairly surprising speeds.', 4: 'Heart conditions have few different causes.', 5: 'Fonts are sets of typographic characters, typically used to write documents on word processors.', 6: 'Some mealworms have exoskeletons.'}
| 4 |
3,384 |
["The statement 'most royal ferns show brown fronds' can be considered false.", 'When ungulates are native to every continent except Antarctica and Australia is true, it follows that if those that suggest if parasite drag is the drag incurred from the nonlifting portions of the aircraft, then most royal ferns show brown fronds are wrong, then colors reproduce with good saturation and without any traces of chroma noise.', 'Many people rightly believe that ungulates are native to every continent except Antarctica and Australia.', "At least one of two things is true: some amphibian skin contains glands, or if those that suggest if parasite drag is the drag incurred from the nonlifting portions of the aircraft, then most royal ferns show brown fronds are wrong, then the statement that 'colors reproduce with good saturation and without any traces of chroma noise' is incorrect.", "The notion that 'some amphibian skin contains glands' is untrue."]
|
The statement 'most royal ferns show brown fronds' can be considered false. When ungulates are native to every continent except Antarctica and Australia is true, it follows that if those that suggest if parasite drag is the drag incurred from the nonlifting portions of the aircraft, then most royal ferns show brown fronds are wrong, then colors reproduce with good saturation and without any traces of chroma noise. Many people rightly believe that ungulates are native to every continent except Antarctica and Australia. At least one of two things is true: some amphibian skin contains glands, or if those that suggest if parasite drag is the drag incurred from the nonlifting portions of the aircraft, then most royal ferns show brown fronds are wrong, then the statement that 'colors reproduce with good saturation and without any traces of chroma noise' is incorrect. The notion that 'some amphibian skin contains glands' is untrue.
|
The statement that 'parasite drag is the drag incurred from the nonlifting portions of the aircraft' is incorrect.
|
The statement that 'parasite drag is the drag incurred from the nonlifting portions of the aircraft' is incorrect.
|
TRUE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then [2]. [SC1-2]
If (Not (If [0], then [1].).), then (Not [2].). [SC2-2]
Therefore, If [0], then [1]..
[SC1-2]
Modus Ponens:
If [3], then (If (Not (If [0], then [1].).), then [2].).
[3]
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC2-2]
Disjunctive Syllogism:
Either [4] or (If (Not (If [0], then [1].).), then (Not [2].).).
Not [4].
Therefore, If (Not (If [0], then [1].).), then (Not [2].)..
|
{0: 'Parasite drag is the drag incurred from the nonlifting portions of the aircraft.', 1: 'Most royal ferns show brown fronds.', 2: 'Colors reproduce with good saturation and without any traces of chroma noise.', 3: 'Ungulates are native to every continent except Antarctica and Australia.', 4: 'Some amphibian skin contains glands.'}
| 4 |
3,395 |
['The claim that fissure is a body part is true.', 'Provided that either animals sense and react to stress just like people or marriage is a contract between husband, wife and the state, we know that if fissure is a body part, then the claim that drugs are substances that alter mood, mind or behavior is false.', 'Given that either roots grow much closer to the soil surface than is often believed or materials require for photosynthesis, it can be inferred that either animals sense and react to stress just like people or marriage is a contract between husband, wife and the state.', "Whenever it is true that green iguanas are diurnal , arboreal , and are often found near water, 'either animals sense and react to stress just like people or marriage is a contract between husband, wife and the state' is true.", 'At least one of two things is true: tea contains more caffeine than coffee by dry weight, or pricing is the root-canal of software marketing.', 'Assuming tea contains more caffeine than coffee by dry weight, we know that either roots grow much closer to the soil surface than is often believed or materials require for photosynthesis.', "Whenever it is true that pricing is the root-canal of software marketing, 'green iguanas are diurnal , arboreal , and are often found near water' is true."]
|
The claim that fissure is a body part is true. Provided that either animals sense and react to stress just like people or marriage is a contract between husband, wife and the state, we know that if fissure is a body part, then the claim that drugs are substances that alter mood, mind or behavior is false. Given that either roots grow much closer to the soil surface than is often believed or materials require for photosynthesis, it can be inferred that either animals sense and react to stress just like people or marriage is a contract between husband, wife and the state. Whenever it is true that green iguanas are diurnal , arboreal , and are often found near water, 'either animals sense and react to stress just like people or marriage is a contract between husband, wife and the state' is true. At least one of two things is true: tea contains more caffeine than coffee by dry weight, or pricing is the root-canal of software marketing. Assuming tea contains more caffeine than coffee by dry weight, we know that either roots grow much closer to the soil surface than is often believed or materials require for photosynthesis. Whenever it is true that pricing is the root-canal of software marketing, 'green iguanas are diurnal , arboreal , and are often found near water' is true.
|
The claim that drugs are substances that alter mood, mind or behavior is false.
|
The claim that drugs are substances that alter mood, mind or behavior is false.
|
TRUE
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If (Either [2] or [3].), then (If [1], then (Not [0].).).
Either [2] or [3]. [SC2-2]
Therefore, If [1], then (Not [0].)..
[SC2-2]
Disjunction Elimination:
Either (Either [4] or [5].) or [6]. [SC1-3]
If (Either [4] or [5].), then (Either [2] or [3].).
If [6], then (Either [2] or [3].).
Therefore, Either [2] or [3]..
[SC1-3]
Constructive Dilemma:
Either [7] or [8].
If [7], then (Either [4] or [5].).
If [8], then [6].
Therefore, Either (Either [4] or [5].) or [6]..
|
{0: 'Drugs are substances that alter mood, mind or behavior.', 1: 'Fissure is a body part.', 2: 'Animals sense and react to stress just like people.', 3: 'Marriage is a contract between husband, wife and the state.', 4: 'Roots grow much closer to the soil surface than is often believed.', 5: 'Materials require for photosynthesis.', 6: 'Green iguanas are diurnal , arboreal , and are often found near water.', 7: 'Tea contains more caffeine than coffee by dry weight.', 8: 'Pricing is the root-canal of software marketing.'}
| 4 |
3,054 |
['Given that we know that the claim that if the claim that lobsters are bottom-dwellers does not reflect reality, then green plants use radiation is false, it can be inferred that driftwood can become the foundation for sand dunes.', 'Given that green plants use radiation, it can be inferred that sediment can also cover the corals directly and kill it.', "So long as green plants use radiation, 'the claim that sediment can also cover the corals directly and kill it does not reflect reality' is true.", 'One may reasonably assume that if institutional violence is violence exercises on behalf or under the protection of the state, then it is not the case that driftwood can become the foundation for sand dunes.', 'The claim that institutional violence is violence exercises on behalf or under the protection of the state holds true.']
|
Given that we know that the claim that if the claim that lobsters are bottom-dwellers does not reflect reality, then green plants use radiation is false, it can be inferred that driftwood can become the foundation for sand dunes. Given that green plants use radiation, it can be inferred that sediment can also cover the corals directly and kill it. So long as green plants use radiation, 'the claim that sediment can also cover the corals directly and kill it does not reflect reality' is true. One may reasonably assume that if institutional violence is violence exercises on behalf or under the protection of the state, then it is not the case that driftwood can become the foundation for sand dunes. The claim that institutional violence is violence exercises on behalf or under the protection of the state holds true.
|
lobsters are bottom-dwellers.
|
Lobsters are bottom-dwellers.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Not [0].), then [1].).), then [3].
Not [3]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Modus Ponens:
If [4], then (Not [3].).
[4]
Therefore, Not [3]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2].
If [1], then (Not [2].).
Therefore, Not [1]..
|
{0: 'Lobsters are bottom-dwellers.', 1: 'Green plants use radiation.', 2: 'Sediment can also cover the corals directly and kill it.', 3: 'Driftwood can become the foundation for sand dunes.', 4: 'Institutional violence is violence exercises on behalf or under the protection of the state.'}
| 4 |
3,034 |
['Should it be the case that it is a common misconception that if we know that the claim that rocks are condensed layers of sediments such as sand or mud is false, then some women contribute to science, it follows that the claim that if pasteurization is a process to destroy harmful bacteria and fungi, then lines are used for traces has no merit.', 'There is good reason to believe that either some eruptions kill animals or if we know that the claim that rocks are condensed layers of sediments such as sand or mud is false, then it is not true that some women contribute to science.', 'We know that the claim that some eruptions kill animals is false.', 'Either scientific inquiry depends on systematic examination of a phenomenon or land use affects likelihood.', "Whenever it is true that scientific inquiry depends on systematic examination of a phenomenon, 'if it is a common misconception that if we know that the claim that rocks are condensed layers of sediments such as sand or mud is false, then some women contribute to science, then if pasteurization is a process to destroy harmful bacteria and fungi, then lines are used for traces' is true.", 'Assuming land use affects likelihood, we know that if it is a common misconception that if we know that the claim that rocks are condensed layers of sediments such as sand or mud is false, then some women contribute to science, then if pasteurization is a process to destroy harmful bacteria and fungi, then lines are used for traces.']
|
Should it be the case that it is a common misconception that if we know that the claim that rocks are condensed layers of sediments such as sand or mud is false, then some women contribute to science, it follows that the claim that if pasteurization is a process to destroy harmful bacteria and fungi, then lines are used for traces has no merit. There is good reason to believe that either some eruptions kill animals or if we know that the claim that rocks are condensed layers of sediments such as sand or mud is false, then it is not true that some women contribute to science. We know that the claim that some eruptions kill animals is false. Either scientific inquiry depends on systematic examination of a phenomenon or land use affects likelihood. Whenever it is true that scientific inquiry depends on systematic examination of a phenomenon, 'if it is a common misconception that if we know that the claim that rocks are condensed layers of sediments such as sand or mud is false, then some women contribute to science, then if pasteurization is a process to destroy harmful bacteria and fungi, then lines are used for traces' is true. Assuming land use affects likelihood, we know that if it is a common misconception that if we know that the claim that rocks are condensed layers of sediments such as sand or mud is false, then some women contribute to science, then if pasteurization is a process to destroy harmful bacteria and fungi, then lines are used for traces.
|
It is true that rocks are condensed layers of sediments such as sand or mud.
|
Rocks are very specific objects from the point of view of magnetism.
|
Uncertain
|
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 (If [2], then [3].). [SC1-2]
If (Not (If (Not [0].), then [1].).), then (Not (If [2], then [3].).).
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Not (If (Not [0].), then [1].).), then (If [2], then [3].).).
If [6], then (If (Not (If (Not [0].), then [1].).), then (If [2], then [3].).).
Therefore, If (Not (If (Not [0].), then [1].).), then (If [2], then [3].)..
[SC2-1]
Disjunctive Syllogism:
Either [4] or (If (Not [0].), then (Not [1].).).
Not [4].
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Rocks are condensed layers of sediments such as sand or mud.', 1: 'Some women contribute to science.', 2: 'Pasteurization is a process to destroy harmful bacteria and fungi.', 3: 'Lines are used for traces.', 4: 'Some eruptions kill animals.', 5: 'Scientific inquiry depends on systematic examination of a phenomenon.', 6: 'Land use affects likelihood.'}
| 4 |
3,271 |
["So long as some caterpillars feed on willows, 'if gurus are leaders, then shock waves compress the tissues and travel ahead and to the sides of the bullet' is true.", 'We know that either human culture is culture or gurus are leaders.', "The statement that 'human culture is culture' is incorrect.", "Whenever it is true that the claim that some caterpillars feed on willows does not correspond with reality, 'most voltage creates magnetic fields' is true.", 'It is a common misconception that most voltage creates magnetic fields.']
|
So long as some caterpillars feed on willows, 'if gurus are leaders, then shock waves compress the tissues and travel ahead and to the sides of the bullet' is true. We know that either human culture is culture or gurus are leaders. The statement that 'human culture is culture' is incorrect. Whenever it is true that the claim that some caterpillars feed on willows does not correspond with reality, 'most voltage creates magnetic fields' is true. It is a common misconception that most voltage creates magnetic fields.
|
We can assume that shock waves compress the tissues and travel ahead and to the sides of the bullet.
|
Shock wave is formed if the point source moving faster than the wave speed .
|
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] [SC2-2]
Therefore, If [1], then [0]..
[SC2-2]
Modus Tonens:
If (Not [3].), then [4].
Not [4].
Therefore, [3].
[SC2-1]
Disjunctive Syllogism:
Either [2] or [1].
Not [2].
Therefore, [1].
|
{0: 'Shock waves compress the tissues and travel ahead and to the sides of the bullet.', 1: 'Gurus are leaders.', 2: 'Human culture is culture.', 3: 'Some caterpillars feed on willows.', 4: 'Most voltage creates magnetic fields.'}
| 4 |
3,030 |
['Either one or both of these statements are true: mercury is elements, or whiskey is liquor.', "Whenever it is true that mercury is elements, 'young drivers are over-represented in alcohol related driving accidents' is true.", 'Should it be the case that the statement that states if whiskey is liquor, then young drivers are over-represented in alcohol related driving accidents is false, it follows that seals have greater blood volumes than terrestrial mammals.', 'Assuming locusts have perceptions, we know that if the statement that states if whiskey is liquor, then young drivers are over-represented in alcohol related driving accidents is false, then those that suggest seals have greater blood volumes than terrestrial mammals are wrong.', 'One may reasonably assume that if those that suggest locusts have perceptions are wrong, then gel electrophoresis is used to determine the size of the digested pieces.', "The statement that 'gel electrophoresis is used to determine the size of the digested pieces' is incorrect."]
|
Either one or both of these statements are true: mercury is elements, or whiskey is liquor. Whenever it is true that mercury is elements, 'young drivers are over-represented in alcohol related driving accidents' is true. Should it be the case that the statement that states if whiskey is liquor, then young drivers are over-represented in alcohol related driving accidents is false, it follows that seals have greater blood volumes than terrestrial mammals. Assuming locusts have perceptions, we know that if the statement that states if whiskey is liquor, then young drivers are over-represented in alcohol related driving accidents is false, then those that suggest seals have greater blood volumes than terrestrial mammals are wrong. One may reasonably assume that if those that suggest locusts have perceptions are wrong, then gel electrophoresis is used to determine the size of the digested pieces. The statement that 'gel electrophoresis is used to determine the size of the digested pieces' is incorrect.
|
It is rational to agree that young drivers are over-represented in alcohol related driving accidents.
|
The claim that young drivers are over-represented in alcohol related driving accidents does not reflect reality.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then [0].).), then [3].
If (Not (If [2], then [0].).), then (Not [3].). [SC2-2]
Therefore, If [2], then [0]..
[SC2-2]
Modus Ponens:
If [4], then (If (Not (If [2], then [0].).), then (Not [3].).).
[4] [SC2-3]
Therefore, If (Not (If [2], then [0].).), then (Not [3].)..
[SC2-3]
Modus Tonens:
If (Not [4].), then [5].
Not [5].
Therefore, [4].
|
{0: 'Young drivers are over-represented in alcohol related driving accidents.', 1: 'Mercury is elements.', 2: 'Whiskey is liquor.', 3: 'Seals have greater blood volumes than terrestrial mammals.', 4: 'Locusts have perceptions.', 5: 'Gel electrophoresis is used to determine the size of the digested pieces.'}
| 4 |
3,403 |
['It is rational to believe that either either turkeys have many natural predators, most of which prey extensively on eggs and young poults or approaches indicate patterns or those that suggest some sexual stimulation results in erections are wrong.', 'We know that at least one of two things is true: girdles can offer protection from other hazards, as well, or patients lose significant weight.', "Whenever it is true that girdles can offer protection from other hazards, as well, 'either some energy causes vaporization or those that suggest either turkeys have many natural predators, most of which prey extensively on eggs and young poults or approaches indicate patterns are wrong' is true.", 'Given that patients lose significant weight, it can be inferred that either some energy causes vaporization or those that suggest either turkeys have many natural predators, most of which prey extensively on eggs and young poults or approaches indicate patterns are wrong.', 'We know that either if heart disease is a very serious disease, there are many forms of heart disease and all are deadly, then measurement is the breaking up of a quantum of energy into equal units or nematodes are slender, worm-like animals that live in soil, water, and plant tissues.', "So long as if heart disease is a very serious disease, there are many forms of heart disease and all are deadly, then measurement is the breaking up of a quantum of energy into equal units, 'the claim that some energy causes vaporization has no merit' is true.", 'Given that nematodes are slender, worm-like animals that live in soil, water, and plant tissues, it can be inferred that the claim that some energy causes vaporization has no merit.']
|
It is rational to believe that either either turkeys have many natural predators, most of which prey extensively on eggs and young poults or approaches indicate patterns or those that suggest some sexual stimulation results in erections are wrong. We know that at least one of two things is true: girdles can offer protection from other hazards, as well, or patients lose significant weight. Whenever it is true that girdles can offer protection from other hazards, as well, 'either some energy causes vaporization or those that suggest either turkeys have many natural predators, most of which prey extensively on eggs and young poults or approaches indicate patterns are wrong' is true. Given that patients lose significant weight, it can be inferred that either some energy causes vaporization or those that suggest either turkeys have many natural predators, most of which prey extensively on eggs and young poults or approaches indicate patterns are wrong. We know that either if heart disease is a very serious disease, there are many forms of heart disease and all are deadly, then measurement is the breaking up of a quantum of energy into equal units or nematodes are slender, worm-like animals that live in soil, water, and plant tissues. So long as if heart disease is a very serious disease, there are many forms of heart disease and all are deadly, then measurement is the breaking up of a quantum of energy into equal units, 'the claim that some energy causes vaporization has no merit' is true. Given that nematodes are slender, worm-like animals that live in soil, water, and plant tissues, it can be inferred that the claim that some energy causes vaporization has no merit.
|
Those that suggest some sexual stimulation results in erections are wrong.
|
The claim that some sexual stimulation results in erections holds true.
|
FALSE
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or (Not [0].).
Not (Either [1] or [2].). [SC2-1]
Therefore, Not [0]..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (Not (Either [1] or [2].).). [SC1-2]
Not [3]. [SC2-2]
Therefore, Not (Either [1] or [2].)..
[SC1-2]
Disjunction Elimination:
Either [7] or [8].
If [7], then (Either [3] or (Not (Either [1] or [2].).).).
If [8], then (Either [3] or (Not (Either [1] or [2].).).).
