id
int64 0
7k
| premises
stringlengths 118
4.1k
| paragraph
stringlengths 111
4.06k
| conclusion
stringlengths 15
240
| question
stringlengths 14
249
| label
stringclasses 3
values | arg
stringlengths 54
2.02k
| statements
stringlengths 51
1.12k
| depth
int64 1
7
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|---|---|---|---|---|---|---|---|---|
3,651 |
['Some people mistakenly believe that topiaries come in many sizes and shapes.', 'Should it be the case that some people mistakenly believe that either dependence can develop as a psychological craving or if if most tissue serves functions, then summers are hot, even very hot, then topiaries come in many sizes and shapes, it follows that melanocyte isa cell.', "The statement 'melanocyte isa cell' can be considered false.", 'When ascomycetes come in many shapes and sizes is true, it follows that the claim that dependence can develop as a psychological craving is false.', 'Those that suggest ascomycetes come in many shapes and sizes are right.']
|
Some people mistakenly believe that topiaries come in many sizes and shapes. Should it be the case that some people mistakenly believe that either dependence can develop as a psychological craving or if if most tissue serves functions, then summers are hot, even very hot, then topiaries come in many sizes and shapes, it follows that melanocyte isa cell. The statement 'melanocyte isa cell' can be considered false. When ascomycetes come in many shapes and sizes is true, it follows that the claim that dependence can develop as a psychological craving is false. Those that suggest ascomycetes come in many shapes and sizes are right.
|
The claim that if most tissue serves functions, then summers are hot, even very hot does not reflect reality.
|
Assuming most tissue serves functions, we know that summers are hot, even very hot.
|
FALSE
|
Modus Tonens:
If (If [0], then [1].), then [2]. [SC1-1]
Not [2].
Therefore, Not (If [0], then [1].)..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If (If [0], then [1].), then [2].). [SC1-2]
Not [3]. [SC2-2]
Therefore, If (If [0], then [1].), then [2]..
[SC1-2]
Modus Tonens:
If (Not (Either [3] or (If (If [0], then [1].), then [2].).).), then [5].
Not [5].
Therefore, Either [3] or (If (If [0], then [1].), then [2].)..
[SC2-2]
Modus Ponens:
If [4], then (Not [3].).
[4]
Therefore, Not [3]..
|
{0: 'Most tissue serves functions.', 1: 'Summers are hot, even very hot.', 2: 'Topiaries come in many sizes and shapes.', 3: 'Dependence can develop as a psychological craving.', 4: 'Ascomycetes come in many shapes and sizes.', 5: 'Melanocyte isa cell.'}
| 4 |
3,669 |
['The claim that most turkeys feed in fields is true.', "Whenever it is true that it is not the case that if most turkeys feed in fields, then if education is an investment in the future of our children and our nation, then some viruses cause oral papillomas, 'either most plants protect roots or cats can also do serious damage to dogs' is true.", 'It is a fact that either many pistols have such a low trigger resistance that the trigger can be fired by a very young child or if it is not the case that if most turkeys feed in fields, then if education is an investment in the future of our children and our nation, then some viruses cause oral papillomas, then it is a common misconception that either most plants protect roots or cats can also do serious damage to dogs.', "So long as many pistols have such a low trigger resistance that the trigger can be fired by a very young child, 'geophytes accommodate a high number of medicinal plants' is true.", "Given that many pistols have such a low trigger resistance that the trigger can be fired by a very young child, it can be inferred that the statement that 'geophytes accommodate a high number of medicinal plants' is incorrect."]
|
The claim that most turkeys feed in fields is true. Whenever it is true that it is not the case that if most turkeys feed in fields, then if education is an investment in the future of our children and our nation, then some viruses cause oral papillomas, 'either most plants protect roots or cats can also do serious damage to dogs' is true. It is a fact that either many pistols have such a low trigger resistance that the trigger can be fired by a very young child or if it is not the case that if most turkeys feed in fields, then if education is an investment in the future of our children and our nation, then some viruses cause oral papillomas, then it is a common misconception that either most plants protect roots or cats can also do serious damage to dogs. So long as many pistols have such a low trigger resistance that the trigger can be fired by a very young child, 'geophytes accommodate a high number of medicinal plants' is true. Given that many pistols have such a low trigger resistance that the trigger can be fired by a very young child, it can be inferred that the statement that 'geophytes accommodate a high number of medicinal plants' is incorrect.
|
Given that education is an investment in the future of our children and our nation, it can be inferred that some viruses cause oral papillomas.
|
One may reasonably assume that if education results in learning, then some viruses cause oral papillomas.
|
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 (Either [3] or [4].).
If (Not (If [2], then (If [0], then [1].).).), then (Not (Either [3] or [4].).). [SC2-2]
Therefore, If [2], then (If [0], then [1].)..
[SC2-2]
Disjunctive Syllogism:
Either [5] or (If (Not (If [2], then (If [0], then [1].).).), then (Not (Either [3] or [4].).).).
Not [5]. [SC2-3]
Therefore, If (Not (If [2], then (If [0], then [1].).).), then (Not (Either [3] or [4].).)..
[SC2-3]
Reductio Ad Absurdum:
If [5], then [6].
If [5], then (Not [6].).