Therefore, Either [3] or (Not (Either [1] or [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: 'Some sexual stimulation results in erections.', 1: 'Turkeys have many natural predators, most of which prey extensively on eggs and young poults.', 2: 'Approaches indicate patterns.', 3: 'Some energy causes vaporization.', 4: 'Heart disease is a very serious disease, there are many forms of heart disease and all are deadly.', 5: 'Measurement is the breaking up of a quantum of energy into equal units.', 6: 'Nematodes are slender, worm-like animals that live in soil, water, and plant tissues.', 7: 'Girdles can offer protection from other hazards, as well.', 8: 'Patients lose significant weight.'}
| 4 |
3,757 |
['Provided that most people have a strong visceral reaction to the mere thought of same-gender sexual intimacy, we know that some dorsal spines penetrate skin.', 'Given that other air pollutants have impact, it can be inferred that if the statement, most people have a strong visceral reaction to the mere thought of same-gender sexual intimacy, does not hold, then either important factors influence development or conflict can arise when one person digs in their heals and resists.', 'The statement that states other air pollutants have impact is right.', 'When either important factors influence development or conflict can arise when one person digs in their heals and resists is true, it follows that a seedpod is fruit.', "The statement that 'a seedpod is fruit' is incorrect."]
|
Provided that most people have a strong visceral reaction to the mere thought of same-gender sexual intimacy, we know that some dorsal spines penetrate skin. Given that other air pollutants have impact, it can be inferred that if the statement, most people have a strong visceral reaction to the mere thought of same-gender sexual intimacy, does not hold, then either important factors influence development or conflict can arise when one person digs in their heals and resists. The statement that states other air pollutants have impact is right. When either important factors influence development or conflict can arise when one person digs in their heals and resists is true, it follows that a seedpod is fruit. The statement that 'a seedpod is fruit' is incorrect.
|
It is rational to agree that some dorsal spines penetrate skin.
|
It is rational to agree that some dorsal spines penetrate skin.
|
TRUE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not [1].), then (Either [2] or [3].). [SC1-2]
Not (Either [2] or [3].). [SC2-2]
Therefore, [1].
[SC1-2]
Modus Ponens:
If [4], then (If (Not [1].), then (Either [2] or [3].).).
[4]
Therefore, If (Not [1].), then (Either [2] or [3].)..
[SC2-2]
Modus Tonens:
If (Either [2] or [3].), then [5].
Not [5].
Therefore, Not (Either [2] or [3].)..
|
{0: 'Some dorsal spines penetrate skin.', 1: 'Most people have a strong visceral reaction to the mere thought of same-gender sexual intimacy.', 2: 'Important factors influence development.', 3: 'Conflict can arise when one person digs in their heals and resists.', 4: 'Other air pollutants have impact.', 5: 'A seedpod is fruit.'}
| 4 |
3,975 |
['We know that either striped skunks are the most abundant of the four species or some seizures involve several thousand animals.', 'We know that the claim that title insurance is the way of making certain is false.', 'Provided that some birds have wing tips, we know that title insurance is the way of making certain.', 'We know that at least one of two things is true: sharp points lacerate cheeks and tongue, or language is related to identity, culture, and memory.', 'Given that sharp points lacerate cheeks and tongue, it can be inferred that if striped skunks are the most abundant of the four species, then some birds have wing tips.', "So long as language is related to identity, culture, and memory, 'if striped skunks are the most abundant of the four species, then some birds have wing tips' is true."]
|
We know that either striped skunks are the most abundant of the four species or some seizures involve several thousand animals. We know that the claim that title insurance is the way of making certain is false. Provided that some birds have wing tips, we know that title insurance is the way of making certain. We know that at least one of two things is true: sharp points lacerate cheeks and tongue, or language is related to identity, culture, and memory. Given that sharp points lacerate cheeks and tongue, it can be inferred that if striped skunks are the most abundant of the four species, then some birds have wing tips. So long as language is related to identity, culture, and memory, 'if striped skunks are the most abundant of the four species, then some birds have wing tips' is true.
|
We can assume that some seizures involve several thousand animals.
|
Most seizures involve, in addition to the head lift or tilt, twitching of the muscles and eyes.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If [1], then [2]. [SC1-2]
Not [2].
Therefore, Not [1]..
[SC1-2]
Hypothetical Syllogism:
If [1], then [3]. [SC1-3]
If [3], then [2].
Therefore, If [1], then [2]..
[SC1-3]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [1], then [3].).
If [5], then (If [1], then [3].).
Therefore, If [1], then [3]..
|
{0: 'Some seizures involve several thousand animals.', 1: 'Striped skunks are the most abundant of the four species.', 2: 'Title insurance is the way of making certain.', 3: 'Some birds have wing tips.', 4: 'Sharp points lacerate cheeks and tongue.', 5: 'Language is related to identity, culture, and memory.'}
| 4 |
3,990 |
["Either bluster is confusion or if the statement that 'insects are an important part of the plant and animal life in wetlands' is incorrect, then some allergic reaction causes nausea.", 'We know that the claim that bluster is confusion is false.', 'We know that the claim that honey comes in a variety of forms including liquid, whipped and comb is false.', 'Either facades are fronts or some beans have only one or two seeds, and some beans have as many as nine or ten beans.', "Assuming facades are fronts, we know that either honey comes in a variety of forms including liquid, whipped and comb or the notion that 'some allergic reaction causes nausea' is untrue.", "When some beans have only one or two seeds, and some beans have as many as nine or ten beans is true, it follows that either honey comes in a variety of forms including liquid, whipped and comb or the notion that 'some allergic reaction causes nausea' is untrue."]
|
Either bluster is confusion or if the statement that 'insects are an important part of the plant and animal life in wetlands' is incorrect, then some allergic reaction causes nausea. We know that the claim that bluster is confusion is false. We know that the claim that honey comes in a variety of forms including liquid, whipped and comb is false. Either facades are fronts or some beans have only one or two seeds, and some beans have as many as nine or ten beans. Assuming facades are fronts, we know that either honey comes in a variety of forms including liquid, whipped and comb or the notion that 'some allergic reaction causes nausea' is untrue. When some beans have only one or two seeds, and some beans have as many as nine or ten beans is true, it follows that either honey comes in a variety of forms including liquid, whipped and comb or the notion that 'some allergic reaction causes nausea' is untrue.
|
The idea that insects are an important part of the plant and animal life in wetlands is true.
|
The idea that insects are an important part of the plant and animal life in wetlands is true.
|
TRUE
|
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]
Disjunctive Syllogism:
Either [3] or (Not [1].). [SC1-2]
Not [3].
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Either [3] or (Not [1].).).
If [5], then (Either [3] or (Not [1].).).
Therefore, Either [3] or (Not [1].)..
|
{0: 'Insects are an important part of the plant and animal life in wetlands.', 1: 'Some allergic reaction causes nausea.', 2: 'Bluster is confusion.', 3: 'Honey comes in a variety of forms including liquid, whipped and comb.', 4: 'Facades are fronts.', 5: 'Some beans have only one or two seeds, and some beans have as many as nine or ten beans.'}
| 4 |
3,457 |
["The statement 'unions represent workers' can be considered true.", 'There is good reason to believe that either telomere shortening is believed to play a role in aging or if the statement, if unions represent workers, then breast milk contains the perfect blend of nutrients, does not hold, then ingrown toenails can become inflamed or infected.', 'The statement, telomere shortening is believed to play a role in aging, does not hold.', 'At least one of two things is true: rubber cement is also extremely flammable, or the claim that ingrown toenails can become inflamed or infected is false.', 'Those that suggest rubber cement is also extremely flammable are wrong.']
|
The statement 'unions represent workers' can be considered true. There is good reason to believe that either telomere shortening is believed to play a role in aging or if the statement, if unions represent workers, then breast milk contains the perfect blend of nutrients, does not hold, then ingrown toenails can become inflamed or infected. The statement, telomere shortening is believed to play a role in aging, does not hold. At least one of two things is true: rubber cement is also extremely flammable, or the claim that ingrown toenails can become inflamed or infected is false. Those that suggest rubber cement is also extremely flammable are wrong.
|
The statement 'breast milk contains the perfect blend of nutrients' can be considered true.
|
It is a common misconception that breast milk contains the perfect blend of nutrients.
|
FALSE
|
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]. [SC2-2]
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]..
[SC2-2]
Disjunctive Syllogism:
Either [4] or (Not [2].).
Not [4].
Therefore, Not [2]..
|
{0: 'Breast milk contains the perfect blend of nutrients.', 1: 'Unions represent workers.', 2: 'Ingrown toenails can become inflamed or infected.', 3: 'Telomere shortening is believed to play a role in aging.', 4: 'Rubber cement is also extremely flammable.'}
| 4 |
3,362 |
["Provided that we know that the claim that some native trees bear their pollen early and some late is false, we know that the statement that 'blood can pool if it weakens or leaks, causing heart failure and thousands of deaths each year' is incorrect.", 'The claim that pendants can come in various shapes such as hearts, bottles, balls, saber teeth, and chili peppers has no merit.', 'There is good reason to believe that either some babies have developmental problems or if the claim that if we know that the claim that some native trees bear their pollen early and some late is false, then blood can pool if it weakens or leaks, causing heart failure and thousands of deaths each year does not reflect reality, then pendants can come in various shapes such as hearts, bottles, balls, saber teeth, and chili peppers.', 'We know that at least one of two things is true: insecurities are emotion, or it is a common misconception that some babies have developmental problems.', 'The claim that insecurities are emotion is false.']
|
Provided that we know that the claim that some native trees bear their pollen early and some late is false, we know that the statement that 'blood can pool if it weakens or leaks, causing heart failure and thousands of deaths each year' is incorrect. The claim that pendants can come in various shapes such as hearts, bottles, balls, saber teeth, and chili peppers has no merit. There is good reason to believe that either some babies have developmental problems or if the claim that if we know that the claim that some native trees bear their pollen early and some late is false, then blood can pool if it weakens or leaks, causing heart failure and thousands of deaths each year does not reflect reality, then pendants can come in various shapes such as hearts, bottles, balls, saber teeth, and chili peppers. We know that at least one of two things is true: insecurities are emotion, or it is a common misconception that some babies have developmental problems. The claim that insecurities are emotion is false.
|
It is true that some native trees bear their pollen early and some late.
|
It is true that some native trees bear their pollen early and some late.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (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]
Disjunctive Syllogism:
Either [3] or (If (Not (If (Not [0].), then [1].).), then [2].).
Not [3]. [SC2-3]
Therefore, If (Not (If (Not [0].), then [1].).), then [2]..
[SC2-3]
Disjunctive Syllogism:
Either [4] or (Not [3].).
Not [4].
Therefore, Not [3]..
|
{0: 'Some native trees bear their pollen early and some late.', 1: 'Blood can pool if it weakens or leaks, causing heart failure and thousands of deaths each year.', 2: 'Pendants can come in various shapes such as hearts, bottles, balls, saber teeth, and chili peppers.', 3: 'Some babies have developmental problems.', 4: 'Insecurities are emotion.'}
| 4 |
3,860 |
['The statement that states either vesicles are membrane structures that enclose an internal aqueous space or revenue is a source of income is false.', 'Given that seals have special noses that help keep water out, it can be inferred that either either vesicles are membrane structures that enclose an internal aqueous space or revenue is a source of income or if some hatchling freckled pythons are ferociously nippy for the first few months of their life, then law addresses the legal controls of public authorities and the rights of citizens.', 'Given that either ants consume sweet liquids or most women can wear medium sized earrings, it can be inferred that either either vesicles are membrane structures that enclose an internal aqueous space or revenue is a source of income or if some hatchling freckled pythons are ferociously nippy for the first few months of their life, then law addresses the legal controls of public authorities and the rights of citizens.', 'The claim that many species are able to freely hybridize, further increasing variability and speciation does not correspond with reality.', 'When the claim that if it is not the case that either seals have special noses that help keep water out or either ants consume sweet liquids or most women can wear medium sized earrings, then many species are able to freely hybridize, further increasing variability and speciation does not correspond with reality is true, it follows that if a snap ring is a ring, then human beings act out of earthly desire, fear and anger.', 'It is not true that if a snap ring is a ring, then human beings act out of earthly desire, fear and anger.']
|
The statement that states either vesicles are membrane structures that enclose an internal aqueous space or revenue is a source of income is false. Given that seals have special noses that help keep water out, it can be inferred that either either vesicles are membrane structures that enclose an internal aqueous space or revenue is a source of income or if some hatchling freckled pythons are ferociously nippy for the first few months of their life, then law addresses the legal controls of public authorities and the rights of citizens. Given that either ants consume sweet liquids or most women can wear medium sized earrings, it can be inferred that either either vesicles are membrane structures that enclose an internal aqueous space or revenue is a source of income or if some hatchling freckled pythons are ferociously nippy for the first few months of their life, then law addresses the legal controls of public authorities and the rights of citizens. The claim that many species are able to freely hybridize, further increasing variability and speciation does not correspond with reality. When the claim that if it is not the case that either seals have special noses that help keep water out or either ants consume sweet liquids or most women can wear medium sized earrings, then many species are able to freely hybridize, further increasing variability and speciation does not correspond with reality is true, it follows that if a snap ring is a ring, then human beings act out of earthly desire, fear and anger. It is not true that if a snap ring is a ring, then human beings act out of earthly desire, fear and anger.
|
Provided that some hatchling freckled pythons are ferociously nippy for the first few months of their life, we know that law addresses the legal controls of public authorities and the rights of citizens
|
The statement that 'if some hatchling freckled pythons are ferociously nippy for the first few months of their life, then law addresses the legal controls of public authorities and the rights of citizens' is incorrect.
|
FALSE
|
Disjunctive Syllogism:
Either (Either [2] or [3].) or (If [0], then [1].). [SC1-1]
Not (Either [2] or [3].).
Therefore, If [0], then [1]..
[SC1-1]
Disjunction Elimination:
Either [4] or (Either [5] or [6].). [SC1-2]
If [4], then (Either (Either [2] or [3].) or (If [0], then [1].).).
If (Either [5] or [6].), then (Either (Either [2] or [3].) or (If [0], then [1].).).
Therefore, Either (Either [2] or [3].) or (If [0], then [1].)..
[SC1-2]
Modus Tonens:
If (Not (Either [4] or (Either [5] or [6].).).), then [7]. [SC1-3]
Not [7].
Therefore, Either [4] or (Either [5] or [6].)..
[SC1-3]
Modus Tonens:
If (Not (If (Not (Either [4] or (Either [5] or [6].).).), then [7].).), then (If [8], then [9].).
Not (If [8], then [9].).
Therefore, If (Not (Either [4] or (Either [5] or [6].).).), then [7]..
|
{0: 'Some hatchling freckled pythons are ferociously nippy for the first few months of their life.', 1: 'Law addresses the legal controls of public authorities and the rights of citizens.', 2: 'Vesicles are membrane structures that enclose an internal aqueous space.', 3: 'Revenue is a source of income.', 4: 'Seals have special noses that help keep water out.', 5: 'Ants consume sweet liquids.', 6: 'Most women can wear medium sized earrings.', 7: 'Many species are able to freely hybridize, further increasing variability and speciation.', 8: 'A snap ring is a ring.', 9: 'Human beings act out of earthly desire, fear and anger.'}
| 4 |
3,483 |
["Whenever it is true that it is not true that most women can achieve orgasm from clitoral stimulation, by finger, tongue, or vibrator, 'gladiolas come in a variety of colors' is true.", 'It is the case that some individuals have a greater risk than others for developing diabetes.', 'When the claim that if some individuals have a greater risk than others for developing diabetes, then if it is not true that most women can achieve orgasm from clitoral stimulation, by finger, tongue, or vibrator, then those that suggest gladiolas come in a variety of colors are wrong does not reflect reality is true, it follows that either auricular medicine uses medicine or homeopathics as an aid in diagnosing auricular points or bald eagles use sharp claws.', "We know that either most sharks possess bodies or if the claim that if some individuals have a greater risk than others for developing diabetes, then if it is not true that most women can achieve orgasm from clitoral stimulation, by finger, tongue, or vibrator, then those that suggest gladiolas come in a variety of colors are wrong does not reflect reality, then the statement that 'either auricular medicine uses medicine or homeopathics as an aid in diagnosing auricular points or bald eagles use sharp claws' is incorrect.", 'Some people mistakenly believe that most sharks possess bodies.']
|
Whenever it is true that it is not true that most women can achieve orgasm from clitoral stimulation, by finger, tongue, or vibrator, 'gladiolas come in a variety of colors' is true. It is the case that some individuals have a greater risk than others for developing diabetes. When the claim that if some individuals have a greater risk than others for developing diabetes, then if it is not true that most women can achieve orgasm from clitoral stimulation, by finger, tongue, or vibrator, then those that suggest gladiolas come in a variety of colors are wrong does not reflect reality is true, it follows that either auricular medicine uses medicine or homeopathics as an aid in diagnosing auricular points or bald eagles use sharp claws. We know that either most sharks possess bodies or if the claim that if some individuals have a greater risk than others for developing diabetes, then if it is not true that most women can achieve orgasm from clitoral stimulation, by finger, tongue, or vibrator, then those that suggest gladiolas come in a variety of colors are wrong does not reflect reality, then the statement that 'either auricular medicine uses medicine or homeopathics as an aid in diagnosing auricular points or bald eagles use sharp claws' is incorrect. Some people mistakenly believe that most sharks possess bodies.
|
The claim that most women can achieve orgasm from clitoral stimulation, by finger, tongue, or vibrator is true.
|
The claim that most women can achieve orgasm from clitoral stimulation, by finger, tongue, or vibrator has no merit.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [2], then (If (Not [0].), then (Not [1].).). [SC1-2]
[2]
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then (Either [3] or [4].).
If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then (Not (Either [3] or [4].).). [SC2-3]
Therefore, If [2], then (If (Not [0].), then (Not [1].).)..
[SC2-3]
Disjunctive Syllogism:
Either [5] or (If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then (Not (Either [3] or [4].).).).
Not [5].
Therefore, If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then (Not (Either [3] or [4].).)..
|
{0: 'Most women can achieve orgasm from clitoral stimulation, by finger, tongue, or vibrator.', 1: 'Gladiolas come in a variety of colors.', 2: 'Some individuals have a greater risk than others for developing diabetes.', 3: 'Auricular medicine uses medicine or homeopathics as an aid in diagnosing auricular points.', 4: 'Bald eagles use sharp claws.', 5: 'Most sharks possess bodies.'}
| 4 |
3,580 |
['There is good reason to believe that either either pedophiles tend to be motivated by power, control, and hostility rather than by sexual desire or most woodpeckers nest in holes or bats are rabid and likely to attack people.', 'One may reasonably assume that if bats are rabid and likely to attack people, then internet access is a commodity, and barriers to switching are minimal.', 'On the condition that trends receive attention, it is definitely the case that if either pedophiles tend to be motivated by power, control, and hostility rather than by sexual desire or most woodpeckers nest in holes, then internet access is a commodity, and barriers to switching are minimal.', 'The claim that tidal mud flats, sandbars, and oyster bars commonly occur in salt marshes does not reflect reality.', 'If it is not true that trends receive attention, then medicated baths are also available for pets with specific skin disorders.', 'When medicated baths are also available for pets with specific skin disorders is true, it follows that tidal mud flats, sandbars, and oyster bars commonly occur in salt marshes.']
|
There is good reason to believe that either either pedophiles tend to be motivated by power, control, and hostility rather than by sexual desire or most woodpeckers nest in holes or bats are rabid and likely to attack people. One may reasonably assume that if bats are rabid and likely to attack people, then internet access is a commodity, and barriers to switching are minimal. On the condition that trends receive attention, it is definitely the case that if either pedophiles tend to be motivated by power, control, and hostility rather than by sexual desire or most woodpeckers nest in holes, then internet access is a commodity, and barriers to switching are minimal. The claim that tidal mud flats, sandbars, and oyster bars commonly occur in salt marshes does not reflect reality. If it is not true that trends receive attention, then medicated baths are also available for pets with specific skin disorders. When medicated baths are also available for pets with specific skin disorders is true, it follows that tidal mud flats, sandbars, and oyster bars commonly occur in salt marshes.
|
It is the case that internet access is a commodity, and barriers to switching are minimal.
|
It is the case that internet access is a commodity, and barriers to switching are minimal.
|
TRUE
|
Disjunction Elimination:
Either (Either [1] or [2].) or [3].
If (Either [1] or [2].), then [0]. [SC2-1]
If [3], then [0].
Therefore, [0].
[SC2-1]
Modus Ponens:
If [4], then (If (Either [1] or [2].), then [0].).
[4] [SC2-2]
Therefore, If (Either [1] or [2].), then [0]..
[SC2-2]
Modus Tonens:
If (Not [4].), then [5]. [SC1-3]
Not [5].
Therefore, [4].
[SC1-3]
Hypothetical Syllogism:
If (Not [4].), then [6].
If [6], then [5].
Therefore, If (Not [4].), then [5]..
|
{0: 'Internet access is a commodity, and barriers to switching are minimal.', 1: 'Pedophiles tend to be motivated by power, control, and hostility rather than by sexual desire.', 2: 'Most woodpeckers nest in holes.', 3: 'Bats are rabid and likely to attack people.', 4: 'Trends receive attention.', 5: 'Tidal mud flats, sandbars, and oyster bars commonly occur in salt marshes.', 6: 'Medicated baths are also available for pets with specific skin disorders.'}
| 4 |
3,986 |
['Once we know the claim that if if corticosteroids are potent and highly effective, especially when applied after bathing, then deforestation increases surface run-off, causing river levels to rise more quickly, then cycads are succulents basically and many can be grown similarly to how one grows most succulents is false, we also know that neutrophils infiltrate between and into epithelial cells as well as the lamina propria.', 'Either crabs respond to lunar phases or if corticosteroids are potent and highly effective, especially when applied after bathing, then deforestation increases surface run-off, causing river levels to rise more quickly.', 'The claim that crabs respond to lunar phases does not reflect reality.', 'Once we know some individuals are more susceptible to noise-induced hearing loss than others, we also know that the claim that neutrophils infiltrate between and into epithelial cells as well as the lamina propria does not correspond with reality.', 'We can assume that some individuals are more susceptible to noise-induced hearing loss than others.']
|
Once we know the claim that if if corticosteroids are potent and highly effective, especially when applied after bathing, then deforestation increases surface run-off, causing river levels to rise more quickly, then cycads are succulents basically and many can be grown similarly to how one grows most succulents is false, we also know that neutrophils infiltrate between and into epithelial cells as well as the lamina propria. Either crabs respond to lunar phases or if corticosteroids are potent and highly effective, especially when applied after bathing, then deforestation increases surface run-off, causing river levels to rise more quickly. The claim that crabs respond to lunar phases does not reflect reality. Once we know some individuals are more susceptible to noise-induced hearing loss than others, we also know that the claim that neutrophils infiltrate between and into epithelial cells as well as the lamina propria does not correspond with reality. We can assume that some individuals are more susceptible to noise-induced hearing loss than others.
|
The statement that states cycads are succulents basically and many can be grown similarly to how one grows most succulents is right.
|
The statement that states cycads are succulents basically and many can be grown similarly to how one grows most succulents is right.
|
TRUE
|
Modus Ponens:
If (If [1], then [2].), then [0]. [SC1-1]
If [1], then [2]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (If [1], then [2].), then [0].).), then [4].
Not [4]. [SC2-2]
Therefore, If (If [1], then [2].), then [0]..
[SC2-2]
Modus Ponens:
If [5], then (Not [4].).
[5]
Therefore, Not [4]..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (If [1], then [2].).
Not [3].
Therefore, If [1], then [2]..
|
{0: 'Cycads are succulents basically and many can be grown similarly to how one grows most succulents.', 1: 'Corticosteroids are potent and highly effective, especially when applied after bathing.', 2: 'Deforestation increases surface run-off, causing river levels to rise more quickly.', 3: 'Crabs respond to lunar phases.', 4: 'Neutrophils infiltrate between and into epithelial cells as well as the lamina propria.', 5: 'Some individuals are more susceptible to noise-induced hearing loss than others.'}
| 4 |
3,688 |
['Assuming either higher concentrations tell cancer cells to kill themselves or chlorites are made by reacting chlorous acid with a base, we know that if belts have (part) sections, then centipedes live in soil.', 'Either one or both of these statements are true: higher concentrations tell cancer cells to kill themselves, or chlorites are made by reacting chlorous acid with a base.', 'We know that at least one of two things is true: alcohol is helpful as a reducing solvent for flurorescents, or belts have (part) sections.', 'One may reasonably assume that if alcohol is helpful as a reducing solvent for flurorescents, then sises have (part) material bodies.', 'If alcohol is helpful as a reducing solvent for flurorescents, then those that suggest sises have (part) material bodies are wrong.']
|
Assuming either higher concentrations tell cancer cells to kill themselves or chlorites are made by reacting chlorous acid with a base, we know that if belts have (part) sections, then centipedes live in soil. Either one or both of these statements are true: higher concentrations tell cancer cells to kill themselves, or chlorites are made by reacting chlorous acid with a base. We know that at least one of two things is true: alcohol is helpful as a reducing solvent for flurorescents, or belts have (part) sections. One may reasonably assume that if alcohol is helpful as a reducing solvent for flurorescents, then sises have (part) material bodies. If alcohol is helpful as a reducing solvent for flurorescents, then those that suggest sises have (part) material bodies are wrong.
|
We can assume that centipedes live in soil.
|
Centipedes use long hind legs.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If (Either [3] or [4].), then (If [1], then [0].).
Either [3] or [4].
Therefore, If [1], then [0]..
[SC2-1]
Disjunctive Syllogism:
Either [2] or [1].
Not [2]. [SC2-2]
Therefore, [1].
[SC2-2]
Reductio Ad Absurdum:
If [2], then [5].
If [2], then (Not [5].).
Therefore, Not [2]..
|
{0: 'Centipedes live in soil.', 1: 'Belts have (part) sections.', 2: 'Alcohol is helpful as a reducing solvent for flurorescents.', 3: 'Higher concentrations tell cancer cells to kill themselves.', 4: 'Chlorites are made by reacting chlorous acid with a base.', 5: 'Sises have (part) material bodies.'}
| 4 |
3,864 |
['It is rational to believe that either some chemical compounds accumulate in tissue or if either international migration can have considerable effects upon school systems or development has results, then either population genomics reveal recent speciation and rapid evolutionary adaptation in polar bears or salt marshes are important wetland habitats for many kinds of fish and wildlife.', "The notion that 'some chemical compounds accumulate in tissue' is untrue.", 'Either skinks are different from other lizards or native plants provide benefits.', "So long as native plants provide benefits, 'if either international migration can have considerable effects upon school systems or development has results, then the statement that 'either population genomics reveal recent speciation and rapid evolutionary adaptation in polar bears or salt marshes are important wetland habitats for many kinds of fish and wildlife' is incorrect' is true.", 'It is rational to believe that either authentication is the process of establishing the validity of the user attempting to gain access or xerophytes are categorized into several groups according to their drought resisting power.', "When authentication is the process of establishing the validity of the user attempting to gain access is true, it follows that if skinks are different from other lizards , then if either international migration can have considerable effects upon school systems or development has results, then the statement that 'either population genomics reveal recent speciation and rapid evolutionary adaptation in polar bears or salt marshes are important wetland habitats for many kinds of fish and wildlife' is incorrect.", "If xerophytes are categorized into several groups according to their drought resisting power, then if skinks are different from other lizards , then if either international migration can have considerable effects upon school systems or development has results, then the statement that 'either population genomics reveal recent speciation and rapid evolutionary adaptation in polar bears or salt marshes are important wetland habitats for many kinds of fish and wildlife' is incorrect."]
|
It is rational to believe that either some chemical compounds accumulate in tissue or if either international migration can have considerable effects upon school systems or development has results, then either population genomics reveal recent speciation and rapid evolutionary adaptation in polar bears or salt marshes are important wetland habitats for many kinds of fish and wildlife. The notion that 'some chemical compounds accumulate in tissue' is untrue. Either skinks are different from other lizards or native plants provide benefits. So long as native plants provide benefits, 'if either international migration can have considerable effects upon school systems or development has results, then the statement that 'either population genomics reveal recent speciation and rapid evolutionary adaptation in polar bears or salt marshes are important wetland habitats for many kinds of fish and wildlife' is incorrect' is true. It is rational to believe that either authentication is the process of establishing the validity of the user attempting to gain access or xerophytes are categorized into several groups according to their drought resisting power. When authentication is the process of establishing the validity of the user attempting to gain access is true, it follows that if skinks are different from other lizards , then if either international migration can have considerable effects upon school systems or development has results, then the statement that 'either population genomics reveal recent speciation and rapid evolutionary adaptation in polar bears or salt marshes are important wetland habitats for many kinds of fish and wildlife' is incorrect. If xerophytes are categorized into several groups according to their drought resisting power, then if skinks are different from other lizards , then if either international migration can have considerable effects upon school systems or development has results, then the statement that 'either population genomics reveal recent speciation and rapid evolutionary adaptation in polar bears or salt marshes are important wetland habitats for many kinds of fish and wildlife' is incorrect.
|
Some people mistakenly believe that either international migration can have considerable effects upon school systems or development has results.
|
There is good reason to believe that either international migration can have considerable effects upon school systems or development has results.
|
FALSE
|
Reductio Ad Absurdum:
If (Either [0] or [1].), then (Either [2] or [3].). [SC1-1]
If (Either [0] or [1].), then (Not (Either [2] or [3].).). [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Disjunctive Syllogism:
Either [6] or (If (Either [0] or [1].), then (Either [2] or [3].).).
Not [6].
Therefore, If (Either [0] or [1].), then (Either [2] or [3].)..
[SC2-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Either [0] or [1].), then (Not (Either [2] or [3].).).). [SC2-2]
If [5], then (If (Either [0] or [1].), then (Not (Either [2] or [3].).).).
Therefore, If (Either [0] or [1].), then (Not (Either [2] or [3].).)..
[SC2-2]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If [4], then (If (Either [0] or [1].), then (Not (Either [2] or [3].).).).).
If [8], then (If [4], then (If (Either [0] or [1].), then (Not (Either [2] or [3].).).).).
Therefore, If [4], then (If (Either [0] or [1].), then (Not (Either [2] or [3].).).)..
|
{0: 'International migration can have considerable effects upon school systems.', 1: 'Development has results.', 2: 'Population genomics reveal recent speciation and rapid evolutionary adaptation in polar bears.', 3: 'Salt marshes are important wetland habitats for many kinds of fish and wildlife.', 4: 'Skinks are different from other lizards .', 5: 'Native plants provide benefits.', 6: 'Some chemical compounds accumulate in tissue.', 7: 'Authentication is the process of establishing the validity of the user attempting to gain access.', 8: 'Xerophytes are categorized into several groups according to their drought resisting power.'}
| 4 |
3,927 |
['It is fair to say that open sources are software.', 'Provided that cruise missiles exploit information age technologies to put a bomb on target, we know that some children have a fear of being blamed for problems.', 'On the condition that cruise missiles exploit information age technologies to put a bomb on target, it is definitely the case that it is a common misconception that some children have a fear of being blamed for problems.', "Whenever it is true that open sources are software, 'either silt is a flour fine powder of ground rock or ghanaian festivals are well worth seeing with drumming, dancing and feasting' is true.", "So long as either silt is a flour fine powder of ground rock or ghanaian festivals are well worth seeing with drumming, dancing and feasting, 'either cruise missiles exploit information age technologies to put a bomb on target or if torques are what create spin, and repeated torques are what created rapid rotation, then nursing is a relational discipline' is true."]
|
It is fair to say that open sources are software. Provided that cruise missiles exploit information age technologies to put a bomb on target, we know that some children have a fear of being blamed for problems. On the condition that cruise missiles exploit information age technologies to put a bomb on target, it is definitely the case that it is a common misconception that some children have a fear of being blamed for problems. Whenever it is true that open sources are software, 'either silt is a flour fine powder of ground rock or ghanaian festivals are well worth seeing with drumming, dancing and feasting' is true. So long as either silt is a flour fine powder of ground rock or ghanaian festivals are well worth seeing with drumming, dancing and feasting, 'either cruise missiles exploit information age technologies to put a bomb on target or if torques are what create spin, and repeated torques are what created rapid rotation, then nursing is a relational discipline' is true.
|
Should it be the case that torques are what create spin, and repeated torques are what created rapid rotation, it follows that nursing is a relational discipline.
|
Some people mistakenly believe that if torques are what create spin, and repeated torques are what created rapid rotation, then nursing is a relational discipline.
|
FALSE
|
Disjunctive Syllogism:
Either [2] or (If [0], then [1].). [SC1-1]
Not [2]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Modus Ponens:
If [4], then (Either [2] or (If [0], then [1].).). [SC1-2]
[4]
Therefore, Either [2] or (If [0], then [1].)..
[SC1-2]
Hypothetical Syllogism:
If [4], then (Either [5] or [6].).
If (Either [5] or [6].), then (Either [2] or (If [0], then [1].).).
Therefore, If [4], then (Either [2] or (If [0], then [1].).)..
[SC2-1]
Reductio Ad Absurdum:
If [2], then [3].
If [2], then (Not [3].).
Therefore, Not [2]..
|
{0: 'Torques are what create spin, and repeated torques are what created rapid rotation.', 1: 'Nursing is a relational discipline.', 2: 'Cruise missiles exploit information age technologies to put a bomb on target.', 3: 'Some children have a fear of being blamed for problems.', 4: 'Open sources are software.', 5: 'Silt is a flour fine powder of ground rock.', 6: 'Ghanaian festivals are well worth seeing with drumming, dancing and feasting.'}
| 4 |
3,378 |
['There is good reason to believe that either stalagmites grow up from the floor of the cave from water that has dripped down or open areas are used only when thick shrubs or forest are nearby.', 'On the condition that open areas are used only when thick shrubs or forest are nearby, it is definitely the case that smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts.', 'We know that either a littleneck is a clam or sugar increases growth.', 'When those that suggest if a littleneck is a clam, then if stalagmites grow up from the floor of the cave from water that has dripped down, then smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts are wrong is true, it follows that nakedness is conditions.', "So long as those that suggest if a littleneck is a clam, then if stalagmites grow up from the floor of the cave from water that has dripped down, then smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts are wrong, 'we know that the claim that nakedness is conditions is false' is true.", "Whenever it is true that sugar increases growth, 'if cats scratch to deposit scent from glands in their paws, then egg production varies with the type of worm present' is true.", 'Should it be the case that if cats scratch to deposit scent from glands in their paws, then egg production varies with the type of worm present, it follows that if stalagmites grow up from the floor of the cave from water that has dripped down, then smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts.']
|
There is good reason to believe that either stalagmites grow up from the floor of the cave from water that has dripped down or open areas are used only when thick shrubs or forest are nearby. On the condition that open areas are used only when thick shrubs or forest are nearby, it is definitely the case that smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts. We know that either a littleneck is a clam or sugar increases growth. When those that suggest if a littleneck is a clam, then if stalagmites grow up from the floor of the cave from water that has dripped down, then smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts are wrong is true, it follows that nakedness is conditions. So long as those that suggest if a littleneck is a clam, then if stalagmites grow up from the floor of the cave from water that has dripped down, then smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts are wrong, 'we know that the claim that nakedness is conditions is false' is true. Whenever it is true that sugar increases growth, 'if cats scratch to deposit scent from glands in their paws, then egg production varies with the type of worm present' is true. Should it be the case that if cats scratch to deposit scent from glands in their paws, then egg production varies with the type of worm present, it follows that if stalagmites grow up from the floor of the cave from water that has dripped down, then smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts.
|
It is true that smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts.
|
It is true that smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If [1], then [0].). [SC2-2]
If [4], then (If [1], then [0].). [SC3-2]
Therefore, If [1], then [0]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [3], then (If [1], then [0].).).), then [7].
If (Not (If [3], then (If [1], then [0].).).), then (Not [7].).
Therefore, If [3], then (If [1], then [0].)..
[SC3-2]
Hypothetical Syllogism:
If [4], then (If [5], then [6].).
If (If [5], then [6].), then (If [1], then [0].).
Therefore, If [4], then (If [1], then [0].)..
|
{0: 'Smoking also hinders the blood supply to the bones or interferes with the function of osteoblasts.', 1: 'Stalagmites grow up from the floor of the cave from water that has dripped down.', 2: 'Open areas are used only when thick shrubs or forest are nearby.', 3: 'A littleneck is a clam.', 4: 'Sugar increases growth.', 5: 'Cats scratch to deposit scent from glands in their paws.', 6: 'Egg production varies with the type of worm present.', 7: 'Nakedness is conditions.'}
| 4 |
3,320 |
["One may reasonably assume that if the statement that 'some women gain weight as a side effect of estrogen use' is incorrect, then if smoking causes cancer including lung, bladder, throat and mouth cancer, then tidal currents are negligible at high and low tides.", "We know that at least one of two things is true: if experts have (part) cells, then gambian rats display peculiar behavior, or if vital signs are indicators of one's overall health, then if the statement that 'some women gain weight as a side effect of estrogen use' is incorrect, then the notion that 'if smoking causes cancer including lung, bladder, throat and mouth cancer, then tidal currents are negligible at high and low tides' is untrue.", 'Those that suggest if experts have (part) cells, then gambian rats display peculiar behavior are wrong.', "Given that the claim that vital signs are indicators of one's overall health does not reflect reality, it can be inferred that bungalows have (part) doorsteps.", 'It is a common misconception that bungalows have (part) doorsteps.']
|
One may reasonably assume that if the statement that 'some women gain weight as a side effect of estrogen use' is incorrect, then if smoking causes cancer including lung, bladder, throat and mouth cancer, then tidal currents are negligible at high and low tides. We know that at least one of two things is true: if experts have (part) cells, then gambian rats display peculiar behavior, or if vital signs are indicators of one's overall health, then if the statement that 'some women gain weight as a side effect of estrogen use' is incorrect, then the notion that 'if smoking causes cancer including lung, bladder, throat and mouth cancer, then tidal currents are negligible at high and low tides' is untrue. Those that suggest if experts have (part) cells, then gambian rats display peculiar behavior are wrong. Given that the claim that vital signs are indicators of one's overall health does not reflect reality, it can be inferred that bungalows have (part) doorsteps. It is a common misconception that bungalows have (part) doorsteps.
|
The idea that some women gain weight as a side effect of estrogen use is true.
|
Many women feel nauseated and vomit in early pregnancy.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then (If [1], then [2].).
If (Not [0].), then (Not (If [1], then [2].).). [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [3], then (If (Not [0].), then (Not (If [1], then [2].).).). [SC1-2]
[3] [SC2-2]
Therefore, If (Not [0].), then (Not (If [1], then [2].).)..
[SC1-2]
Disjunctive Syllogism:
Either (If [4], then [5].) or (If [3], then (If (Not [0].), then (Not (If [1], then [2].).).).).
Not (If [4], then [5].).
Therefore, If [3], then (If (Not [0].), then (Not (If [1], then [2].).).)..
[SC2-2]
Modus Tonens:
If (Not [3].), then [6].
Not [6].