Therefore, Not [5]..
|
{0: 'Education is an investment in the future of our children and our nation.', 1: 'Some viruses cause oral papillomas.', 2: 'Most turkeys feed in fields.', 3: 'Most plants protect roots.', 4: 'Cats can also do serious damage to dogs.', 5: 'Many pistols have such a low trigger resistance that the trigger can be fired by a very young child.', 6: 'Geophytes accommodate a high number of medicinal plants.'}
| 4 |
3,504 |
['Either one or both of these statements are true: either green lacewings can control mealybug fairly well and can be bought commercially from insectaries or involuntary smoking is just as harmful as direct smoking, or tendons can have very fast contraction times.', 'Given that either green lacewings can control mealybug fairly well and can be bought commercially from insectaries or involuntary smoking is just as harmful as direct smoking, it can be inferred that most lemurs feed in trees.', 'One may reasonably assume that if tendons can have very fast contraction times, then crocodiles are dinosaurs.', 'There is good reason to believe that either cocoa butter is a vegetable fat that looks like caramel or if most lemurs feed in trees, then either agricultural statistics Contains both current and historical data or menstruation is looked upon as a normal, healthy function.', 'The statement that states cocoa butter is a vegetable fat that looks like caramel is false.', 'One may reasonably assume that if if some people get queasy when riding in a car, on a train or in a plane, then silt is carried by moving water, then if crocodiles are dinosaurs, then either agricultural statistics Contains both current and historical data or menstruation is looked upon as a normal, healthy function.', 'Once we know some people get queasy when riding in a car, on a train or in a plane, we also know that silt is carried by moving water.']
|
Either one or both of these statements are true: either green lacewings can control mealybug fairly well and can be bought commercially from insectaries or involuntary smoking is just as harmful as direct smoking, or tendons can have very fast contraction times. Given that either green lacewings can control mealybug fairly well and can be bought commercially from insectaries or involuntary smoking is just as harmful as direct smoking, it can be inferred that most lemurs feed in trees. One may reasonably assume that if tendons can have very fast contraction times, then crocodiles are dinosaurs. There is good reason to believe that either cocoa butter is a vegetable fat that looks like caramel or if most lemurs feed in trees, then either agricultural statistics Contains both current and historical data or menstruation is looked upon as a normal, healthy function. The statement that states cocoa butter is a vegetable fat that looks like caramel is false. One may reasonably assume that if if some people get queasy when riding in a car, on a train or in a plane, then silt is carried by moving water, then if crocodiles are dinosaurs, then either agricultural statistics Contains both current and historical data or menstruation is looked upon as a normal, healthy function. Once we know some people get queasy when riding in a car, on a train or in a plane, we also know that silt is carried by moving water.
|
We know that at least one of two things is true: agricultural statistics Contains both current and historical data, or menstruation is looked upon as a normal, healthy function.
|
We know that at least one of two things is true: agricultural statistics Contains both current and historical data, or menstruation is looked upon as a normal, healthy function.
|
TRUE
|
Disjunction Elimination:
Either [2] or [3]. [SC1-1]
If [2], then (Either [0] or [1].). [SC2-1]
If [3], then (Either [0] or [1].). [SC3-1]
Therefore, Either [0] or [1]..
[SC1-1]
Constructive Dilemma:
Either (Either [4] or [5].) or [6].
If (Either [4] or [5].), then [2].
If [6], then [3].
Therefore, Either [2] or [3]..
[SC2-1]
Disjunctive Syllogism:
Either [7] or (If [2], then (Either [0] or [1].).).
Not [7].
Therefore, If [2], then (Either [0] or [1].)..
[SC3-1]
Modus Ponens:
If (If [8], then [9].), then (If [3], then (Either [0] or [1].).).
If [8], then [9].
Therefore, If [3], then (Either [0] or [1].)..
|
{0: 'Agricultural statistics Contains both current and historical data.', 1: 'Menstruation is looked upon as a normal, healthy function.', 2: 'Most lemurs feed in trees.', 3: 'Crocodiles are dinosaurs.', 4: 'Green lacewings can control mealybug fairly well and can be bought commercially from insectaries.', 5: 'Involuntary smoking is just as harmful as direct smoking.', 6: 'Tendons can have very fast contraction times.', 7: 'Cocoa butter is a vegetable fat that looks like caramel.', 8: 'Some people get queasy when riding in a car, on a train or in a plane.', 9: 'Silt is carried by moving water.'}
| 4 |
3,900 |
["Once we know the notion that 'biodiversity plays a powerful role in ecosystems by indicating the condition of the environment' is untrue, we also know that forests are clear cut for living space, crop growing, grazing for domestic livestock.", 'We know that at least one of two things is true: individuals consume red meat, or diversity is the life-blood of freelancing.', "Given that individuals consume red meat, it can be inferred that either intelligence is information gathering or if the notion that 'biodiversity plays a powerful role in ecosystems by indicating the condition of the environment' is untrue, then the claim that forests are clear cut for living space, crop growing, grazing for domestic livestock does not correspond with reality.", "So long as diversity is the life-blood of freelancing, 'either intelligence is information gathering or if the notion that 'biodiversity plays a powerful role in ecosystems by indicating the condition of the environment' is untrue, then the claim that forests are clear cut for living space, crop growing, grazing for domestic livestock does not correspond with reality' is true.", 'It is a fact that either earwigs are insects or if some parasites cause anemia, then source files are the files that programmers create when they write a program.', 'Given that earwigs are insects, it can be inferred that we know that the claim that intelligence is information gathering is false.', 'Given that if some parasites cause anemia, then source files are the files that programmers create when they write a program, it can be inferred that we know that the claim that intelligence is information gathering is false.']
|
Once we know the notion that 'biodiversity plays a powerful role in ecosystems by indicating the condition of the environment' is untrue, we also know that forests are clear cut for living space, crop growing, grazing for domestic livestock. We know that at least one of two things is true: individuals consume red meat, or diversity is the life-blood of freelancing. Given that individuals consume red meat, it can be inferred that either intelligence is information gathering or if the notion that 'biodiversity plays a powerful role in ecosystems by indicating the condition of the environment' is untrue, then the claim that forests are clear cut for living space, crop growing, grazing for domestic livestock does not correspond with reality. So long as diversity is the life-blood of freelancing, 'either intelligence is information gathering or if the notion that 'biodiversity plays a powerful role in ecosystems by indicating the condition of the environment' is untrue, then the claim that forests are clear cut for living space, crop growing, grazing for domestic livestock does not correspond with reality' is true. It is a fact that either earwigs are insects or if some parasites cause anemia, then source files are the files that programmers create when they write a program. Given that earwigs are insects, it can be inferred that we know that the claim that intelligence is information gathering is false. Given that if some parasites cause anemia, then source files are the files that programmers create when they write a program, it can be inferred that we know that the claim that intelligence is information gathering is false.
|
Many people rightly believe that biodiversity plays a powerful role in ecosystems by indicating the condition of the environment.
|
Many people rightly believe that biodiversity plays a powerful role in ecosystems by indicating the condition of the environment.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then (Not [1].).). [SC1-2]
Not [2]. [SC2-2]
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Either [2] or (If (Not [0].), then (Not [1].).).).