Therefore, [3].
|
{0: 'Some women gain weight as a side effect of estrogen use.', 1: 'Smoking causes cancer including lung, bladder, throat and mouth cancer.', 2: 'Tidal currents are negligible at high and low tides.', 3: "Vital signs are indicators of one's overall health.", 4: 'Experts have (part) cells.', 5: 'Gambian rats display peculiar behavior.', 6: 'Bungalows have (part) doorsteps.'}
| 4 |
3,942 |
['One may reasonably assume that if dormancy tends to be closely associated with environmental conditions, then it is a common misconception that wars compel people to flee.', 'Should it be the case that bankers are the most powerful people on earth, it follows that it is a common misconception that wars compel people to flee.', 'We know that at least one of two things is true: some aquaria have mats, or if if long claws help cheetahs as they grip the ground as they run, then modern starfish holds hydraulic water vascular system that assists in locomotion, then either dormancy tends to be closely associated with environmental conditions or bankers are the most powerful people on earth.', 'The claim that some aquaria have mats does not reflect reality.', "It is rational to believe that either some thunderstorms produce damage tornado or studies show that fear, for example, can increase a man's attraction to a woman.", 'Provided that some thunderstorms produce damage tornado, we know that if long claws help cheetahs as they grip the ground as they run, then modern starfish holds hydraulic water vascular system that assists in locomotion.', "If studies show that fear, for example, can increase a man's attraction to a woman, then if long claws help cheetahs as they grip the ground as they run, then modern starfish holds hydraulic water vascular system that assists in locomotion."]
|
One may reasonably assume that if dormancy tends to be closely associated with environmental conditions, then it is a common misconception that wars compel people to flee. Should it be the case that bankers are the most powerful people on earth, it follows that it is a common misconception that wars compel people to flee. We know that at least one of two things is true: some aquaria have mats, or if if long claws help cheetahs as they grip the ground as they run, then modern starfish holds hydraulic water vascular system that assists in locomotion, then either dormancy tends to be closely associated with environmental conditions or bankers are the most powerful people on earth. The claim that some aquaria have mats does not reflect reality. It is rational to believe that either some thunderstorms produce damage tornado or studies show that fear, for example, can increase a man's attraction to a woman. Provided that some thunderstorms produce damage tornado, we know that if long claws help cheetahs as they grip the ground as they run, then modern starfish holds hydraulic water vascular system that assists in locomotion. If studies show that fear, for example, can increase a man's attraction to a woman, then if long claws help cheetahs as they grip the ground as they run, then modern starfish holds hydraulic water vascular system that assists in locomotion.
|
It is a common misconception that wars compel people to flee.
|
Many people rightly believe that wars compel people to flee.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].).
If [2], then (Not [0].).
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If (If [3], then [4].), then (Either [1] or [2].). [SC1-2]
If [3], then [4]. [SC2-2]
Therefore, Either [1] or [2]..
[SC1-2]
Disjunctive Syllogism:
Either [5] or (If (If [3], then [4].), then (Either [1] or [2].).).
Not [5].
Therefore, If (If [3], then [4].), then (Either [1] or [2].)..
[SC2-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If [3], then [4].).
If [7], then (If [3], then [4].).
Therefore, If [3], then [4]..
|
{0: 'Wars compel people to flee.', 1: 'Dormancy tends to be closely associated with environmental conditions.', 2: 'Bankers are the most powerful people on earth.', 3: 'Long claws help cheetahs as they grip the ground as they run.', 4: 'Modern starfish holds hydraulic water vascular system that assists in locomotion.', 5: 'Some aquaria have mats.', 6: 'Some thunderstorms produce damage tornado.', 7: "Studies show that fear, for example, can increase a man's attraction to a woman."}
| 4 |
3,351 |
['At least one of two things is true: copper plays an important role in chlorophyll production and protein synthesis, or chemotherapy can cause numerous side effects, depending in the medication being used.', "Should it be the case that sites support few individuals, it follows that the statement that 'copper plays an important role in chlorophyll production and protein synthesis' is incorrect.", 'At least one of two things is true: larkspur needs light to germinate, or intracellular infection can occur in all mammalian cells except anuclear erythrocytes.', 'If larkspur needs light to germinate, then either sites support few individuals or brachiopods live only in the sea, and most species avoid locations with strong currents or waves.', 'Provided that intracellular infection can occur in all mammalian cells except anuclear erythrocytes, we know that either sites support few individuals or brachiopods live only in the sea, and most species avoid locations with strong currents or waves.', 'Given that brachiopods live only in the sea, and most species avoid locations with strong currents or waves, it can be inferred that dogs are omnivores.', "Provided that dogs are omnivores, we know that the statement that 'copper plays an important role in chlorophyll production and protein synthesis' is incorrect."]
|
At least one of two things is true: copper plays an important role in chlorophyll production and protein synthesis, or chemotherapy can cause numerous side effects, depending in the medication being used. Should it be the case that sites support few individuals, it follows that the statement that 'copper plays an important role in chlorophyll production and protein synthesis' is incorrect. At least one of two things is true: larkspur needs light to germinate, or intracellular infection can occur in all mammalian cells except anuclear erythrocytes. If larkspur needs light to germinate, then either sites support few individuals or brachiopods live only in the sea, and most species avoid locations with strong currents or waves. Provided that intracellular infection can occur in all mammalian cells except anuclear erythrocytes, we know that either sites support few individuals or brachiopods live only in the sea, and most species avoid locations with strong currents or waves. Given that brachiopods live only in the sea, and most species avoid locations with strong currents or waves, it can be inferred that dogs are omnivores. Provided that dogs are omnivores, we know that the statement that 'copper plays an important role in chlorophyll production and protein synthesis' is incorrect.
|
The idea that chemotherapy can cause numerous side effects, depending in the medication being used is true.
|
Chemotherapy causes episodes.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [2] or [3]. [SC1-2]
If [2], then (Not [1].).
If [3], then (Not [1].). [SC3-2]
Therefore, Not [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]..
[SC3-2]
Hypothetical Syllogism:
If [3], then [6].
If [6], then (Not [1].).
Therefore, If [3], then (Not [1].)..
|
{0: 'Chemotherapy can cause numerous side effects, depending in the medication being used.', 1: 'Copper plays an important role in chlorophyll production and protein synthesis.', 2: 'Sites support few individuals.', 3: 'Brachiopods live only in the sea, and most species avoid locations with strong currents or waves.', 4: 'Larkspur needs light to germinate.', 5: 'Intracellular infection can occur in all mammalian cells except anuclear erythrocytes.', 6: 'Dogs are omnivores.'}
| 4 |
3,418 |
['Given that it is a common misconception that either a safety hat is a helmet or some wood attracts woodpeckers, it can be inferred that axises are stalks.', 'When it is a common misconception that either a safety hat is a helmet or some wood attracts woodpeckers is true, it follows that it is not true that axises are stalks.', 'Provided that the statement, if a safety hat is a helmet, then an olive is fruit, does not hold, we know that most reproduction occurs over time.', "When the statement, if a safety hat is a helmet, then an olive is fruit, does not hold is true, it follows that the statement that 'most reproduction occurs over time' is incorrect.", "Whenever it is true that we know that the claim that if some wood attracts woodpeckers, then an olive is fruit is false, 'either earth is part of universes or grease accumulates in sewers, causing blockage' is true.", 'Once we know we know that the claim that if some wood attracts woodpeckers, then an olive is fruit is false, we also know that those that suggest either earth is part of universes or grease accumulates in sewers, causing blockage are wrong.']
|
Given that it is a common misconception that either a safety hat is a helmet or some wood attracts woodpeckers, it can be inferred that axises are stalks. When it is a common misconception that either a safety hat is a helmet or some wood attracts woodpeckers is true, it follows that it is not true that axises are stalks. Provided that the statement, if a safety hat is a helmet, then an olive is fruit, does not hold, we know that most reproduction occurs over time. When the statement, if a safety hat is a helmet, then an olive is fruit, does not hold is true, it follows that the statement that 'most reproduction occurs over time' is incorrect. Whenever it is true that we know that the claim that if some wood attracts woodpeckers, then an olive is fruit is false, 'either earth is part of universes or grease accumulates in sewers, causing blockage' is true. Once we know we know that the claim that if some wood attracts woodpeckers, then an olive is fruit is false, we also know that those that suggest either earth is part of universes or grease accumulates in sewers, causing blockage are wrong.
|
It is true that an olive is fruit.
|
The statement that 'an olive is fruit' is incorrect.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or [2].).), then [3].
If (Not (Either [1] or [2].).), then (Not [3].).
Therefore, Either [1] or [2]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [1], then [0].).), then [4].
If (Not (If [1], then [0].).), then (Not [4].).
Therefore, If [1], then [0]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then [0].).), then (Either [5] or [6].).
If (Not (If [2], then [0].).), then (Not (Either [5] or [6].).).
Therefore, If [2], then [0]..
|
{0: 'An olive is fruit.', 1: 'A safety hat is a helmet.', 2: 'Some wood attracts woodpeckers.', 3: 'Axises are stalks.', 4: 'Most reproduction occurs over time.', 5: 'Earth is part of universes.', 6: 'Grease accumulates in sewers, causing blockage.'}
| 4 |
3,945 |
["Once we know the claim that if the statement 'either american flags abound on postcards, greeting cards, invitations and the like or operant conditioning forms an association between a behavior and a consequence' can be considered false, then boys inherit male baldness is false, we also know that women die in circumstances.", 'Those that suggest women die in circumstances are wrong.', "On the condition that those that suggest if the statement 'either american flags abound on postcards, greeting cards, invitations and the like or operant conditioning forms an association between a behavior and a consequence' can be considered false, then the statement, boys inherit male baldness, does not hold are wrong, it is definitely the case that if widow spiders feed on a wide variety of arthropods, then spiders detect prey.", 'It is a fact that either suicidal people are fully intent on killing themselves or drumlins are hills of glacial debris.', "Provided that suicidal people are fully intent on killing themselves, we know that if those that suggest if the statement 'either american flags abound on postcards, greeting cards, invitations and the like or operant conditioning forms an association between a behavior and a consequence' can be considered false, then the statement, boys inherit male baldness, does not hold are wrong, then the claim that if widow spiders feed on a wide variety of arthropods, then spiders detect prey does not correspond with reality.", "Once we know drumlins are hills of glacial debris, we also know that if those that suggest if the statement 'either american flags abound on postcards, greeting cards, invitations and the like or operant conditioning forms an association between a behavior and a consequence' can be considered false, then the statement, boys inherit male baldness, does not hold are wrong, then the claim that if widow spiders feed on a wide variety of arthropods, then spiders detect prey does not correspond with reality."]
|
Once we know the claim that if the statement 'either american flags abound on postcards, greeting cards, invitations and the like or operant conditioning forms an association between a behavior and a consequence' can be considered false, then boys inherit male baldness is false, we also know that women die in circumstances. Those that suggest women die in circumstances are wrong. On the condition that those that suggest if the statement 'either american flags abound on postcards, greeting cards, invitations and the like or operant conditioning forms an association between a behavior and a consequence' can be considered false, then the statement, boys inherit male baldness, does not hold are wrong, it is definitely the case that if widow spiders feed on a wide variety of arthropods, then spiders detect prey. It is a fact that either suicidal people are fully intent on killing themselves or drumlins are hills of glacial debris. Provided that suicidal people are fully intent on killing themselves, we know that if those that suggest if the statement 'either american flags abound on postcards, greeting cards, invitations and the like or operant conditioning forms an association between a behavior and a consequence' can be considered false, then the statement, boys inherit male baldness, does not hold are wrong, then the claim that if widow spiders feed on a wide variety of arthropods, then spiders detect prey does not correspond with reality. Once we know drumlins are hills of glacial debris, we also know that if those that suggest if the statement 'either american flags abound on postcards, greeting cards, invitations and the like or operant conditioning forms an association between a behavior and a consequence' can be considered false, then the statement, boys inherit male baldness, does not hold are wrong, then the claim that if widow spiders feed on a wide variety of arthropods, then spiders detect prey does not correspond with reality.
|
We know that either american flags abound on postcards, greeting cards, invitations and the like or operant conditioning forms an association between a behavior and a consequence.
|
We know that the claim that either american flags abound on postcards, greeting cards, invitations and the like or operant conditioning forms an association between a behavior and a consequence is false.
|
FALSE
|
Reductio Ad Absurdum:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
If (Not (Either [0] or [1].).), then (Not [2].). [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Modus Tonens:
If (Not (If (Not (Either [0] or [1].).), then [2].).), then [5].
Not [5].
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (If [3], then [4].).
If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (Not (If [3], then [4].).). [SC2-2]
Therefore, If (Not (Either [0] or [1].).), then (Not [2].)..
[SC2-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (Not (If [3], then [4].).).).
If [7], then (If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (Not (If [3], then [4].).).).
Therefore, If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (Not (If [3], then [4].).)..
|
{0: 'American flags abound on postcards, greeting cards, invitations and the like.', 1: 'Operant conditioning forms an association between a behavior and a consequence.', 2: 'Boys inherit male baldness.', 3: 'Widow spiders feed on a wide variety of arthropods.', 4: 'Spiders detect prey.', 5: 'Women die in circumstances.', 6: 'Suicidal people are fully intent on killing themselves.', 7: 'Drumlins are hills of glacial debris.'}
| 4 |
3,795 |
['Assuming some people mistakenly believe that either discoveries relate to behavior or it is a common misconception that some animals have dens, we know that large frogs are more likely to lunge at their targets.', "Once we know an apotheosis is worship, we also know that the statement 'discoveries relate to behavior' can be considered false.", "The statement 'an apotheosis is worship' can be considered true.", "One may reasonably assume that if carpet cleaner contains toxic substances, then if some people mistakenly believe that either discoveries relate to behavior or it is a common misconception that some animals have dens, then the statement 'large frogs are more likely to lunge at their targets' can be considered false.", "The statement 'carpet cleaner contains toxic substances' is true."]
|
Assuming some people mistakenly believe that either discoveries relate to behavior or it is a common misconception that some animals have dens, we know that large frogs are more likely to lunge at their targets. Once we know an apotheosis is worship, we also know that the statement 'discoveries relate to behavior' can be considered false. The statement 'an apotheosis is worship' can be considered true. One may reasonably assume that if carpet cleaner contains toxic substances, then if some people mistakenly believe that either discoveries relate to behavior or it is a common misconception that some animals have dens, then the statement 'large frogs are more likely to lunge at their targets' can be considered false. The statement 'carpet cleaner contains toxic substances' is true.
|
It is a common misconception that some animals have dens.
|
It is a common misconception that some animals have dens.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or (Not [0].).).), then [2].
If (Not (Either [1] or (Not [0].).).), then (Not [2].). [SC2-2]
Therefore, Either [1] or (Not [0].)..
[SC2-2]
Modus Ponens:
If [4], then (If (Not (Either [1] or (Not [0].).).), then (Not [2].).).
[4]
Therefore, If (Not (Either [1] or (Not [0].).).), then (Not [2].)..
[SC2-1]
Modus Ponens:
If [3], then (Not [1].).
[3]
Therefore, Not [1]..
|
{0: 'Some animals have dens.', 1: 'Discoveries relate to behavior.', 2: 'Large frogs are more likely to lunge at their targets.', 3: 'An apotheosis is worship.', 4: 'Carpet cleaner contains toxic substances.'}
| 4 |
3,145 |
['At least one of two things is true: mistakes are reality checks on the road of life, or people die of shock from extreme depression as well as extreme joy.', 'Once we know mistakes are reality checks on the road of life, we also know that either either slate is metamorphic rocks or most churches only keep records back to the date the church or parish was formed or if collateral covers margins for options over stocks and indices, then height is a result of growth only in apical meristems at the very tips of the twigs.', 'If people die of shock from extreme depression as well as extreme joy, then either either slate is metamorphic rocks or most churches only keep records back to the date the church or parish was formed or if collateral covers margins for options over stocks and indices, then height is a result of growth only in apical meristems at the very tips of the twigs.', 'At least one of two things is true: either most fruit protects mango seeds or antibiotic fermentations are notoriously susceptible to variations in yield, or a fjord is an inlet.', 'If either most fruit protects mango seeds or antibiotic fermentations are notoriously susceptible to variations in yield, then if either slate is metamorphic rocks or most churches only keep records back to the date the church or parish was formed, then some ewes die of complications such as infected uteri, fetal retentions or peritonitis.', "So long as a fjord is an inlet, 'if either slate is metamorphic rocks or most churches only keep records back to the date the church or parish was formed, then some ewes die of complications such as infected uteri, fetal retentions or peritonitis' is true.", 'One may reasonably assume that if if collateral covers margins for options over stocks and indices, then height is a result of growth only in apical meristems at the very tips of the twigs, then osmosis is the diffusion of water across a cell membrane.', 'Once we know osmosis is the diffusion of water across a cell membrane, we also know that some ewes die of complications such as infected uteri, fetal retentions or peritonitis.']
|
At least one of two things is true: mistakes are reality checks on the road of life, or people die of shock from extreme depression as well as extreme joy. Once we know mistakes are reality checks on the road of life, we also know that either either slate is metamorphic rocks or most churches only keep records back to the date the church or parish was formed or if collateral covers margins for options over stocks and indices, then height is a result of growth only in apical meristems at the very tips of the twigs. If people die of shock from extreme depression as well as extreme joy, then either either slate is metamorphic rocks or most churches only keep records back to the date the church or parish was formed or if collateral covers margins for options over stocks and indices, then height is a result of growth only in apical meristems at the very tips of the twigs. At least one of two things is true: either most fruit protects mango seeds or antibiotic fermentations are notoriously susceptible to variations in yield, or a fjord is an inlet. If either most fruit protects mango seeds or antibiotic fermentations are notoriously susceptible to variations in yield, then if either slate is metamorphic rocks or most churches only keep records back to the date the church or parish was formed, then some ewes die of complications such as infected uteri, fetal retentions or peritonitis. So long as a fjord is an inlet, 'if either slate is metamorphic rocks or most churches only keep records back to the date the church or parish was formed, then some ewes die of complications such as infected uteri, fetal retentions or peritonitis' is true. One may reasonably assume that if if collateral covers margins for options over stocks and indices, then height is a result of growth only in apical meristems at the very tips of the twigs, then osmosis is the diffusion of water across a cell membrane. Once we know osmosis is the diffusion of water across a cell membrane, we also know that some ewes die of complications such as infected uteri, fetal retentions or peritonitis.
|
It is true that some ewes die of complications such as infected uteri, fetal retentions or peritonitis.
|
It is true that some ewes die of complications such as infected uteri, fetal retentions or peritonitis.
|
TRUE
|
Disjunction Elimination:
Either (Either [1] or [2].) or (If [3], then [4].). [SC1-1]
If (Either [1] or [2].), then [0]. [SC2-1]
If (If [3], then [4].), then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [8] or [9].
If [8], then (Either (Either [1] or [2].) or (If [3], then [4].).).
If [9], then (Either (Either [1] or [2].) or (If [3], then [4].).).
Therefore, Either (Either [1] or [2].) or (If [3], then [4].)..
[SC2-1]
Disjunction Elimination:
Either (Either [5] or [6].) or [7].
If (Either [5] or [6].), then (If (Either [1] or [2].), then [0].).
If [7], then (If (Either [1] or [2].), then [0].).
Therefore, If (Either [1] or [2].), then [0]..
[SC3-1]
Hypothetical Syllogism:
If (If [3], then [4].), then [10].