If [4], then (Either [2] or (If (Not [0].), then (Not [1].).).).
Therefore, Either [2] or (If (Not [0].), then (Not [1].).)..
[SC2-2]
Disjunction Elimination:
Either [5] or (If [6], then [7].).
If [5], then (Not [2].).
If (If [6], then [7].), then (Not [2].).
Therefore, Not [2]..
|
{0: 'Biodiversity plays a powerful role in ecosystems by indicating the condition of the environment.', 1: 'Forests are clear cut for living space, crop growing, grazing for domestic livestock.', 2: 'Intelligence is information gathering.', 3: 'Individuals consume red meat.', 4: 'Diversity is the life-blood of freelancing.', 5: 'Earwigs are insects.', 6: 'Some parasites cause anemia.', 7: 'Source files are the files that programmers create when they write a program.'}
| 4 |
3,649 |
["One may reasonably assume that if some people mistakenly believe that hieroglyphics are bands, then the notion that 'wheat germ is sold in grocery stores and food markets' is untrue.", 'Provided that it is not the case that if some people mistakenly believe that hieroglyphics are bands, then wheat germ is sold in grocery stores and food markets, we know that if tapirs have (part) cells, then pancreatic supplements reduce symptomatic response of healthy subjects to a high fat meal.', 'Provided that if tapirs have (part) cells, then pancreatic supplements reduce symptomatic response of healthy subjects to a high fat meal, we know that authors give final approval.', 'On the condition that authors give final approval, it is definitely the case that anger causes heating of the blood and an unpleasant appearance.', 'Assuming authors give final approval, we know that we know that the claim that anger causes heating of the blood and an unpleasant appearance is false.']
|
One may reasonably assume that if some people mistakenly believe that hieroglyphics are bands, then the notion that 'wheat germ is sold in grocery stores and food markets' is untrue. Provided that it is not the case that if some people mistakenly believe that hieroglyphics are bands, then wheat germ is sold in grocery stores and food markets, we know that if tapirs have (part) cells, then pancreatic supplements reduce symptomatic response of healthy subjects to a high fat meal. Provided that if tapirs have (part) cells, then pancreatic supplements reduce symptomatic response of healthy subjects to a high fat meal, we know that authors give final approval. On the condition that authors give final approval, it is definitely the case that anger causes heating of the blood and an unpleasant appearance. Assuming authors give final approval, we know that we know that the claim that anger causes heating of the blood and an unpleasant appearance is false.
|
It is the case that hieroglyphics are bands.
|
Hieroglyphics usually refers to the writing of ancient Egypt.
|
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]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Hypothetical Syllogism:
If (Not (If (Not [0].), then [1].).), then (If [4], then [5].).
If (If [4], then [5].), then [2].
Therefore, If (Not (If (Not [0].), then [1].).), then [2]..
[SC2-2]
Reductio Ad Absurdum:
If [2], then [3].
If [2], then (Not [3].).
Therefore, Not [2]..
|
{0: 'Hieroglyphics are bands.', 1: 'Wheat germ is sold in grocery stores and food markets.', 2: 'Authors give final approval.', 3: 'Anger causes heating of the blood and an unpleasant appearance.', 4: 'Tapirs have (part) cells.', 5: 'Pancreatic supplements reduce symptomatic response of healthy subjects to a high fat meal.'}
| 4 |
3,931 |
['Either some glossy privets have flowers or either otterhounds can be very bright dogs - at least when it comes to getting something they want or cocaine can be a very addictive drug.', 'Some people mistakenly believe that some glossy privets have flowers.', 'We know that either some willows contain substances or surgery can remove a tumor but it is the body that heals.', 'On the condition that some willows contain substances, it is definitely the case that if otterhounds can be very bright dogs - at least when it comes to getting something they want, then electric current is the flow of charges through a metal wire or through an electrical conductor.', "So long as surgery can remove a tumor but it is the body that heals, 'if otterhounds can be very bright dogs - at least when it comes to getting something they want, then electric current is the flow of charges through a metal wire or through an electrical conductor' is true.", 'There is good reason to believe that either trimmers is machines or if cocaine can be a very addictive drug, then electric current is the flow of charges through a metal wire or through an electrical conductor.', "The statement that 'trimmers is machines' is incorrect."]
|
Either some glossy privets have flowers or either otterhounds can be very bright dogs - at least when it comes to getting something they want or cocaine can be a very addictive drug. Some people mistakenly believe that some glossy privets have flowers. We know that either some willows contain substances or surgery can remove a tumor but it is the body that heals. On the condition that some willows contain substances, it is definitely the case that if otterhounds can be very bright dogs - at least when it comes to getting something they want, then electric current is the flow of charges through a metal wire or through an electrical conductor. So long as surgery can remove a tumor but it is the body that heals, 'if otterhounds can be very bright dogs - at least when it comes to getting something they want, then electric current is the flow of charges through a metal wire or through an electrical conductor' is true. There is good reason to believe that either trimmers is machines or if cocaine can be a very addictive drug, then electric current is the flow of charges through a metal wire or through an electrical conductor. The statement that 'trimmers is machines' is incorrect.
|
It is the case that electric current is the flow of charges through a metal wire or through an electrical conductor.
|
It is a common misconception that electric current is the flow of charges through a metal wire or through an electrical conductor.
|
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]
Disjunctive Syllogism:
Either [5] or (Either [1] or [2].).
Not [5].
Therefore, Either [1] or [2]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If [1], then [0].).
If [4], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC3-1]
Disjunctive Syllogism:
Either [6] or (If [2], then [0].).
Not [6].