If [10], then [0].
Therefore, If (If [3], then [4].), then [0]..
|
{0: 'Some ewes die of complications such as infected uteri, fetal retentions or peritonitis.', 1: 'Slate is metamorphic rocks.', 2: 'Most churches only keep records back to the date the church or parish was formed.', 3: 'Collateral covers margins for options over stocks and indices.', 4: 'Height is a result of growth only in apical meristems at the very tips of the twigs.', 5: 'Most fruit protects mango seeds.', 6: 'Antibiotic fermentations are notoriously susceptible to variations in yield.', 7: 'A fjord is an inlet.', 8: 'Mistakes are reality checks on the road of life.', 9: 'People die of shock from extreme depression as well as extreme joy.', 10: 'Osmosis is the diffusion of water across a cell membrane.'}
| 4 |
3,826 |
['There is good reason to believe that either wealth can be a necessity or a luxury or emery is a mineral.', 'Provided that wealth can be a necessity or a luxury, we know that it is a common misconception that either words are part of sentences or manatees are usually grayish brown.', 'When many countries has their own manga production and especially in Asia some time ago is true, it follows that if emery is a mineral, then it is a common misconception that either words are part of sentences or manatees are usually grayish brown.', 'Given that the claim that either internal fertilization occurs mainly in cartilaginous fishes or many countries has their own manga production and especially in Asia some time ago does not correspond with reality, it can be inferred that goodness is always the target of evil.', 'When the claim that either internal fertilization occurs mainly in cartilaginous fishes or many countries has their own manga production and especially in Asia some time ago does not correspond with reality is true, it follows that it is a common misconception that goodness is always the target of evil.', 'At least one of two things is true: potassium is the key component of commonly-used potash fertilizer, and is abundant in animal waste, or fireflies have (part) sections.', 'On the condition that potassium is the key component of commonly-used potash fertilizer, and is abundant in animal waste, it is definitely the case that if internal fertilization occurs mainly in cartilaginous fishes, then if emery is a mineral, then it is a common misconception that either words are part of sentences or manatees are usually grayish brown.', "So long as fireflies have (part) sections, 'if internal fertilization occurs mainly in cartilaginous fishes, then if emery is a mineral, then it is a common misconception that either words are part of sentences or manatees are usually grayish brown' is true."]
|
There is good reason to believe that either wealth can be a necessity or a luxury or emery is a mineral. Provided that wealth can be a necessity or a luxury, we know that it is a common misconception that either words are part of sentences or manatees are usually grayish brown. When many countries has their own manga production and especially in Asia some time ago is true, it follows that if emery is a mineral, then it is a common misconception that either words are part of sentences or manatees are usually grayish brown. Given that the claim that either internal fertilization occurs mainly in cartilaginous fishes or many countries has their own manga production and especially in Asia some time ago does not correspond with reality, it can be inferred that goodness is always the target of evil. When the claim that either internal fertilization occurs mainly in cartilaginous fishes or many countries has their own manga production and especially in Asia some time ago does not correspond with reality is true, it follows that it is a common misconception that goodness is always the target of evil. At least one of two things is true: potassium is the key component of commonly-used potash fertilizer, and is abundant in animal waste, or fireflies have (part) sections. On the condition that potassium is the key component of commonly-used potash fertilizer, and is abundant in animal waste, it is definitely the case that if internal fertilization occurs mainly in cartilaginous fishes, then if emery is a mineral, then it is a common misconception that either words are part of sentences or manatees are usually grayish brown. So long as fireflies have (part) sections, 'if internal fertilization occurs mainly in cartilaginous fishes, then if emery is a mineral, then it is a common misconception that either words are part of sentences or manatees are usually grayish brown' is true.
|
It is a common misconception that either words are part of sentences or manatees are usually grayish brown.
|
It is a fact that either words are part of sentences or manatees are usually grayish brown.
|
FALSE
|
Disjunction Elimination:
Either [2] or [3].
If [2], then (Not (Either [0] or [1].).).
If [3], then (Not (Either [0] or [1].).). [SC3-1]
Therefore, Not (Either [0] or [1].)..
[SC3-1]
Disjunction Elimination:
Either [4] or [5]. [SC1-2]
If [4], then (If [3], then (Not (Either [0] or [1].).).). [SC2-2]
If [5], then (If [3], then (Not (Either [0] or [1].).).).
Therefore, If [3], then (Not (Either [0] or [1].).)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [4] or [5].).), then [6].
If (Not (Either [4] or [5].).), then (Not [6].).
Therefore, Either [4] or [5]..
[SC2-2]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If [4], then (If [3], then (Not (Either [0] or [1].).).).).
If [8], then (If [4], then (If [3], then (Not (Either [0] or [1].).).).).
Therefore, If [4], then (If [3], then (Not (Either [0] or [1].).).)..
|
{0: 'Words are part of sentences.', 1: 'Manatees are usually grayish brown.', 2: 'Wealth can be a necessity or a luxury.', 3: 'Emery is a mineral.', 4: 'Internal fertilization occurs mainly in cartilaginous fishes.', 5: 'Many countries has their own manga production and especially in Asia some time ago.', 6: 'Goodness is always the target of evil.', 7: 'Potassium is the key component of commonly-used potash fertilizer, and is abundant in animal waste.', 8: 'Fireflies have (part) sections.'}
| 4 |
3,492 |
['There is good reason to believe that either large companies have divisions and subsidiaries with different names or vertebrates synthesize urea in the liver using the ornithine-urea cycle.', "Assuming large companies have divisions and subsidiaries with different names, we know that the notion that 'either wetlands are the whole world for many salamanders, snakes, turtles, and aquatic insects or children grow and develop at different rates' is untrue.", 'Should it be the case that the statement, if vertebrates synthesize urea in the liver using the ornithine-urea cycle, then ferns like to be sheltered from extreme hot or cold winds, does not hold, it follows that art is the language that communicates all changes in human activities.', 'When the statement, if vertebrates synthesize urea in the liver using the ornithine-urea cycle, then ferns like to be sheltered from extreme hot or cold winds, does not hold is true, it follows that it is a common misconception that art is the language that communicates all changes in human activities.', 'It is a fact that either coral reefs are a different matter or oil is extracted from seeds.', "If coral reefs are a different matter, then if ferns like to be sheltered from extreme hot or cold winds, then the notion that 'either wetlands are the whole world for many salamanders, snakes, turtles, and aquatic insects or children grow and develop at different rates' is untrue.", "Provided that oil is extracted from seeds, we know that if ferns like to be sheltered from extreme hot or cold winds, then the notion that 'either wetlands are the whole world for many salamanders, snakes, turtles, and aquatic insects or children grow and develop at different rates' is untrue."]
|
There is good reason to believe that either large companies have divisions and subsidiaries with different names or vertebrates synthesize urea in the liver using the ornithine-urea cycle. Assuming large companies have divisions and subsidiaries with different names, we know that the notion that 'either wetlands are the whole world for many salamanders, snakes, turtles, and aquatic insects or children grow and develop at different rates' is untrue. Should it be the case that the statement, if vertebrates synthesize urea in the liver using the ornithine-urea cycle, then ferns like to be sheltered from extreme hot or cold winds, does not hold, it follows that art is the language that communicates all changes in human activities. When the statement, if vertebrates synthesize urea in the liver using the ornithine-urea cycle, then ferns like to be sheltered from extreme hot or cold winds, does not hold is true, it follows that it is a common misconception that art is the language that communicates all changes in human activities. It is a fact that either coral reefs are a different matter or oil is extracted from seeds. If coral reefs are a different matter, then if ferns like to be sheltered from extreme hot or cold winds, then the notion that 'either wetlands are the whole world for many salamanders, snakes, turtles, and aquatic insects or children grow and develop at different rates' is untrue. Provided that oil is extracted from seeds, we know that if ferns like to be sheltered from extreme hot or cold winds, then the notion that 'either wetlands are the whole world for many salamanders, snakes, turtles, and aquatic insects or children grow and develop at different rates' is untrue.
|
The notion that 'either wetlands are the whole world for many salamanders, snakes, turtles, and aquatic insects or children grow and develop at different rates' is untrue.
|
Either one or both of these statements are true: wetlands are the whole world for many salamanders, snakes, turtles, and aquatic insects, or children grow and develop at different rates.
|
FALSE
|
Disjunction Elimination:
Either [2] or [3].
If [2], then (Not (Either [0] or [1].).).
If [3], then (Not (Either [0] or [1].).). [SC3-1]
Therefore, Not (Either [0] or [1].)..
[SC3-1]
Hypothetical Syllogism:
If [3], then [4]. [SC1-2]
If [4], then (Not (Either [0] or [1].).). [SC2-2]
Therefore, If [3], then (Not (Either [0] or [1].).)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [3], then [4].).), then [7].
If (Not (If [3], then [4].).), then (Not [7].).
Therefore, If [3], then [4]..
[SC2-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [4], then (Not (Either [0] or [1].).).).
If [6], then (If [4], then (Not (Either [0] or [1].).).).
Therefore, If [4], then (Not (Either [0] or [1].).)..
|
{0: 'Wetlands are the whole world for many salamanders, snakes, turtles, and aquatic insects.', 1: 'Children grow and develop at different rates.', 2: 'Large companies have divisions and subsidiaries with different names.', 3: 'Vertebrates synthesize urea in the liver using the ornithine-urea cycle.', 4: 'Ferns like to be sheltered from extreme hot or cold winds.', 5: 'Coral reefs are a different matter.', 6: 'Oil is extracted from seeds.', 7: 'Art is the language that communicates all changes in human activities.'}
| 4 |
3,751 |
["One may reasonably assume that if the claim that if the statement that 'genes come in pairs, with one copy inherited from each parent' is incorrect, then water tends to percolate slowly through overly clayey soils , and that can lead to puddling does not reflect reality, then the statement that states if motion also exists from eternity, then most dust enters atmospheres is false.", "Either if walking are movement, then every polygon has a label and all polygons are closed or the notion that 'water tends to percolate slowly through overly clayey soils , and that can lead to puddling' is untrue.", 'The claim that if walking are movement, then every polygon has a label and all polygons are closed does not reflect reality.', "There is good reason to believe that either management is the process of getting activities done efficiently with and through other people or if the claim that if the statement that 'genes come in pairs, with one copy inherited from each parent' is incorrect, then water tends to percolate slowly through overly clayey soils , and that can lead to puddling does not reflect reality, then if motion also exists from eternity, then most dust enters atmospheres.", 'It is not the case that management is the process of getting activities done efficiently with and through other people.']
|
One may reasonably assume that if the claim that if the statement that 'genes come in pairs, with one copy inherited from each parent' is incorrect, then water tends to percolate slowly through overly clayey soils , and that can lead to puddling does not reflect reality, then the statement that states if motion also exists from eternity, then most dust enters atmospheres is false. Either if walking are movement, then every polygon has a label and all polygons are closed or the notion that 'water tends to percolate slowly through overly clayey soils , and that can lead to puddling' is untrue. The claim that if walking are movement, then every polygon has a label and all polygons are closed does not reflect reality. There is good reason to believe that either management is the process of getting activities done efficiently with and through other people or if the claim that if the statement that 'genes come in pairs, with one copy inherited from each parent' is incorrect, then water tends to percolate slowly through overly clayey soils , and that can lead to puddling does not reflect reality, then if motion also exists from eternity, then most dust enters atmospheres. It is not the case that management is the process of getting activities done efficiently with and through other people.
|
The statement 'genes come in pairs, with one copy inherited from each parent' is true.
|
The statement 'genes come in pairs, with one copy inherited from each parent' is true.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then [1].).), then (If [4], then [5].). [SC1-2]
If (Not (If (Not [0].), then [1].).), then (Not (If [4], then [5].).).
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunctive Syllogism:
Either [6] or (If (Not (If (Not [0].), then [1].).), then (If [4], then [5].).).
Not [6].
Therefore, If (Not (If (Not [0].), then [1].).), then (If [4], then [5].)..
[SC2-1]
Disjunctive Syllogism:
Either (If [2], then [3].) or (Not [1].).
Not (If [2], then [3].).
Therefore, Not [1]..
|
{0: 'Genes come in pairs, with one copy inherited from each parent.', 1: 'Water tends to percolate slowly through overly clayey soils , and that can lead to puddling.', 2: 'Walking are movement.', 3: 'Every polygon has a label and all polygons are closed.', 4: 'Motion also exists from eternity.', 5: 'Most dust enters atmospheres.', 6: 'Management is the process of getting activities done efficiently with and through other people.'}
| 4 |
3,240 |
["The statement 'validity is situations' can be considered true.", "Provided that the claim that if validity is situations, then compassion matures by understanding of one's self in others and others in one's self is false, we know that people create rules that affect their choices and how they act.", 'Those that suggest people create rules that affect their choices and how they act are wrong.', "Given that the claim that if compassion matures by understanding of one's self in others and others in one's self, then duck season is in the fall and spring when the cadets wear white ducks and white shirts does not reflect reality, it can be inferred that either most goats graze in fields or francois langurs are monkeys that live in southwest China and northeast Vietnam.", "Given that the claim that if compassion matures by understanding of one's self in others and others in one's self, then duck season is in the fall and spring when the cadets wear white ducks and white shirts does not reflect reality, it can be inferred that we know that the claim that either most goats graze in fields or francois langurs are monkeys that live in southwest China and northeast Vietnam is false."]
|
The statement 'validity is situations' can be considered true. Provided that the claim that if validity is situations, then compassion matures by understanding of one's self in others and others in one's self is false, we know that people create rules that affect their choices and how they act. Those that suggest people create rules that affect their choices and how they act are wrong. Given that the claim that if compassion matures by understanding of one's self in others and others in one's self, then duck season is in the fall and spring when the cadets wear white ducks and white shirts does not reflect reality, it can be inferred that either most goats graze in fields or francois langurs are monkeys that live in southwest China and northeast Vietnam. Given that the claim that if compassion matures by understanding of one's self in others and others in one's self, then duck season is in the fall and spring when the cadets wear white ducks and white shirts does not reflect reality, it can be inferred that we know that the claim that either most goats graze in fields or francois langurs are monkeys that live in southwest China and northeast Vietnam is false.
|
The statement 'duck season is in the fall and spring when the cadets wear white ducks and white shirts' can be considered true.
|
The statement 'duck season is in the fall and spring when the cadets wear white ducks and white shirts' can be considered true.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If [1], then [2]. [SC1-2]
If [2], then [0]. [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Modus Tonens:
If (Not (If [1], then [2].).), then [3].
Not [3].
Therefore, If [1], then [2]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [2], then [0].).), then (Either [4] or [5].).
If (Not (If [2], then [0].).), then (Not (Either [4] or [5].).).
Therefore, If [2], then [0]..
|
{0: 'Duck season is in the fall and spring when the cadets wear white ducks and white shirts.', 1: 'Validity is situations.', 2: "Compassion matures by understanding of one's self in others and others in one's self.", 3: 'People create rules that affect their choices and how they act.', 4: 'Most goats graze in fields.', 5: 'Francois langurs are monkeys that live in southwest China and northeast Vietnam.'}
| 4 |
3,648 |
['One may reasonably assume that if if some disorder involves gigantisms, then pinecones are cones, then aromatic hydrocarbons help determine the rate at which gasoline burns.', "Given that the statement 'either if some disorder involves gigantisms, then pinecones are cones or some individuals are family dogs, and some bond only to one person' can be considered false, it can be inferred that some hormones trigger dormancy.", "When the statement 'either if some disorder involves gigantisms, then pinecones are cones or some individuals are family dogs, and some bond only to one person' can be considered false is true, it follows that the claim that some hormones trigger dormancy has no merit.", 'On the condition that the statement, if some individuals are family dogs, and some bond only to one person, then aromatic hydrocarbons help determine the rate at which gasoline burns, does not hold, it is definitely the case that doctors have (part) corpi.', "Whenever it is true that the statement that states if the statement, if some individuals are family dogs, and some bond only to one person, then aromatic hydrocarbons help determine the rate at which gasoline burns, does not hold, then those that suggest doctors have (part) corpi are wrong is false, 'many hospitals have rehabilitation programs to help people with chronic breathing problems' is true.", 'When the statement that states if the statement, if some individuals are family dogs, and some bond only to one person, then aromatic hydrocarbons help determine the rate at which gasoline burns, does not hold, then those that suggest doctors have (part) corpi are wrong is false is true, it follows that it is a common misconception that many hospitals have rehabilitation programs to help people with chronic breathing problems.']
|
One may reasonably assume that if if some disorder involves gigantisms, then pinecones are cones, then aromatic hydrocarbons help determine the rate at which gasoline burns. Given that the statement 'either if some disorder involves gigantisms, then pinecones are cones or some individuals are family dogs, and some bond only to one person' can be considered false, it can be inferred that some hormones trigger dormancy. When the statement 'either if some disorder involves gigantisms, then pinecones are cones or some individuals are family dogs, and some bond only to one person' can be considered false is true, it follows that the claim that some hormones trigger dormancy has no merit. On the condition that the statement, if some individuals are family dogs, and some bond only to one person, then aromatic hydrocarbons help determine the rate at which gasoline burns, does not hold, it is definitely the case that doctors have (part) corpi. Whenever it is true that the statement that states if the statement, if some individuals are family dogs, and some bond only to one person, then aromatic hydrocarbons help determine the rate at which gasoline burns, does not hold, then those that suggest doctors have (part) corpi are wrong is false, 'many hospitals have rehabilitation programs to help people with chronic breathing problems' is true. When the statement that states if the statement, if some individuals are family dogs, and some bond only to one person, then aromatic hydrocarbons help determine the rate at which gasoline burns, does not hold, then those that suggest doctors have (part) corpi are wrong is false is true, it follows that it is a common misconception that many hospitals have rehabilitation programs to help people with chronic breathing problems.
|
It is true that aromatic hydrocarbons help determine the rate at which gasoline burns.
|
It is true that aromatic hydrocarbons help determine the rate at which gasoline burns.
|
TRUE
|
Disjunction Elimination:
Either (If [1], then [2].) or [3]. [SC1-1]
If (If [1], then [2].), then [0].
If [3], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either (If [1], then [2].) or [3].).), then [4].
If (Not (Either (If [1], then [2].) or [3].).), then (Not [4].).
Therefore, Either (If [1], then [2].) or [3]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [3], then [0].).), then [5].
If (Not (If [3], then [0].).), then (Not [5].). [SC2-2]
Therefore, If [3], then [0]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (If [3], then [0].).), then (Not [5].).).), then [6].
If (Not (If (Not (If [3], then [0].).), then (Not [5].).).), then (Not [6].).