Therefore, If [2], then [0]..
|
{0: 'Electric current is the flow of charges through a metal wire or through an electrical conductor.', 1: 'Otterhounds can be very bright dogs - at least when it comes to getting something they want.', 2: 'Cocaine can be a very addictive drug.', 3: 'Some willows contain substances.', 4: 'Surgery can remove a tumor but it is the body that heals.', 5: 'Some glossy privets have flowers.', 6: 'Trimmers is machines.'}
| 4 |
3,300 |
['It is a fact that either chronic pancreatitis can lead to diabetes, inability to digest food, or cancer of the pancreas or if most snails adapt to habitats, then milk has zero fiber.', 'Some people mistakenly believe that chronic pancreatitis can lead to diabetes, inability to digest food, or cancer of the pancreas.', "Once we know the notion that 'most snails adapt to habitats' is untrue, we also know that we know that the claim that soft layers tend to form slopes and harder layers form cliffs is false.", "If some people mistakenly believe that if the notion that 'most snails adapt to habitats' is untrue, then soft layers tend to form slopes and harder layers form cliffs, then rock pocket mice have dark fur.", "One may reasonably assume that if some people mistakenly believe that if the notion that 'most snails adapt to habitats' is untrue, then soft layers tend to form slopes and harder layers form cliffs, then the claim that rock pocket mice have dark fur does not correspond with reality."]
|
It is a fact that either chronic pancreatitis can lead to diabetes, inability to digest food, or cancer of the pancreas or if most snails adapt to habitats, then milk has zero fiber. Some people mistakenly believe that chronic pancreatitis can lead to diabetes, inability to digest food, or cancer of the pancreas. Once we know the notion that 'most snails adapt to habitats' is untrue, we also know that we know that the claim that soft layers tend to form slopes and harder layers form cliffs is false. If some people mistakenly believe that if the notion that 'most snails adapt to habitats' is untrue, then soft layers tend to form slopes and harder layers form cliffs, then rock pocket mice have dark fur. One may reasonably assume that if some people mistakenly believe that if the notion that 'most snails adapt to habitats' is untrue, then soft layers tend to form slopes and harder layers form cliffs, then the claim that rock pocket mice have dark fur does not correspond with reality.
|
It is a simple truth that milk has zero fiber.
|
It is a simple truth that milk has zero fiber.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [1], then [0].).
Not [2].
Therefore, If [1], then [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then [3]. [SC1-2]
If (Not [1].), then (Not [3].).
Therefore, [1].
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not [1].), then [3].).), then [4].
If (Not (If (Not [1].), then [3].).), then (Not [4].).
Therefore, If (Not [1].), then [3]..
|
{0: 'Milk has zero fiber.', 1: 'Most snails adapt to habitats.', 2: 'Chronic pancreatitis can lead to diabetes, inability to digest food, or cancer of the pancreas.', 3: 'Soft layers tend to form slopes and harder layers form cliffs.', 4: 'Rock pocket mice have dark fur.'}
| 4 |
3,674 |
["Once we know it is not the case that calves are likely more vulnerable than adults to such hunters, we also know that the statement that 'drugs can also help patients manage anemia' is incorrect.", 'It is a fact that either government exercises a great deal of power in modern society or most flowers absorb sunlight.', 'Should it be the case that most flowers absorb sunlight, it follows that if it is not the case that calves are likely more vulnerable than adults to such hunters, then drugs can also help patients manage anemia.', 'Given that oil is a fossil fuel that emits carbon dioxide and other pollutants when burned, it can be inferred that if government exercises a great deal of power in modern society, then if it is not the case that calves are likely more vulnerable than adults to such hunters, then drugs can also help patients manage anemia.', 'We know that either hedgehogs have (part) piluses or oil is a fossil fuel that emits carbon dioxide and other pollutants when burned.', 'The claim that hedgehogs have (part) piluses does not correspond with reality.']
|
Once we know it is not the case that calves are likely more vulnerable than adults to such hunters, we also know that the statement that 'drugs can also help patients manage anemia' is incorrect. It is a fact that either government exercises a great deal of power in modern society or most flowers absorb sunlight. Should it be the case that most flowers absorb sunlight, it follows that if it is not the case that calves are likely more vulnerable than adults to such hunters, then drugs can also help patients manage anemia. Given that oil is a fossil fuel that emits carbon dioxide and other pollutants when burned, it can be inferred that if government exercises a great deal of power in modern society, then if it is not the case that calves are likely more vulnerable than adults to such hunters, then drugs can also help patients manage anemia. We know that either hedgehogs have (part) piluses or oil is a fossil fuel that emits carbon dioxide and other pollutants when burned. The claim that hedgehogs have (part) piluses does not correspond with reality.
|
calves are likely more vulnerable than adults to such hunters.
|
Calves are likely more vulnerable than adults to such hunters.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If (Not [0].), then [1].). [SC2-2]
If [3], then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC2-2]
Modus Ponens:
If [4], then (If [2], then (If (Not [0].), then [1].).).
[4] [SC2-3]
Therefore, If [2], then (If (Not [0].), then [1].)..
[SC2-3]
Disjunctive Syllogism:
Either [5] or [4].
Not [5].
Therefore, [4].
|
{0: 'Calves are likely more vulnerable than adults to such hunters.', 1: 'Drugs can also help patients manage anemia.', 2: 'Government exercises a great deal of power in modern society.', 3: 'Most flowers absorb sunlight.', 4: 'Oil is a fossil fuel that emits carbon dioxide and other pollutants when burned.', 5: 'Hedgehogs have (part) piluses.'}
| 4 |
3,665 |
['There is good reason to believe that either some rays have teeth or if purulent drainage is present in the superior meatus, then sex has very little to do with thinking and a lot to do with instinct.', 'Assuming some rays have teeth, we know that if implants can impart on patients the well being of having regained their lost teeth, then mutant culture is tribal and primative and mutant language consists of grumbles and growls.', "So long as if purulent drainage is present in the superior meatus, then sex has very little to do with thinking and a lot to do with instinct, 'if implants can impart on patients the well being of having regained their lost teeth, then mutant culture is tribal and primative and mutant language consists of grumbles and growls' is true.", 'It is not true that if children to say goodbyes, then bigger fish mean more fish since large fish lay more eggs.', 'It is a fact that either some tail fins are part of argentines or either if children to say goodbyes, then bigger fish mean more fish since large fish lay more eggs or if implants can impart on patients the well being of having regained their lost teeth, then those that suggest mutant culture is tribal and primative and mutant language consists of grumbles and growls are wrong.', 'Some people mistakenly believe that some tail fins are part of argentines.']
|
There is good reason to believe that either some rays have teeth or if purulent drainage is present in the superior meatus, then sex has very little to do with thinking and a lot to do with instinct. Assuming some rays have teeth, we know that if implants can impart on patients the well being of having regained their lost teeth, then mutant culture is tribal and primative and mutant language consists of grumbles and growls. So long as if purulent drainage is present in the superior meatus, then sex has very little to do with thinking and a lot to do with instinct, 'if implants can impart on patients the well being of having regained their lost teeth, then mutant culture is tribal and primative and mutant language consists of grumbles and growls' is true. It is not true that if children to say goodbyes, then bigger fish mean more fish since large fish lay more eggs. It is a fact that either some tail fins are part of argentines or either if children to say goodbyes, then bigger fish mean more fish since large fish lay more eggs or if implants can impart on patients the well being of having regained their lost teeth, then those that suggest mutant culture is tribal and primative and mutant language consists of grumbles and growls are wrong. Some people mistakenly believe that some tail fins are part of argentines.
|
The statement, implants can impart on patients the well being of having regained their lost teeth, does not hold.
|
Some people mistakenly believe that implants interfere with mammograms making breast cancer detection more difficult.
|
Uncertain
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [2] or (If [3], then [4].).
If [2], then (If [0], then [1].).
If (If [3], then [4].), then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC2-1]
Disjunctive Syllogism:
Either (If [5], then [6].) or (If [0], then (Not [1].).). [SC1-2]
Not (If [5], then [6].).
Therefore, If [0], then (Not [1].)..
[SC1-2]
Disjunctive Syllogism:
Either [7] or (Either (If [5], then [6].) or (If [0], then (Not [1].).).).
Not [7].
Therefore, Either (If [5], then [6].) or (If [0], then (Not [1].).)..
|
{0: 'Implants can impart on patients the well being of having regained their lost teeth.', 1: 'Mutant culture is tribal and primative and mutant language consists of grumbles and growls.', 2: 'Some rays have teeth.', 3: 'Purulent drainage is present in the superior meatus.', 4: 'Sex has very little to do with thinking and a lot to do with instinct.', 5: 'Children to say goodbyes.', 6: 'Bigger fish mean more fish since large fish lay more eggs.', 7: 'Some tail fins are part of argentines.'}
| 4 |
3,570 |
["Given that the statement that 'all butterflies undergo a series of stages of development' is incorrect, it can be inferred that it is not true that toxins produce symptoms.", "Provided that it is a common misconception that if humidity increases while temperature decreases with altitude, then if the statement that 'all butterflies undergo a series of stages of development' is incorrect, then toxins produce symptoms, we know that spores formed in the capsules are released and grow to produce new plants.", 'The statement, spores formed in the capsules are released and grow to produce new plants, does not hold.', 'When young people fight, tend the wounded, and die is true, it follows that humidity increases while temperature decreases with altitude.', 'It is a simple truth that young people fight, tend the wounded, and die.']
|
Given that the statement that 'all butterflies undergo a series of stages of development' is incorrect, it can be inferred that it is not true that toxins produce symptoms. Provided that it is a common misconception that if humidity increases while temperature decreases with altitude, then if the statement that 'all butterflies undergo a series of stages of development' is incorrect, then toxins produce symptoms, we know that spores formed in the capsules are released and grow to produce new plants. The statement, spores formed in the capsules are released and grow to produce new plants, does not hold. When young people fight, tend the wounded, and die is true, it follows that humidity increases while temperature decreases with altitude. It is a simple truth that young people fight, tend the wounded, and die.
|
It is true that all butterflies undergo a series of stages of development.
|
Butterflies live anywhere from a few days to a few weeks.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (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]
Modus Tonens:
If (Not (If [2], then (If (Not [0].), then [1].).).), then [4].
Not [4].
Therefore, If [2], then (If (Not [0].), then [1].)..
[SC2-2]
Modus Ponens:
If [3], then [2].
[3]
Therefore, [2].
|
{0: 'All butterflies undergo a series of stages of development.', 1: 'Toxins produce symptoms.', 2: 'Humidity increases while temperature decreases with altitude.', 3: 'Young people fight, tend the wounded, and die.', 4: 'Spores formed in the capsules are released and grow to produce new plants.'}
| 4 |
3,163 |
["The statement 'core strength refers to abdominal strength' can be considered false.", 'The claim that fear is what makes bull riding the most popular of all rodeo events has no merit.', 'Should it be the case that it is a common misconception that either fear is what makes bull riding the most popular of all rodeo events or if carrot juice is juice, then core strength refers to abdominal strength, it follows that those that suggest sound becomes noise when it is unwanted, bothersome or painful are wrong.', 'On the condition that it is a common misconception that either fear is what makes bull riding the most popular of all rodeo events or if carrot juice is juice, then core strength refers to abdominal strength, it is definitely the case that metals used for plating include chromium, nickel, tin, and zinc.', "Whenever it is true that metals used for plating include chromium, nickel, tin, and zinc, 'sound becomes noise when it is unwanted, bothersome or painful' is true."]
|
The statement 'core strength refers to abdominal strength' can be considered false. The claim that fear is what makes bull riding the most popular of all rodeo events has no merit. Should it be the case that it is a common misconception that either fear is what makes bull riding the most popular of all rodeo events or if carrot juice is juice, then core strength refers to abdominal strength, it follows that those that suggest sound becomes noise when it is unwanted, bothersome or painful are wrong. On the condition that it is a common misconception that either fear is what makes bull riding the most popular of all rodeo events or if carrot juice is juice, then core strength refers to abdominal strength, it is definitely the case that metals used for plating include chromium, nickel, tin, and zinc. Whenever it is true that metals used for plating include chromium, nickel, tin, and zinc, 'sound becomes noise when it is unwanted, bothersome or painful' is true.
|
Some people mistakenly believe that carrot juice is juice.
|
The claim that carrot juice is juice is true.
|
FALSE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [0], then [1].). [SC1-2]
Not [2].