Therefore, If (Not (If [3], then [0].).), then (Not [5].)..
|
{0: 'Aromatic hydrocarbons help determine the rate at which gasoline burns.', 1: 'Some disorder involves gigantisms.', 2: 'Pinecones are cones.', 3: 'Some individuals are family dogs, and some bond only to one person.', 4: 'Some hormones trigger dormancy.', 5: 'Doctors have (part) corpi.', 6: 'Many hospitals have rehabilitation programs to help people with chronic breathing problems.'}
| 4 |
3,886 |
['On the condition that the claim that if specific gravity is the ratio of density of a substance compared to that of water, then transformers are products does not reflect reality, it is definitely the case that most evergreens can stay in the same pot for several years.', 'It is a fact that either flickers reside in lightly wooded areas near farmlands or all languages have grammar rules, whether they are formal rules or informal patterns.', "So long as flickers reside in lightly wooded areas near farmlands, 'it is not true that transformers are products' is true.", 'Once we know all languages have grammar rules, whether they are formal rules or informal patterns, we also know that it is not true that transformers are products.', 'Provided that some little crabs live in edges, we know that it is not true that most evergreens can stay in the same pot for several years.', 'It is fair to say that some little crabs live in edges.']
|
On the condition that the claim that if specific gravity is the ratio of density of a substance compared to that of water, then transformers are products does not reflect reality, it is definitely the case that most evergreens can stay in the same pot for several years. It is a fact that either flickers reside in lightly wooded areas near farmlands or all languages have grammar rules, whether they are formal rules or informal patterns. So long as flickers reside in lightly wooded areas near farmlands, 'it is not true that transformers are products' is true. Once we know all languages have grammar rules, whether they are formal rules or informal patterns, we also know that it is not true that transformers are products. Provided that some little crabs live in edges, we know that it is not true that most evergreens can stay in the same pot for several years. It is fair to say that some little crabs live in edges.
|
It is a common misconception that specific gravity is the ratio of density of a substance compared to that of water.
|
It is not true that specific gravity is relative density.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (If [0], then [1].).), then [4].
Not [4]. [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Modus Ponens:
If [5], then (Not [4].).
[5]
Therefore, Not [4]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (Not [1].).
If [3], then (Not [1].).
Therefore, Not [1]..
|
{0: 'Specific gravity is the ratio of density of a substance compared to that of water.', 1: 'Transformers are products.', 2: 'Flickers reside in lightly wooded areas near farmlands.', 3: 'All languages have grammar rules, whether they are formal rules or informal patterns.', 4: 'Most evergreens can stay in the same pot for several years.', 5: 'Some little crabs live in edges.'}
| 4 |
3,144 |
['We know that either witchcraft is the illegitimate use of authority in a spiritual dimension or either plants take in air through their leaves or bones come in all shapes and sizes.', 'It is a common misconception that witchcraft is the illegitimate use of authority in a spiritual dimension.', "Once we know ringworm infection causes symptoms, we also know that the statement 'plants take in air through their leaves' can be considered false.", 'One may reasonably assume that if the claim that ringworm infection causes symptoms does not reflect reality, then manes are a ruff of long hair around the neck which is brown in the front and black in the back.', 'Given that the claim that ringworm infection causes symptoms does not reflect reality, it can be inferred that the statement that states manes are a ruff of long hair around the neck which is brown in the front and black in the back is false.']
|
We know that either witchcraft is the illegitimate use of authority in a spiritual dimension or either plants take in air through their leaves or bones come in all shapes and sizes. It is a common misconception that witchcraft is the illegitimate use of authority in a spiritual dimension. Once we know ringworm infection causes symptoms, we also know that the statement 'plants take in air through their leaves' can be considered false. One may reasonably assume that if the claim that ringworm infection causes symptoms does not reflect reality, then manes are a ruff of long hair around the neck which is brown in the front and black in the back. Given that the claim that ringworm infection causes symptoms does not reflect reality, it can be inferred that the statement that states manes are a ruff of long hair around the neck which is brown in the front and black in the back is false.
|
Many people rightly believe that bones come in all shapes and sizes.
|
The notion that 'bones come in all shapes and sizes' is untrue.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [3] or (Either [1] or [0].).
Not [3].
Therefore, Either [1] or [0]..
[SC2-1]
Modus Ponens:
If [2], then (Not [1].).
[2] [SC2-2]
Therefore, Not [1]..
[SC2-2]
Reductio Ad Absurdum:
If (Not [2].), then [4].
If (Not [2].), then (Not [4].).
Therefore, [2].
|
{0: 'Bones come in all shapes and sizes.', 1: 'Plants take in air through their leaves.', 2: 'Ringworm infection causes symptoms.', 3: 'Witchcraft is the illegitimate use of authority in a spiritual dimension.', 4: 'Manes are a ruff of long hair around the neck which is brown in the front and black in the back.'}
| 4 |
3,767 |
['One may reasonably assume that if bacteria are both useful and harmful to humans, then the claim that biodiversity is important to people in many ways is false.', 'Either basketball players sprain their ankles more often than they nail groupies or either bacteria are both useful and harmful to humans or either statistics show that nearly all sexual assaults are committed by men against women or girls or every signal has a frequency spectrum.', 'We know that the claim that basketball players sprain their ankles more often than they nail groupies is false.', 'Provided that some people mistakenly believe that if either statistics show that nearly all sexual assaults are committed by men against women or girls or every signal has a frequency spectrum, then the claim that biodiversity is important to people in many ways is false, we know that the statement, if most spiders prey on diamondback moth larvae, then an internal representation is content, does not hold.', 'One may reasonably assume that if if most bees survive, the hornets are toast, then magnetism also has two distinct and separate fields and a neutral zone, then if some people mistakenly believe that if either statistics show that nearly all sexual assaults are committed by men against women or girls or every signal has a frequency spectrum, then the claim that biodiversity is important to people in many ways is false, then if most spiders prey on diamondback moth larvae, then an internal representation is content.', 'Once we know most bees survive, the hornets are toast, we also know that magnetism also has two distinct and separate fields and a neutral zone.']
|
One may reasonably assume that if bacteria are both useful and harmful to humans, then the claim that biodiversity is important to people in many ways is false. Either basketball players sprain their ankles more often than they nail groupies or either bacteria are both useful and harmful to humans or either statistics show that nearly all sexual assaults are committed by men against women or girls or every signal has a frequency spectrum. We know that the claim that basketball players sprain their ankles more often than they nail groupies is false. Provided that some people mistakenly believe that if either statistics show that nearly all sexual assaults are committed by men against women or girls or every signal has a frequency spectrum, then the claim that biodiversity is important to people in many ways is false, we know that the statement, if most spiders prey on diamondback moth larvae, then an internal representation is content, does not hold. One may reasonably assume that if if most bees survive, the hornets are toast, then magnetism also has two distinct and separate fields and a neutral zone, then if some people mistakenly believe that if either statistics show that nearly all sexual assaults are committed by men against women or girls or every signal has a frequency spectrum, then the claim that biodiversity is important to people in many ways is false, then if most spiders prey on diamondback moth larvae, then an internal representation is content. Once we know most bees survive, the hornets are toast, we also know that magnetism also has two distinct and separate fields and a neutral zone.
|
The claim that biodiversity is important to people in many ways is false.
|
The claim that biodiversity is important to people in many ways is false.
|
TRUE
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].). [SC1-1]
If [1], then (Not [0].).
If (Either [2] or [3].), then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [4] or (Either [1] or (Either [2] or [3].).).
Not [4].
Therefore, Either [1] or (Either [2] or [3].)..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If (Either [2] or [3].), then (Not [0].).).), then (If [5], then [6].). [SC1-2]
If (Not (If (Either [2] or [3].), then (Not [0].).).), then (Not (If [5], then [6].).).
Therefore, If (Either [2] or [3].), then (Not [0].)..
[SC1-2]
Modus Ponens:
If (If [7], then [8].), then (If (Not (If (Either [2] or [3].), then (Not [0].).).), then (If [5], then [6].).).
If [7], then [8].
Therefore, If (Not (If (Either [2] or [3].), then (Not [0].).).), then (If [5], then [6].)..
|
{0: 'Biodiversity is important to people in many ways.', 1: 'Bacteria are both useful and harmful to humans.', 2: 'Statistics show that nearly all sexual assaults are committed by men against women or girls.', 3: 'Every signal has a frequency spectrum.', 4: 'Basketball players sprain their ankles more often than they nail groupies.', 5: 'Most spiders prey on diamondback moth larvae.', 6: 'An internal representation is content.', 7: 'Most bees survive, the hornets are toast.', 8: 'Magnetism also has two distinct and separate fields and a neutral zone.'}
| 4 |
3,999 |
["So long as the statement, atheists trust in the ability of people to find solutions to their problems, does not hold, 'sleep is a well-studied means of escape from stress, confusion, and conflict for many people' is true.", "So long as sleep is a well-studied means of escape from stress, confusion, and conflict for many people, 'young people care about their appearance' is true.", 'Some people mistakenly believe that heterotrophs eat ready - made complex organic food.', 'Given that the statement that states if young people care about their appearance, then heterotrophs eat ready - made complex organic food is false, it can be inferred that infidelity is usually a sign of something wrong within the marriage.', 'If the statement that states if young people care about their appearance, then heterotrophs eat ready - made complex organic food is false, then the statement, infidelity is usually a sign of something wrong within the marriage, does not hold.']
|
So long as the statement, atheists trust in the ability of people to find solutions to their problems, does not hold, 'sleep is a well-studied means of escape from stress, confusion, and conflict for many people' is true. So long as sleep is a well-studied means of escape from stress, confusion, and conflict for many people, 'young people care about their appearance' is true. Some people mistakenly believe that heterotrophs eat ready - made complex organic food. Given that the statement that states if young people care about their appearance, then heterotrophs eat ready - made complex organic food is false, it can be inferred that infidelity is usually a sign of something wrong within the marriage. If the statement that states if young people care about their appearance, then heterotrophs eat ready - made complex organic food is false, then the statement, infidelity is usually a sign of something wrong within the marriage, does not hold.
|
It is rational to agree that atheists trust in the ability of people to find solutions to their problems.
|
The statement that states atheists trust in the ability of people to find solutions to their problems is false.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [2].
If [2], then [1].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Modus Tonens:
If [1], then [3]. [SC1-2]
Not [3].
Therefore, Not [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [1], then [3].).), then [4].
If (Not (If [1], then [3].).), then (Not [4].).
Therefore, If [1], then [3]..
|
{0: 'Atheists trust in the ability of people to find solutions to their problems.', 1: 'Young people care about their appearance.', 2: 'Sleep is a well-studied means of escape from stress, confusion, and conflict for many people.', 3: 'Heterotrophs eat ready - made complex organic food.', 4: 'Infidelity is usually a sign of something wrong within the marriage.'}
| 4 |
3,467 |
['We know that either electricity only runs at certain times during the day or asteroids move and their apparent emission levels can vary by large amounts.', 'When electricity only runs at certain times during the day is true, it follows that if yeast are microscopic, single-celled organisms that are classified in the family Fungi, then most connective tissue contains collagen fiber.', 'Once we know asteroids move and their apparent emission levels can vary by large amounts, we also know that if yeast are microscopic, single-celled organisms that are classified in the family Fungi, then most connective tissue contains collagen fiber.', 'It is not true that weather is an entity that dictates our lives.', 'There is good reason to believe that either gypsum occurs as micro crystals or either weather is an entity that dictates our lives or the statement, most connective tissue contains collagen fiber, does not hold.', 'It is not the case that gypsum occurs as micro crystals.']
|
We know that either electricity only runs at certain times during the day or asteroids move and their apparent emission levels can vary by large amounts. When electricity only runs at certain times during the day is true, it follows that if yeast are microscopic, single-celled organisms that are classified in the family Fungi, then most connective tissue contains collagen fiber. Once we know asteroids move and their apparent emission levels can vary by large amounts, we also know that if yeast are microscopic, single-celled organisms that are classified in the family Fungi, then most connective tissue contains collagen fiber. It is not true that weather is an entity that dictates our lives. There is good reason to believe that either gypsum occurs as micro crystals or either weather is an entity that dictates our lives or the statement, most connective tissue contains collagen fiber, does not hold. It is not the case that gypsum occurs as micro crystals.
|
The notion that 'yeast are microscopic, single-celled organisms that are classified in the family Fungi' is untrue.
|
It is a common misconception that yeast is actually a type of fungus related to mushrooms.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If [0], then [1].).
If [3], then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC2-1]
Disjunctive Syllogism:
Either [4] or (Not [1].). [SC1-2]
Not [4].
Therefore, Not [1]..
[SC1-2]
Disjunctive Syllogism:
Either [5] or (Either [4] or (Not [1].).).
Not [5].
Therefore, Either [4] or (Not [1].)..
|
{0: 'Yeast are microscopic, single-celled organisms that are classified in the family Fungi.', 1: 'Most connective tissue contains collagen fiber.', 2: 'Electricity only runs at certain times during the day.', 3: 'Asteroids move and their apparent emission levels can vary by large amounts.', 4: 'Weather is an entity that dictates our lives.', 5: 'Gypsum occurs as micro crystals.'}
| 4 |
3,315 |
['It is a fact that either cancer is a water sign known for being loyal or liquid waste is piped into lagoons.', "The statement 'most hippopotamuses emerge at nights' can be considered false.", 'One may reasonably assume that if the statement that states either most hippopotamuses emerge at nights or the claim that cancer is a water sign known for being loyal does not reflect reality is false, then some reactions occurring in stars are neither pure fusion nor pure fission reactions.', 'Should it be the case that some reactions occurring in stars are neither pure fusion nor pure fission reactions, it follows that p waves are sound waves and propagate through both solids and liquids.', 'Assuming some reactions occurring in stars are neither pure fusion nor pure fission reactions, we know that those that suggest p waves are sound waves and propagate through both solids and liquids are wrong.']
|
It is a fact that either cancer is a water sign known for being loyal or liquid waste is piped into lagoons. The statement 'most hippopotamuses emerge at nights' can be considered false. One may reasonably assume that if the statement that states either most hippopotamuses emerge at nights or the claim that cancer is a water sign known for being loyal does not reflect reality is false, then some reactions occurring in stars are neither pure fusion nor pure fission reactions. Should it be the case that some reactions occurring in stars are neither pure fusion nor pure fission reactions, it follows that p waves are sound waves and propagate through both solids and liquids. Assuming some reactions occurring in stars are neither pure fusion nor pure fission reactions, we know that those that suggest p waves are sound waves and propagate through both solids and liquids are wrong.
|
The idea that liquid waste is piped into lagoons is true.
|
The idea that liquid waste is piped into lagoons is true.
|
TRUE
|
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 Tonens:
If (Not (Either [2] or (Not [1].).).), then [3].
Not [3]. [SC2-3]
Therefore, Either [2] or (Not [1].)..
[SC2-3]
Reductio Ad Absurdum:
If [3], then [4].
If [3], then (Not [4].).
Therefore, Not [3]..
|
{0: 'Liquid waste is piped into lagoons.', 1: 'Cancer is a water sign known for being loyal.', 2: 'Most hippopotamuses emerge at nights.', 3: 'Some reactions occurring in stars are neither pure fusion nor pure fission reactions.', 4: 'P waves are sound waves and propagate through both solids and liquids.'}
| 4 |
3,989 |
['On the condition that some people really believe Witches can fly, it is definitely the case that capital punishment is a contradiction in every sense of the word.', 'Should it be the case that multimedia is the integration of numerous types of media, it follows that if temperature control is a factor in disease control, then sanctification involves a real change of qualities and disposition.', "The notion that 'if temperature control is a factor in disease control, then sanctification involves a real change of qualities and disposition' is untrue.", "So long as dining rooms are part of dwellings, 'if capital punishment is a contradiction in every sense of the word, then multimedia is the integration of numerous types of media' is true.", 'It is reasonable to believe that dining rooms are part of dwellings.']
|
On the condition that some people really believe Witches can fly, it is definitely the case that capital punishment is a contradiction in every sense of the word. Should it be the case that multimedia is the integration of numerous types of media, it follows that if temperature control is a factor in disease control, then sanctification involves a real change of qualities and disposition. The notion that 'if temperature control is a factor in disease control, then sanctification involves a real change of qualities and disposition' is untrue. So long as dining rooms are part of dwellings, 'if capital punishment is a contradiction in every sense of the word, then multimedia is the integration of numerous types of media' is true. It is reasonable to believe that dining rooms are part of dwellings.
|
We know that the claim that some people really believe Witches can fly is false.
|
It is not true that some people call rainforest the air condition of the planet earth.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Hypothetical Syllogism:
If [0], then [4].
If [4], then [1]. [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Modus Ponens:
If [5], then (If [4], then [1].).
[5]
Therefore, If [4], then [1]..
[SC2-1]
Modus Tonens:
If [1], then (If [2], then [3].).
Not (If [2], then [3].).
Therefore, Not [1]..
|
{0: 'Some people really believe Witches can fly.', 1: 'Multimedia is the integration of numerous types of media.', 2: 'Temperature control is a factor in disease control.', 3: 'Sanctification involves a real change of qualities and disposition.', 4: 'Capital punishment is a contradiction in every sense of the word.', 5: 'Dining rooms are part of dwellings.'}
| 4 |
3,922 |
["The statement that 'heads are used for accumulate knowledge' is incorrect.", 'The statement, most cobras live in areas, does not hold.', 'It is rational to believe that either some pine grows in other countries or tiger barbs feature various colored stripes on their bodies.', 'Once we know tiger barbs feature various colored stripes on their bodies, we also know that either most cobras live in areas or if the claim that linear algebra has many applications - in engineering, science, and social science is false, then heads are used for accumulate knowledge.', 'Once we know armies are military forces, we also know that if some pine grows in other countries, then either most cobras live in areas or if the claim that linear algebra has many applications - in engineering, science, and social science is false, then heads are used for accumulate knowledge.', 'It is reasonable to believe that armies are military forces.']
|
The statement that 'heads are used for accumulate knowledge' is incorrect. The statement, most cobras live in areas, does not hold. It is rational to believe that either some pine grows in other countries or tiger barbs feature various colored stripes on their bodies. Once we know tiger barbs feature various colored stripes on their bodies, we also know that either most cobras live in areas or if the claim that linear algebra has many applications - in engineering, science, and social science is false, then heads are used for accumulate knowledge. Once we know armies are military forces, we also know that if some pine grows in other countries, then either most cobras live in areas or if the claim that linear algebra has many applications - in engineering, science, and social science is false, then heads are used for accumulate knowledge. It is reasonable to believe that armies are military forces.
|
The statement 'linear algebra has many applications - in engineering, science, and social science' can be considered true.
|
The statement 'linear algebra has many applications - in engineering, science, and social science' can be considered true.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then [1].). [SC1-2]
Not [2].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Either [2] or (If (Not [0].), then [1].).). [SC2-3]
If [4], then (Either [2] or (If (Not [0].), then [1].).).
Therefore, Either [2] or (If (Not [0].), then [1].)..
[SC2-3]
Modus Ponens:
If [5], then (If [3], then (Either [2] or (If (Not [0].), then [1].).).).