Therefore, If [0], then [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [2] or (If [0], then [1].).).), then [3]. [SC1-3]
If (Not (Either [2] or (If [0], then [1].).).), then (Not [3].).
Therefore, Either [2] or (If [0], then [1].)..
[SC1-3]
Hypothetical Syllogism:
If (Not (Either [2] or (If [0], then [1].).).), then [4].
If [4], then [3].
Therefore, If (Not (Either [2] or (If [0], then [1].).).), then [3]..
|
{0: 'Carrot juice is juice.', 1: 'Core strength refers to abdominal strength.', 2: 'Fear is what makes bull riding the most popular of all rodeo events.', 3: 'Sound becomes noise when it is unwanted, bothersome or painful.', 4: 'Metals used for plating include chromium, nickel, tin, and zinc.'}
| 4 |
3,336 |
["Whenever it is true that the statement that 'if goats desire food, then joint pain is common in infected adults, especially women' is incorrect, 'it is not the case that biomedical engineers design and develop medical instruments and equipment' is true.", 'Assuming goats desire food, we know that scrapers have (part) sections.', "If scrapers have (part) sections, then the statement 'joint pain is common in infected adults, especially women' can be considered false.", "So long as soldiers take arms, 'if the statement that 'if goats desire food, then joint pain is common in infected adults, especially women' is incorrect, then biomedical engineers design and develop medical instruments and equipment' is true.", 'It is fair to say that soldiers take arms.']
|
Whenever it is true that the statement that 'if goats desire food, then joint pain is common in infected adults, especially women' is incorrect, 'it is not the case that biomedical engineers design and develop medical instruments and equipment' is true. Assuming goats desire food, we know that scrapers have (part) sections. If scrapers have (part) sections, then the statement 'joint pain is common in infected adults, especially women' can be considered false. So long as soldiers take arms, 'if the statement that 'if goats desire food, then joint pain is common in infected adults, especially women' is incorrect, then biomedical engineers design and develop medical instruments and equipment' is true. It is fair to say that soldiers take arms.
|
The statement that states goats desire food is false.
|
The statement that states goats desire food is false.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then [3]. [SC1-2]
If (Not (If [0], then [1].).), then (Not [3].).
Therefore, If [0], then [1]..
[SC1-2]
Modus Ponens:
If [4], then (If (Not (If [0], then [1].).), then [3].).
[4]
Therefore, If (Not (If [0], then [1].).), then [3]..
[SC2-1]
Hypothetical Syllogism:
If [0], then [2].
If [2], then (Not [1].).
Therefore, If [0], then (Not [1].)..
|
{0: 'Goats desire food.', 1: 'Joint pain is common in infected adults, especially women.', 2: 'Scrapers have (part) sections.', 3: 'Biomedical engineers design and develop medical instruments and equipment.', 4: 'Soldiers take arms.'}
| 4 |
3,059 |
['There is good reason to believe that either either white sturgeon is fish or proteins need for growth or geographers continue to explore the relation between scale of representation and the issues studied.', "Whenever it is true that either white sturgeon is fish or proteins need for growth, 'either family rooms are used for family gathering or the claim that several sports involve domestic and farm animals, mostly dogs, oxen and formerly rams is false' is true.", 'Should it be the case that geographers continue to explore the relation between scale of representation and the issues studied, it follows that either family rooms are used for family gathering or the claim that several sports involve domestic and farm animals, mostly dogs, oxen and formerly rams is false.', 'We can assume that hand washing is a very simple, inexpensive way to prevent the transmission of infection.', "So long as it is not the case that if hand washing is a very simple, inexpensive way to prevent the transmission of infection, then it is a common misconception that family rooms are used for family gathering, 'an aberrant is a person' is true.", 'When it is not the case that if hand washing is a very simple, inexpensive way to prevent the transmission of infection, then it is a common misconception that family rooms are used for family gathering is true, it follows that some people mistakenly believe that an aberrant is a person.']
|
There is good reason to believe that either either white sturgeon is fish or proteins need for growth or geographers continue to explore the relation between scale of representation and the issues studied. Whenever it is true that either white sturgeon is fish or proteins need for growth, 'either family rooms are used for family gathering or the claim that several sports involve domestic and farm animals, mostly dogs, oxen and formerly rams is false' is true. Should it be the case that geographers continue to explore the relation between scale of representation and the issues studied, it follows that either family rooms are used for family gathering or the claim that several sports involve domestic and farm animals, mostly dogs, oxen and formerly rams is false. We can assume that hand washing is a very simple, inexpensive way to prevent the transmission of infection. So long as it is not the case that if hand washing is a very simple, inexpensive way to prevent the transmission of infection, then it is a common misconception that family rooms are used for family gathering, 'an aberrant is a person' is true. When it is not the case that if hand washing is a very simple, inexpensive way to prevent the transmission of infection, then it is a common misconception that family rooms are used for family gathering is true, it follows that some people mistakenly believe that an aberrant is a person.
|
The claim that several sports involve domestic and farm animals, mostly dogs, oxen and formerly rams is false.
|
The claim that several sports involve domestic and farm animals, mostly dogs, oxen and formerly rams is false.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either (Either [2] or [3].) or [4].
If (Either [2] or [3].), then (Either [1] or (Not [0].).).
If [4], then (Either [1] or (Not [0].).).
Therefore, Either [1] or (Not [0].)..
[SC2-1]
Modus Ponens:
If [5], then (Not [1].). [SC1-2]
[5]
Therefore, Not [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [5], then (Not [1].).).), then [6].
If (Not (If [5], then (Not [1].).).), then (Not [6].).
Therefore, If [5], then (Not [1].)..
|
{0: 'Several sports involve domestic and farm animals, mostly dogs, oxen and formerly rams.', 1: 'Family rooms are used for family gathering.', 2: 'White sturgeon is fish.', 3: 'Proteins need for growth.', 4: 'Geographers continue to explore the relation between scale of representation and the issues studied.', 5: 'Hand washing is a very simple, inexpensive way to prevent the transmission of infection.', 6: 'An aberrant is a person.'}
| 4 |
3,821 |
["It is a fact that either ice is a potent norepinephrine modulator, increasing it's effect or either windows require regular maintenance or if fuel system is used also as heat sink and to maintain aircraft trim, then lemurs have skulls.", "The statement that states ice is a potent norepinephrine modulator, increasing it's effect is false.", 'We know that the claim that rice is grown on natural flatlands is false.', 'We know that at least one of two things is true: mullets have (part) nuclei, or grain is of more value than blood.', 'If mullets have (part) nuclei, then if windows require regular maintenance, then rice is grown on natural flatlands.', "Whenever it is true that grain is of more value than blood, 'if windows require regular maintenance, then rice is grown on natural flatlands' is true."]
|
It is a fact that either ice is a potent norepinephrine modulator, increasing it's effect or either windows require regular maintenance or if fuel system is used also as heat sink and to maintain aircraft trim, then lemurs have skulls. The statement that states ice is a potent norepinephrine modulator, increasing it's effect is false. We know that the claim that rice is grown on natural flatlands is false. We know that at least one of two things is true: mullets have (part) nuclei, or grain is of more value than blood. If mullets have (part) nuclei, then if windows require regular maintenance, then rice is grown on natural flatlands. Whenever it is true that grain is of more value than blood, 'if windows require regular maintenance, then rice is grown on natural flatlands' is true.
|
When fuel system is used also as heat sink and to maintain aircraft trim is true, it follows that lemurs have skulls.
|
Some people mistakenly believe that if fuel system is used also as heat sink and to maintain aircraft trim, then lemurs have skulls.
|
FALSE
|
Disjunctive Syllogism:
Either [2] or (If [0], then [1].). [SC1-1]
Not [2]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (Either [2] or (If [0], then [1].).).
Not [3].
Therefore, Either [2] or (If [0], then [1].)..
[SC2-1]
Modus Tonens:
If [2], then [4]. [SC1-2]
Not [4].
Therefore, Not [2]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [2], then [4].).
If [6], then (If [2], then [4].).
Therefore, If [2], then [4]..
|
{0: 'Fuel system is used also as heat sink and to maintain aircraft trim.', 1: 'Lemurs have skulls.', 2: 'Windows require regular maintenance.', 3: "Ice is a potent norepinephrine modulator, increasing it's effect.", 4: 'Rice is grown on natural flatlands.', 5: 'Mullets have (part) nuclei.', 6: 'Grain is of more value than blood.'}
| 4 |
3,933 |
['Assuming it is not the case that if it is not the case that if cholesterol levels seem to be normally distributed, then human milk is the ultimate in renewable resources, then browns usually remain invisible until sun is off the water, we know that most walls go down thousands of feet.', "So long as it is not the case that if it is not the case that if cholesterol levels seem to be normally distributed, then human milk is the ultimate in renewable resources, then browns usually remain invisible until sun is off the water, 'the statement 'most walls go down thousands of feet' can be considered false' is true.", 'Assuming blame is placed on the relationship between men and their fathers or women and their mothers, we know that if it is not the case that if cholesterol levels seem to be normally distributed, then human milk is the ultimate in renewable resources, then the claim that browns usually remain invisible until sun is off the water does not correspond with reality.', "Either calves adopt their mother's status in hierarchy or blame is placed on the relationship between men and their fathers or women and their mothers.", "The claim that calves adopt their mother's status in hierarchy does not correspond with reality."]
|
Assuming it is not the case that if it is not the case that if cholesterol levels seem to be normally distributed, then human milk is the ultimate in renewable resources, then browns usually remain invisible until sun is off the water, we know that most walls go down thousands of feet. So long as it is not the case that if it is not the case that if cholesterol levels seem to be normally distributed, then human milk is the ultimate in renewable resources, then browns usually remain invisible until sun is off the water, 'the statement 'most walls go down thousands of feet' can be considered false' is true. Assuming blame is placed on the relationship between men and their fathers or women and their mothers, we know that if it is not the case that if cholesterol levels seem to be normally distributed, then human milk is the ultimate in renewable resources, then the claim that browns usually remain invisible until sun is off the water does not correspond with reality. Either calves adopt their mother's status in hierarchy or blame is placed on the relationship between men and their fathers or women and their mothers. The claim that calves adopt their mother's status in hierarchy does not correspond with reality.
|
One may reasonably assume that if cholesterol levels seem to be normally distributed, then human milk is the ultimate in renewable resources.
|
Provided that cholesterol levels are of great interest to consumers, we know that human milk is the ultimate in renewable resources
|
Uncertain
|
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then [2]. [SC1-1]
If (Not (If [0], then [1].).), then (Not [2].). [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not (If [0], then [1].).), then [2].).), then [4].
If (Not (If (Not (If [0], then [1].).), then [2].).), then (Not [4].).
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC2-1]
Modus Ponens:
If [3], then (If (Not (If [0], then [1].).), then (Not [2].).).
[3] [SC2-2]
Therefore, If (Not (If [0], then [1].).), then (Not [2].)..
[SC2-2]
Disjunctive Syllogism:
Either [5] or [3].
Not [5].