[5]
Therefore, If [3], then (Either [2] or (If (Not [0].), then [1].).)..
|
{0: 'Linear algebra has many applications - in engineering, science, and social science.', 1: 'Heads are used for accumulate knowledge.', 2: 'Most cobras live in areas.', 3: 'Some pine grows in other countries.', 4: 'Tiger barbs feature various colored stripes on their bodies.', 5: 'Armies are military forces.'}
| 4 |
3,717 |
['At least one of two things is true: lullabies are a universal expression of love, or either higher fungi are almost unique in their ability to decay the chemical components of timber or aBA is do novo synthesized in response to osmotic stress.', 'Given that lullabies are a universal expression of love, it can be inferred that either spoiled fish have a sharp, peppery taste or some plantains have starches.', 'Once we know either spoiled fish have a sharp, peppery taste or some plantains have starches, we also know that some cats create litterboxes in places like playgrounds and sandpits.', 'Assuming either spoiled fish have a sharp, peppery taste or some plantains have starches, we know that the statement, some cats create litterboxes in places like playgrounds and sandpits, does not hold.', "Whenever it is true that we know that the claim that if either higher fungi are almost unique in their ability to decay the chemical components of timber or aBA is do novo synthesized in response to osmotic stress, then ammonia levels are pH dependent, and can fluctuate throughout the day is false, 'bull giraffes have necks' is true.", 'The statement, bull giraffes have necks, does not hold.']
|
At least one of two things is true: lullabies are a universal expression of love, or either higher fungi are almost unique in their ability to decay the chemical components of timber or aBA is do novo synthesized in response to osmotic stress. Given that lullabies are a universal expression of love, it can be inferred that either spoiled fish have a sharp, peppery taste or some plantains have starches. Once we know either spoiled fish have a sharp, peppery taste or some plantains have starches, we also know that some cats create litterboxes in places like playgrounds and sandpits. Assuming either spoiled fish have a sharp, peppery taste or some plantains have starches, we know that the statement, some cats create litterboxes in places like playgrounds and sandpits, does not hold. Whenever it is true that we know that the claim that if either higher fungi are almost unique in their ability to decay the chemical components of timber or aBA is do novo synthesized in response to osmotic stress, then ammonia levels are pH dependent, and can fluctuate throughout the day is false, 'bull giraffes have necks' is true. The statement, bull giraffes have necks, does not hold.
|
It is true that ammonia levels are pH dependent, and can fluctuate throughout the day.
|
It is true that ammonia levels are pH dependent, and can fluctuate throughout the day.
|
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 [3] or (Either [4] or [5].).
If [3], then (Either [1] or [2].).
If (Either [4] or [5].), then [0]. [SC3-2]
Therefore, Either (Either [1] or [2].) or [0]..
[SC3-2]
Modus Tonens:
If (Not (If (Either [4] or [5].), then [0].).), then [7].
Not [7].
Therefore, If (Either [4] or [5].), then [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Either [1] or [2].), then [6].
If (Either [1] or [2].), then (Not [6].).
Therefore, Not (Either [1] or [2].)..
|
{0: 'Ammonia levels are pH dependent, and can fluctuate throughout the day.', 1: 'Spoiled fish have a sharp, peppery taste.', 2: 'Some plantains have starches.', 3: 'Lullabies are a universal expression of love.', 4: 'Higher fungi are almost unique in their ability to decay the chemical components of timber.', 5: 'ABA is do novo synthesized in response to osmotic stress.', 6: 'Some cats create litterboxes in places like playgrounds and sandpits.', 7: 'Bull giraffes have necks.'}
| 4 |
3,458 |
['The claim that cambers are alignment holds true.', 'Once we know some people mistakenly believe that if cambers are alignment, then associations represent relationships between objects in associated classes, we also know that fish living in cold water have slower metabolic rates.', 'It is a common misconception that fish living in cold water have slower metabolic rates.', 'Once we know some people mistakenly believe that if associations represent relationships between objects in associated classes, then peonies require winter cold to flower, we also know that either kelp forests draw their name from an analogy to forests on land or syringes have removable needles with flexible tips.', 'The claim that either kelp forests draw their name from an analogy to forests on land or syringes have removable needles with flexible tips is false.']
|
The claim that cambers are alignment holds true. Once we know some people mistakenly believe that if cambers are alignment, then associations represent relationships between objects in associated classes, we also know that fish living in cold water have slower metabolic rates. It is a common misconception that fish living in cold water have slower metabolic rates. Once we know some people mistakenly believe that if associations represent relationships between objects in associated classes, then peonies require winter cold to flower, we also know that either kelp forests draw their name from an analogy to forests on land or syringes have removable needles with flexible tips. The claim that either kelp forests draw their name from an analogy to forests on land or syringes have removable needles with flexible tips is false.
|
The statement 'peonies require winter cold to flower' can be considered true.
|
The statement 'peonies require winter cold to flower' can be considered true.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If [1], then [2]. [SC1-2]
If [2], then [0]. [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Modus Tonens:
If (Not (If [1], then [2].).), then [5].
Not [5].
Therefore, If [1], then [2]..
[SC2-2]
Modus Tonens:
If (Not (If [2], then [0].).), then (Either [3] or [4].).
Not (Either [3] or [4].).
Therefore, If [2], then [0]..
|
{0: 'Peonies require winter cold to flower.', 1: 'Cambers are alignment.', 2: 'Associations represent relationships between objects in associated classes.', 3: 'Kelp forests draw their name from an analogy to forests on land.', 4: 'Syringes have removable needles with flexible tips.', 5: 'Fish living in cold water have slower metabolic rates.'}
| 4 |
3,773 |
['There is good reason to believe that either food passes through the pylorus and into the duodenum where further digestion occurs or iridium is used principally in alloys.', "Assuming food passes through the pylorus and into the duodenum where further digestion occurs, we know that if the statement 'peru has (part) Amazon' can be considered false, then most plants contain water.", 'Once we know either virtual reality is a three-dimensional world that has interaction with the user or retinal detachments can occur, we also know that the claim that most plants contain water does not reflect reality.', 'There is good reason to believe that either virtual reality is a three-dimensional world that has interaction with the user or retinal detachments can occur.', "One may reasonably assume that if the notion that 'if iridium is used principally in alloys, then if the statement 'peru has (part) Amazon' can be considered false, then most plants contain water' is untrue, then either biological value is a measure of the food nitrogen in protein that the body retains or some cats are quite content to live their lives behind closed doors.", 'The statement, either biological value is a measure of the food nitrogen in protein that the body retains or some cats are quite content to live their lives behind closed doors, does not hold.']
|
There is good reason to believe that either food passes through the pylorus and into the duodenum where further digestion occurs or iridium is used principally in alloys. Assuming food passes through the pylorus and into the duodenum where further digestion occurs, we know that if the statement 'peru has (part) Amazon' can be considered false, then most plants contain water. Once we know either virtual reality is a three-dimensional world that has interaction with the user or retinal detachments can occur, we also know that the claim that most plants contain water does not reflect reality. There is good reason to believe that either virtual reality is a three-dimensional world that has interaction with the user or retinal detachments can occur. One may reasonably assume that if the notion that 'if iridium is used principally in alloys, then if the statement 'peru has (part) Amazon' can be considered false, then most plants contain water' is untrue, then either biological value is a measure of the food nitrogen in protein that the body retains or some cats are quite content to live their lives behind closed doors. The statement, either biological value is a measure of the food nitrogen in protein that the body retains or some cats are quite content to live their lives behind closed doors, does not hold.
|
It is reasonable to believe that peru has (part) Amazon.
|
It is reasonable to believe that peru has (part) Amazon.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not [0].), then [1].).
If [5], then (If (Not [0].), then [1].). [SC3-2]
Therefore, If (Not [0].), then [1]..
[SC3-2]
Modus Tonens:
If (Not (If [5], then (If (Not [0].), then [1].).).), then (Either [6] or [7].).
Not (Either [6] or [7].).
Therefore, If [5], then (If (Not [0].), then [1].)..
[SC2-1]
Modus Ponens:
If (Either [2] or [3].), then (Not [1].).
Either [2] or [3].
Therefore, Not [1]..
|
{0: 'Peru has (part) Amazon.', 1: 'Most plants contain water.', 2: 'Virtual reality is a three-dimensional world that has interaction with the user.', 3: 'Retinal detachments can occur.', 4: 'Food passes through the pylorus and into the duodenum where further digestion occurs.', 5: 'Iridium is used principally in alloys.', 6: 'Biological value is a measure of the food nitrogen in protein that the body retains.', 7: 'Some cats are quite content to live their lives behind closed doors.'}
| 4 |
3,204 |
['The statement that states most trees live in tropical areas is false.', 'The statement, melons are a tender annual, does not hold.', 'Should it be the case that it is not the case that either melons are a tender annual or either most trees live in tropical areas or air is mixture, it follows that implementation inheritance is a mechanism by which classes share implementation.', 'One may reasonably assume that if it is not true that if it is not the case that either melons are a tender annual or either most trees live in tropical areas or air is mixture, then we know that the claim that implementation inheritance is a mechanism by which classes share implementation is false, then most microscopic plants use energy.', "On the condition that it is not true that if it is not the case that either melons are a tender annual or either most trees live in tropical areas or air is mixture, then we know that the claim that implementation inheritance is a mechanism by which classes share implementation is false, it is definitely the case that the statement 'most microscopic plants use energy' can be considered false."]
|
The statement that states most trees live in tropical areas is false. The statement, melons are a tender annual, does not hold. Should it be the case that it is not the case that either melons are a tender annual or either most trees live in tropical areas or air is mixture, it follows that implementation inheritance is a mechanism by which classes share implementation. One may reasonably assume that if it is not true that if it is not the case that either melons are a tender annual or either most trees live in tropical areas or air is mixture, then we know that the claim that implementation inheritance is a mechanism by which classes share implementation is false, then most microscopic plants use energy. On the condition that it is not true that if it is not the case that either melons are a tender annual or either most trees live in tropical areas or air is mixture, then we know that the claim that implementation inheritance is a mechanism by which classes share implementation is false, it is definitely the case that the statement 'most microscopic plants use energy' can be considered false.
|
It is a simple truth that air is mixture.
|
Air contains nitrogen, which is harmful for some steel grades.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (Either [1] or [0].). [SC1-2]
Not [2].
Therefore, Either [1] or [0]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [2] or (Either [1] or [0].).).), then [3].
If (Not (Either [2] or (Either [1] or [0].).).), then (Not [3].). [SC2-3]
Therefore, Either [2] or (Either [1] or [0].)..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If (Not (Either [2] or (Either [1] or [0].).).), then (Not [3].).).), then [4].
If (Not (If (Not (Either [2] or (Either [1] or [0].).).), then (Not [3].).).), then (Not [4].).
Therefore, If (Not (Either [2] or (Either [1] or [0].).).), then (Not [3].)..
|
{0: 'Air is mixture.', 1: 'Most trees live in tropical areas.', 2: 'Melons are a tender annual.', 3: 'Implementation inheritance is a mechanism by which classes share implementation.', 4: 'Most microscopic plants use energy.'}
| 4 |
3,834 |
['Provided that those that suggest camellias rival the azaleas for ease of growth and beauty of form and foliage throughout the year are wrong, we know that most women experience severe breast pain.', 'One may reasonably assume that if some people mistakenly believe that if regression testing can also relate to data validation, then the claim that most women experience severe breast pain is false, then home education occurs when parents choose to educate their children from a home base.', 'When some people mistakenly believe that if regression testing can also relate to data validation, then the claim that most women experience severe breast pain is false is true, it follows that some people mistakenly believe that home education occurs when parents choose to educate their children from a home base.', 'Assuming if latex gloves are the most common cause of latex allergies and severe latex allergic reactions, then preschoolers choose friends based on who they see regularly, we know that regression testing can also relate to data validation.', "So long as latex gloves are the most common cause of latex allergies and severe latex allergic reactions, 'preschoolers choose friends based on who they see regularly' is true."]
|
Provided that those that suggest camellias rival the azaleas for ease of growth and beauty of form and foliage throughout the year are wrong, we know that most women experience severe breast pain. One may reasonably assume that if some people mistakenly believe that if regression testing can also relate to data validation, then the claim that most women experience severe breast pain is false, then home education occurs when parents choose to educate their children from a home base. When some people mistakenly believe that if regression testing can also relate to data validation, then the claim that most women experience severe breast pain is false is true, it follows that some people mistakenly believe that home education occurs when parents choose to educate their children from a home base. Assuming if latex gloves are the most common cause of latex allergies and severe latex allergic reactions, then preschoolers choose friends based on who they see regularly, we know that regression testing can also relate to data validation. So long as latex gloves are the most common cause of latex allergies and severe latex allergic reactions, 'preschoolers choose friends based on who they see regularly' is true.
|
Many people rightly believe that camellias rival the azaleas for ease of growth and beauty of form and foliage throughout the year.
|
Camellias are common in warm temperate climates and bloom generally while it is cool outside.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [2], then (Not [1].). [SC1-2]
[2] [SC2-2]
Therefore, Not [1]..
[SC1-2]
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].)..
[SC2-2]
Modus Ponens:
If (If [4], then [5].), then [2].
If [4], then [5].
Therefore, [2].
|
{0: 'Camellias rival the azaleas for ease of growth and beauty of form and foliage throughout the year.', 1: 'Most women experience severe breast pain.', 2: 'Regression testing can also relate to data validation.', 3: 'Home education occurs when parents choose to educate their children from a home base.', 4: 'Latex gloves are the most common cause of latex allergies and severe latex allergic reactions.', 5: 'Preschoolers choose friends based on who they see regularly.'}
| 4 |
3,832 |
['When the claim that either some women fight with their in-laws or some serious diseases cause death does not correspond with reality is true, it follows that dehydration is an issue in cold winter months just as it is in the summer.', 'Provided that dehydration is an issue in cold winter months just as it is in the summer, we know that some broccolis belong to families.', 'It is rational to believe that either ayurvedic medicine has several key foundations that pertain to health and disease or most organisms obtain food.', "One may reasonably assume that if most organisms obtain food, then the statement 'some broccolis belong to families' can be considered false.", "Should it be the case that the statement 'if ayurvedic medicine has several key foundations that pertain to health and disease, then the statement 'some broccolis belong to families' can be considered false' can be considered false, it follows that flash animation is used to give interaction and animation .", "Once we know the statement 'if ayurvedic medicine has several key foundations that pertain to health and disease, then the statement 'some broccolis belong to families' can be considered false' can be considered false, we also know that the claim that flash animation is used to give interaction and animation has no merit."]
|
When the claim that either some women fight with their in-laws or some serious diseases cause death does not correspond with reality is true, it follows that dehydration is an issue in cold winter months just as it is in the summer. Provided that dehydration is an issue in cold winter months just as it is in the summer, we know that some broccolis belong to families. It is rational to believe that either ayurvedic medicine has several key foundations that pertain to health and disease or most organisms obtain food. One may reasonably assume that if most organisms obtain food, then the statement 'some broccolis belong to families' can be considered false. Should it be the case that the statement 'if ayurvedic medicine has several key foundations that pertain to health and disease, then the statement 'some broccolis belong to families' can be considered false' can be considered false, it follows that flash animation is used to give interaction and animation . Once we know the statement 'if ayurvedic medicine has several key foundations that pertain to health and disease, then the statement 'some broccolis belong to families' can be considered false' can be considered false, we also know that the claim that flash animation is used to give interaction and animation has no merit.
|
We know that either some women fight with their in-laws or some serious diseases cause death.
|
Those that suggest either some women fight with their in-laws or some serious diseases cause death are wrong.
|
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 [3].
If [3], then [2].
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC2-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Not [2].). [SC2-2]
If [5], then (Not [2].).
Therefore, Not [2]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [4], then (Not [2].).).), then [6].
If (Not (If [4], then (Not [2].).).), then (Not [6].).
Therefore, If [4], then (Not [2].)..
|
{0: 'Some women fight with their in-laws.', 1: 'Some serious diseases cause death.', 2: 'Some broccolis belong to families.', 3: 'Dehydration is an issue in cold winter months just as it is in the summer.', 4: 'Ayurvedic medicine has several key foundations that pertain to health and disease.', 5: 'Most organisms obtain food.', 6: 'Flash animation is used to give interaction and animation .'}
| 4 |
3,435 |
['We know that at least one of two things is true: scallops are curves, or most plants have hereditary factors.', 'Should it be the case that scallops are curves, it follows that either natural selection is a kind of combinatorial optimiation process or drug abuse can have serious legal consequences.', 'One may reasonably assume that if most plants have hereditary factors, then either natural selection is a kind of combinatorial optimiation process or drug abuse can have serious legal consequences.', 'When latex paints use water as the solvent and are therefore less toxic is true, it follows that if natural selection is a kind of combinatorial optimiation process, then if gonadotropins are natural human hormones that can cause a powerful stimulation of the ovaries, then potassium promotes healthy digestion.', 'The statement that states latex paints use water as the solvent and are therefore less toxic is right.', "Whenever it is true that drug abuse can have serious legal consequences, 'longitude is a series of imaginary lines radiating from the North and South poles' is true.", 'One may reasonably assume that if longitude is a series of imaginary lines radiating from the North and South poles, then if gonadotropins are natural human hormones that can cause a powerful stimulation of the ovaries, then potassium promotes healthy digestion.']
|
We know that at least one of two things is true: scallops are curves, or most plants have hereditary factors. Should it be the case that scallops are curves, it follows that either natural selection is a kind of combinatorial optimiation process or drug abuse can have serious legal consequences. One may reasonably assume that if most plants have hereditary factors, then either natural selection is a kind of combinatorial optimiation process or drug abuse can have serious legal consequences. When latex paints use water as the solvent and are therefore less toxic is true, it follows that if natural selection is a kind of combinatorial optimiation process, then if gonadotropins are natural human hormones that can cause a powerful stimulation of the ovaries, then potassium promotes healthy digestion. The statement that states latex paints use water as the solvent and are therefore less toxic is right. Whenever it is true that drug abuse can have serious legal consequences, 'longitude is a series of imaginary lines radiating from the North and South poles' is true. One may reasonably assume that if longitude is a series of imaginary lines radiating from the North and South poles, then if gonadotropins are natural human hormones that can cause a powerful stimulation of the ovaries, then potassium promotes healthy digestion.
|
Should it be the case that gonadotropins are natural human hormones that can cause a powerful stimulation of the ovaries, it follows that potassium promotes healthy digestion.
|
It is a common misconception that if gonadotropins are natural human hormones that can cause a powerful stimulation of the ovaries, then potassium promotes healthy digestion.
|
FALSE
|
Disjunction Elimination:
Either [2] or [3]. [SC1-1]
If [2], then (If [0], then [1].). [SC2-1]
If [3], then (If [0], then [1].). [SC3-1]
Therefore, If [0], then [1]..
[SC1-1]
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]..
[SC2-1]
Modus Ponens:
If [7], then (If [2], then (If [0], then [1].).).
[7]
Therefore, If [2], then (If [0], then [1].)..
[SC3-1]
Hypothetical Syllogism:
If [3], then [6].
If [6], then (If [0], then [1].).
Therefore, If [3], then (If [0], then [1].)..
|
{0: 'Gonadotropins are natural human hormones that can cause a powerful stimulation of the ovaries.', 1: 'Potassium promotes healthy digestion.', 2: 'Natural selection is a kind of combinatorial optimiation process.', 3: 'Drug abuse can have serious legal consequences.', 4: 'Scallops are curves.', 5: 'Most plants have hereditary factors.', 6: 'Longitude is a series of imaginary lines radiating from the North and South poles.', 7: 'Latex paints use water as the solvent and are therefore less toxic.'}
| 4 |
3,005 |
['Either one or both of these statements are true: dams die shortly after they abort, or homos have (part) sections.', "So long as homos have (part) sections, 'smoking affects pregnancy ' is true.", 'Provided that those that suggest either investigations explore same issues or if dams die shortly after they abort, then smoking affects pregnancy are wrong, we know that different animals rely on different food sources.', 'One may reasonably assume that if those that suggest either investigations explore same issues or if dams die shortly after they abort, then smoking affects pregnancy are wrong, then the statement that states different animals rely on different food sources is false.', "Whenever it is true that investigations explore same issues, 'fruits are the normal source of alkali in the diet' is true.", 'The claim that fruits are the normal source of alkali in the diet has no merit.']
|
Either one or both of these statements are true: dams die shortly after they abort, or homos have (part) sections. So long as homos have (part) sections, 'smoking affects pregnancy ' is true. Provided that those that suggest either investigations explore same issues or if dams die shortly after they abort, then smoking affects pregnancy are wrong, we know that different animals rely on different food sources. One may reasonably assume that if those that suggest either investigations explore same issues or if dams die shortly after they abort, then smoking affects pregnancy are wrong, then the statement that states different animals rely on different food sources is false. Whenever it is true that investigations explore same issues, 'fruits are the normal source of alkali in the diet' is true. The claim that fruits are the normal source of alkali in the diet has no merit.
|
It is the case that smoking affects pregnancy .
|
Smoking causes changes in blood levels of certain nutrients such as carbohydrates and proteins.
|
Uncertain
|
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]. [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [3] or (If [1], then [0].).).), then [4].
If (Not (Either [3] or (If [1], then [0].).).), then (Not [4].).
Therefore, Either [3] or (If [1], then [0].)..
[SC2-2]
Modus Tonens:
If [3], then [5].
Not [5].
Therefore, Not [3]..
|
{0: 'Smoking affects pregnancy .', 1: 'Dams die shortly after they abort.', 2: 'Homos have (part) sections.', 3: 'Investigations explore same issues.', 4: 'Different animals rely on different food sources.', 5: 'Fruits are the normal source of alkali in the diet.'}
| 4 |
3,769 |
["The statement 'posture greatly influences breathing' can be considered true.", "Given that the statement that 'if it is a common misconception that if posture greatly influences breathing, then if thin membranes protect the beaver's eyes when underwater, then disc golf is more popular today than ever, then electronic communities connect government, education, and business' is incorrect, it can be inferred that some people also question the morality of manipulating the genetic material of living creatures.", 'It is a common misconception that some people also question the morality of manipulating the genetic material of living creatures.', "Should it be the case that it is a common misconception that if posture greatly influences breathing, then if thin membranes protect the beaver's eyes when underwater, then disc golf is more popular today than ever, it follows that barn owls rely on open fields for hunting.", 'On the condition that barn owls rely on open fields for hunting, it is definitely the case that we know that the claim that electronic communities connect government, education, and business is false.']
|
The statement 'posture greatly influences breathing' can be considered true. Given that the statement that 'if it is a common misconception that if posture greatly influences breathing, then if thin membranes protect the beaver's eyes when underwater, then disc golf is more popular today than ever, then electronic communities connect government, education, and business' is incorrect, it can be inferred that some people also question the morality of manipulating the genetic material of living creatures. It is a common misconception that some people also question the morality of manipulating the genetic material of living creatures. Should it be the case that it is a common misconception that if posture greatly influences breathing, then if thin membranes protect the beaver's eyes when underwater, then disc golf is more popular today than ever, it follows that barn owls rely on open fields for hunting. On the condition that barn owls rely on open fields for hunting, it is definitely the case that we know that the claim that electronic communities connect government, education, and business is false.
|
Once we know thin membranes protect the beaver's eyes when underwater, we also know that disc golf is more popular today than ever.
|
Whenever it is true that thin membranes protect the beaver's eyes when underwater, 'disc golf is an affordable family activity that can be enjoyed by all ages' is true.
|
Uncertain
|
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]. [SC1-2]
If (Not (If [2], then (If [0], then [1].).).), then (Not [3].). [SC2-2]
Therefore, If [2], then (If [0], then [1].)..
[SC1-2]
Modus Tonens:
If (Not (If (Not (If [2], then (If [0], then [1].).).), then [3].).), then [4].
Not [4].
Therefore, If (Not (If [2], then (If [0], then [1].).).), then [3]..
[SC2-2]
Hypothetical Syllogism:
If (Not (If [2], then (If [0], then [1].).).), then [5].
If [5], then (Not [3].).
Therefore, If (Not (If [2], then (If [0], then [1].).).), then (Not [3].)..
|
{0: "Thin membranes protect the beaver's eyes when underwater.", 1: 'Disc golf is more popular today than ever.', 2: 'Posture greatly influences breathing.', 3: 'Electronic communities connect government, education, and business.', 4: 'Some people also question the morality of manipulating the genetic material of living creatures.', 5: 'Barn owls rely on open fields for hunting.'}
| 4 |
3,679 |
['Given that if eugenic abortion is justified as being a kindness to defectives, then personal hygiene is important during a herpes outbreak, it can be inferred that paralysis is thought to have been the cause of death.', 'If chemicals help keep our food fresh and our bodies clean, then either if eugenic abortion is justified as being a kindness to defectives, then personal hygiene is important during a herpes outbreak or most turtles have prey.', 'The statement that states chemicals help keep our food fresh and our bodies clean is right.', "When the notion that 'if most turtles have prey, then paralysis is thought to have been the cause of death' is untrue is true, it follows that poverty is bearable when it is bereft of debt.", "Whenever it is true that poverty is bearable when it is bereft of debt, 'most elephant tusks grow throughout lifetimes' is true.", "The notion that 'most elephant tusks grow throughout lifetimes' is untrue."]
|
Given that if eugenic abortion is justified as being a kindness to defectives, then personal hygiene is important during a herpes outbreak, it can be inferred that paralysis is thought to have been the cause of death. If chemicals help keep our food fresh and our bodies clean, then either if eugenic abortion is justified as being a kindness to defectives, then personal hygiene is important during a herpes outbreak or most turtles have prey. The statement that states chemicals help keep our food fresh and our bodies clean is right. When the notion that 'if most turtles have prey, then paralysis is thought to have been the cause of death' is untrue is true, it follows that poverty is bearable when it is bereft of debt. Whenever it is true that poverty is bearable when it is bereft of debt, 'most elephant tusks grow throughout lifetimes' is true. The notion that 'most elephant tusks grow throughout lifetimes' is untrue.
|
The statement 'paralysis is thought to have been the cause of death' is true.
|
Paralysis leads to breathe difficulty.
|
Uncertain
|
Disjunction Elimination:
Either (If [1], then [2].) or [3]. [SC1-1]
If (If [1], then [2].), then [0].
If [3], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [4], then (Either (If [1], then [2].) or [3].).
[4]
Therefore, Either (If [1], then [2].) or [3]..
[SC3-1]
Modus Tonens:
If (Not (If [3], then [0].).), then [5].
Not [5]. [SC2-2]
Therefore, If [3], then [0]..
[SC2-2]
Modus Tonens:
If [5], then [6].
Not [6].
Therefore, Not [5]..
|
{0: 'Paralysis is thought to have been the cause of death.', 1: 'Eugenic abortion is justified as being a kindness to defectives.', 2: 'Personal hygiene is important during a herpes outbreak.', 3: 'Most turtles have prey.', 4: 'Chemicals help keep our food fresh and our bodies clean.', 5: 'Poverty is bearable when it is bereft of debt.', 6: 'Most elephant tusks grow throughout lifetimes.'}
| 4 |
3,722 |
['Either one or both of these statements are true: if spirituality is a broad concept that encompasses values, meaning and purpose, then some minerals can be both crystalline and amorphous, or fifth grade is a time to prepare children for middle school.', "So long as if spirituality is a broad concept that encompasses values, meaning and purpose, then some minerals can be both crystalline and amorphous, 'a neuroblast is a cell' is true.", 'One may reasonably assume that if a neuroblast is a cell, then if cranes continue to be used in new symbolic ways around the world, then handles are part of racket.', 'Assuming if cranes continue to be used in new symbolic ways around the world, then handles are part of racket, we know that suburban sprawl is the result of zoning.', "The notion that 'suburban sprawl is the result of zoning' is untrue."]
|
Either one or both of these statements are true: if spirituality is a broad concept that encompasses values, meaning and purpose, then some minerals can be both crystalline and amorphous, or fifth grade is a time to prepare children for middle school. So long as if spirituality is a broad concept that encompasses values, meaning and purpose, then some minerals can be both crystalline and amorphous, 'a neuroblast is a cell' is true. One may reasonably assume that if a neuroblast is a cell, then if cranes continue to be used in new symbolic ways around the world, then handles are part of racket. Assuming if cranes continue to be used in new symbolic ways around the world, then handles are part of racket, we know that suburban sprawl is the result of zoning. The notion that 'suburban sprawl is the result of zoning' is untrue.
|
The statement that states fifth grade is a time to prepare children for middle school is right.
|
The statement, fifth grade is a time to prepare children for middle school, does not hold.
|
FALSE
|
Disjunctive Syllogism:
Either (If [1], then [2].) or [0].
Not (If [1], then [2].). [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (If [1], then [2].), then [3].
Not [3]. [SC2-2]
Therefore, Not (If [1], then [2].)..
[SC2-2]
Modus Tonens:
If [3], then (If [4], then [5].).
Not (If [4], then [5].). [SC2-3]
Therefore, Not [3]..
[SC2-3]
Modus Tonens:
If (If [4], then [5].), then [6].
Not [6].
Therefore, Not (If [4], then [5].)..
|
{0: 'Fifth grade is a time to prepare children for middle school.', 1: 'Spirituality is a broad concept that encompasses values, meaning and purpose.', 2: 'Some minerals can be both crystalline and amorphous.', 3: 'A neuroblast is a cell.', 4: 'Cranes continue to be used in new symbolic ways around the world.', 5: 'Handles are part of racket.', 6: 'Suburban sprawl is the result of zoning.'}
| 4 |
3,215 |
["So long as digital mammograms allow an immediate picture of the full breast, including tissue nearest the skin, 'either humans have intestinal infection or if some scientists believe that there is a growing shortage of fish in the sea, then roses are sensitive to gases in the atmosphere' is true.", "The statement 'digital mammograms allow an immediate picture of the full breast, including tissue nearest the skin' is true.", 'It is not true that if teachs communicates, then vapor is heavier than air and can cause suffocation by reducing the available oxygen for breathing.', 'On the condition that those that suggest if humans have intestinal infection, then if teachs communicates, then vapor is heavier than air and can cause suffocation by reducing the available oxygen for breathing are wrong, it is definitely the case that gophers clip off roots and strip bark below ground from young trees in windbreaks and orchards.', 'It is not the case that gophers clip off roots and strip bark below ground from young trees in windbreaks and orchards.']
|
So long as digital mammograms allow an immediate picture of the full breast, including tissue nearest the skin, 'either humans have intestinal infection or if some scientists believe that there is a growing shortage of fish in the sea, then roses are sensitive to gases in the atmosphere' is true. The statement 'digital mammograms allow an immediate picture of the full breast, including tissue nearest the skin' is true. It is not true that if teachs communicates, then vapor is heavier than air and can cause suffocation by reducing the available oxygen for breathing. On the condition that those that suggest if humans have intestinal infection, then if teachs communicates, then vapor is heavier than air and can cause suffocation by reducing the available oxygen for breathing are wrong, it is definitely the case that gophers clip off roots and strip bark below ground from young trees in windbreaks and orchards. It is not the case that gophers clip off roots and strip bark below ground from young trees in windbreaks and orchards.
|
Assuming some scientists believe that there is a growing shortage of fish in the sea, we know that roses are sensitive to gases in the atmosphere.
|
Assuming some scientists believe that there is a growing shortage of fish in the sea, we know that roses are sensitive to gases in the atmosphere.
|
TRUE
|
Disjunctive Syllogism:
Either [2] or (If [0], then [1].). [SC1-1]
Not [2]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Modus Ponens:
If [3], then (Either [2] or (If [0], then [1].).).
[3]
Therefore, Either [2] or (If [0], then [1].)..
[SC2-1]
Modus Tonens:
If [2], then (If [4], then [5].). [SC1-2]
Not (If [4], then [5].).
Therefore, Not [2]..
[SC1-2]
Modus Tonens:
If (Not (If [2], then (If [4], then [5].).).), then [6].
Not [6].
Therefore, If [2], then (If [4], then [5].)..
|
{0: 'Some scientists believe that there is a growing shortage of fish in the sea.', 1: 'Roses are sensitive to gases in the atmosphere.', 2: 'Humans have intestinal infection.', 3: 'Digital mammograms allow an immediate picture of the full breast, including tissue nearest the skin.', 4: 'Teachs communicates.', 5: 'Vapor is heavier than air and can cause suffocation by reducing the available oxygen for breathing.', 6: 'Gophers clip off roots and strip bark below ground from young trees in windbreaks and orchards.'}
| 4 |
3,653 |
['We know that either mammals adapt for life or indestructible plastic is used extensively in construction of vehicles, buildings, and machinery.', 'Given that mammals adapt for life, it can be inferred that either if large waves generate plumes of spray and thunderous explosions as they surge into the sea caves, then snakes have sharp senses or some people mistakenly believe that auditory learners tend to spell phonetically.', "Whenever it is true that if large waves generate plumes of spray and thunderous explosions as they surge into the sea caves, then snakes have sharp senses, 'monosaccharides are sweet-tasting solids that are very soluble in water' is true.", "Once we know if large waves generate plumes of spray and thunderous explosions as they surge into the sea caves, then snakes have sharp senses, we also know that the notion that 'monosaccharides are sweet-tasting solids that are very soluble in water' is untrue.", 'Assuming it is not the case that if indestructible plastic is used extensively in construction of vehicles, buildings, and machinery, then either if large waves generate plumes of spray and thunderous explosions as they surge into the sea caves, then snakes have sharp senses or some people mistakenly believe that auditory learners tend to spell phonetically, we know that married couples can volunteer to mentor the life of a child.', "One may reasonably assume that if it is not the case that if indestructible plastic is used extensively in construction of vehicles, buildings, and machinery, then either if large waves generate plumes of spray and thunderous explosions as they surge into the sea caves, then snakes have sharp senses or some people mistakenly believe that auditory learners tend to spell phonetically, then the statement that 'married couples can volunteer to mentor the life of a child' is incorrect."]
|
We know that either mammals adapt for life or indestructible plastic is used extensively in construction of vehicles, buildings, and machinery. Given that mammals adapt for life, it can be inferred that either if large waves generate plumes of spray and thunderous explosions as they surge into the sea caves, then snakes have sharp senses or some people mistakenly believe that auditory learners tend to spell phonetically. Whenever it is true that if large waves generate plumes of spray and thunderous explosions as they surge into the sea caves, then snakes have sharp senses, 'monosaccharides are sweet-tasting solids that are very soluble in water' is true. Once we know if large waves generate plumes of spray and thunderous explosions as they surge into the sea caves, then snakes have sharp senses, we also know that the notion that 'monosaccharides are sweet-tasting solids that are very soluble in water' is untrue. Assuming it is not the case that if indestructible plastic is used extensively in construction of vehicles, buildings, and machinery, then either if large waves generate plumes of spray and thunderous explosions as they surge into the sea caves, then snakes have sharp senses or some people mistakenly believe that auditory learners tend to spell phonetically, we know that married couples can volunteer to mentor the life of a child. One may reasonably assume that if it is not the case that if indestructible plastic is used extensively in construction of vehicles, buildings, and machinery, then either if large waves generate plumes of spray and thunderous explosions as they surge into the sea caves, then snakes have sharp senses or some people mistakenly believe that auditory learners tend to spell phonetically, then the statement that 'married couples can volunteer to mentor the life of a child' is incorrect.
|
Some people mistakenly believe that auditory learners tend to spell phonetically.
|
The statement, auditory learners do better when they hear information presented, does not hold.
|
Uncertain
|
Disjunctive Syllogism:
Either (If [1], then [2].) or (Not [0].). [SC1-1]
Not (If [1], then [2].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Either (If [1], then [2].) or (Not [0].).).
If [5], then (Either (If [1], then [2].) or (Not [0].).). [SC3-2]
Therefore, Either (If [1], then [2].) or (Not [0].)..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If [5], then (Either (If [1], then [2].) or (Not [0].).).).), then [6].
If (Not (If [5], then (Either (If [1], then [2].) or (Not [0].).).).), then (Not [6].).
Therefore, If [5], then (Either (If [1], then [2].) or (Not [0].).)..
[SC2-1]
Reductio Ad Absurdum:
If (If [1], then [2].), then [3].
If (If [1], then [2].), then (Not [3].).
Therefore, Not (If [1], then [2].)..
|
{0: 'Auditory learners tend to spell phonetically.', 1: 'Large waves generate plumes of spray and thunderous explosions as they surge into the sea caves.', 2: 'Snakes have sharp senses.', 3: 'Monosaccharides are sweet-tasting solids that are very soluble in water.', 4: 'Mammals adapt for life.', 5: 'Indestructible plastic is used extensively in construction of vehicles, buildings, and machinery.', 6: 'Married couples can volunteer to mentor the life of a child.'}
| 4 |
3,150 |
["Should it be the case that livestock is seen as a symbol of wealth and is often exchanged for bride prices, it follows that either if nature is the world's most prestigious weekly journal of science, then most retail stores sell cheese by weight or the claim that monocytes evolve into macrophages does not correspond with reality.", "The statement 'livestock is seen as a symbol of wealth and is often exchanged for bride prices' is true.", 'Those that suggest most cats drink liquids are wrong.', "So long as resiliency can emerge at any time in one's life, 'either most cats drink liquids or those that suggest if nature is the world's most prestigious weekly journal of science, then most retail stores sell cheese by weight are wrong' is true.", "The claim that resiliency can emerge at any time in one's life is true."]
|
Should it be the case that livestock is seen as a symbol of wealth and is often exchanged for bride prices, it follows that either if nature is the world's most prestigious weekly journal of science, then most retail stores sell cheese by weight or the claim that monocytes evolve into macrophages does not correspond with reality. The statement 'livestock is seen as a symbol of wealth and is often exchanged for bride prices' is true. Those that suggest most cats drink liquids are wrong. So long as resiliency can emerge at any time in one's life, 'either most cats drink liquids or those that suggest if nature is the world's most prestigious weekly journal of science, then most retail stores sell cheese by weight are wrong' is true. The claim that resiliency can emerge at any time in one's life is true.
|
The claim that monocytes evolve into macrophages does not correspond with reality.
|
The claim that monocytes evolve into macrophages does not correspond with reality.
|
TRUE
|
Disjunctive Syllogism:
Either (If [1], then [2].) or (Not [0].). [SC1-1]
Not (If [1], then [2].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [3], then (Either (If [1], then [2].) or (Not [0].).).
[3]
Therefore, Either (If [1], then [2].) or (Not [0].)..
[SC2-1]
Disjunctive Syllogism:
Either [4] or (Not (If [1], then [2].).). [SC1-2]
Not [4].
Therefore, Not (If [1], then [2].)..
[SC1-2]
Modus Ponens:
If [5], then (Either [4] or (Not (If [1], then [2].).).).
[5]
Therefore, Either [4] or (Not (If [1], then [2].).)..
|
{0: 'Monocytes evolve into macrophages.', 1: "Nature is the world's most prestigious weekly journal of science.", 2: 'Most retail stores sell cheese by weight.', 3: 'Livestock is seen as a symbol of wealth and is often exchanged for bride prices.', 4: 'Most cats drink liquids.', 5: "Resiliency can emerge at any time in one's life."}
| 4 |
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