Therefore, [3].
|
{0: 'Cholesterol levels seem to be normally distributed.', 1: 'Human milk is the ultimate in renewable resources.', 2: 'Browns usually remain invisible until sun is off the water.', 3: 'Blame is placed on the relationship between men and their fathers or women and their mothers.', 4: 'Most walls go down thousands of feet.', 5: "Calves adopt their mother's status in hierarchy."}
| 4 |
3,490 |
['If the claim that reasonable valuations are now the driving force on stock prices everywhere in the world has no merit, then the claim that fat cells respond by giving up their little lives as they are burned for energy has no merit.', 'Should it be the case that spiritual muscles are like body muscles, it follows that aboriginal groups occupy the upland area around the borders of Cambodia.', 'If aboriginal groups occupy the upland area around the borders of Cambodia, then if the claim that reasonable valuations are now the driving force on stock prices everywhere in the world has no merit, then fat cells respond by giving up their little lives as they are burned for energy.', 'Either one or both of these statements are true: most large vessels carry blood, or if most snack food contains flour, then a rivet is a pin.', "Whenever it is true that most large vessels carry blood, 'spiritual muscles are like body muscles' is true.", 'Given that if most snack food contains flour, then a rivet is a pin, it can be inferred that spiritual muscles are like body muscles.']
|
If the claim that reasonable valuations are now the driving force on stock prices everywhere in the world has no merit, then the claim that fat cells respond by giving up their little lives as they are burned for energy has no merit. Should it be the case that spiritual muscles are like body muscles, it follows that aboriginal groups occupy the upland area around the borders of Cambodia. If aboriginal groups occupy the upland area around the borders of Cambodia, then if the claim that reasonable valuations are now the driving force on stock prices everywhere in the world has no merit, then fat cells respond by giving up their little lives as they are burned for energy. Either one or both of these statements are true: most large vessels carry blood, or if most snack food contains flour, then a rivet is a pin. Whenever it is true that most large vessels carry blood, 'spiritual muscles are like body muscles' is true. Given that if most snack food contains flour, then a rivet is a pin, it can be inferred that spiritual muscles are like body muscles.
|
reasonable valuations are now the driving force on stock prices everywhere in the world.
|
It is not the case that reasonable valuations are now the driving force on stock prices everywhere in the world.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (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 [6].
If [6], then (If (Not [0].), then [1].).
Therefore, If [2], then (If (Not [0].), then [1].)..
[SC2-2]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then [2].
If (If [4], then [5].), then [2].
Therefore, [2].
|
{0: 'Reasonable valuations are now the driving force on stock prices everywhere in the world.', 1: 'Fat cells respond by giving up their little lives as they are burned for energy.', 2: 'Spiritual muscles are like body muscles.', 3: 'Most large vessels carry blood.', 4: 'Most snack food contains flour.', 5: 'A rivet is a pin.', 6: 'Aboriginal groups occupy the upland area around the borders of Cambodia.'}
| 4 |
3,787 |
['One may reasonably assume that if the statement that states search engines are software applications that retrieve information from databases is false, then complex scenarios include fluid motion.', 'Provided that a kelpie is evil spirit, we know that if the statement that states search engines are software applications that retrieve information from databases is false, then those that suggest complex scenarios include fluid motion are wrong.', "Once we know the statement 'either neighbors keep dogs or a kelpie is evil spirit' can be considered false, we also know that extension is when bones move away from each other at a joint.", "The notion that 'extension is when bones move away from each other at a joint' is untrue.", 'On the condition that those that suggest if neighbors keep dogs, then if the statement that states search engines are software applications that retrieve information from databases is false, then those that suggest complex scenarios include fluid motion are wrong are wrong, it is definitely the case that many people fear and hate wolves.', "The notion that 'many people fear and hate wolves' is untrue."]
|
One may reasonably assume that if the statement that states search engines are software applications that retrieve information from databases is false, then complex scenarios include fluid motion. Provided that a kelpie is evil spirit, we know that if the statement that states search engines are software applications that retrieve information from databases is false, then those that suggest complex scenarios include fluid motion are wrong. Once we know the statement 'either neighbors keep dogs or a kelpie is evil spirit' can be considered false, we also know that extension is when bones move away from each other at a joint. The notion that 'extension is when bones move away from each other at a joint' is untrue. On the condition that those that suggest if neighbors keep dogs, then if the statement that states search engines are software applications that retrieve information from databases is false, then those that suggest complex scenarios include fluid motion are wrong are wrong, it is definitely the case that many people fear and hate wolves. The notion that 'many people fear and hate wolves' is untrue.
|
It is true that search engines are software applications that retrieve information from databases.
|
It is not true that search engines are software applications that retrieve information from databases.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [2] or [3]. [SC1-2]
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].)..
[SC1-2]
Modus Tonens:
If (Not (Either [2] or [3].).), then [5].
Not [5].
Therefore, Either [2] or [3]..
[SC2-2]
Modus Tonens:
If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then [4].
Not [4].
Therefore, If [2], then (If (Not [0].), then (Not [1].).)..
|
{0: 'Search engines are software applications that retrieve information from databases.', 1: 'Complex scenarios include fluid motion.', 2: 'Neighbors keep dogs.', 3: 'A kelpie is evil spirit.', 4: 'Many people fear and hate wolves.', 5: 'Extension is when bones move away from each other at a joint.'}
| 4 |
3,449 |
['Either art exists in movies, games, and nature or if birds lack teeth, and the grit which is kept in the gizzard is used to grind up seeds, then the statement that states either cookies become moister and sweeter when frozen or officers have probable causes is false.', "The statement 'art exists in movies, games, and nature' can be considered false.", 'It is a common misconception that designs follow patterns.', 'We know that either fish possess gills or if forfeiture is when legal title is permanently transferred to the state, then most refrigeration causes moisture.', 'Provided that fish possess gills, we know that either designs follow patterns or birds lack teeth, and the grit which is kept in the gizzard is used to grind up seeds.', 'If if forfeiture is when legal title is permanently transferred to the state, then most refrigeration causes moisture, then either designs follow patterns or birds lack teeth, and the grit which is kept in the gizzard is used to grind up seeds.']
|
Either art exists in movies, games, and nature or if birds lack teeth, and the grit which is kept in the gizzard is used to grind up seeds, then the statement that states either cookies become moister and sweeter when frozen or officers have probable causes is false. The statement 'art exists in movies, games, and nature' can be considered false. It is a common misconception that designs follow patterns. We know that either fish possess gills or if forfeiture is when legal title is permanently transferred to the state, then most refrigeration causes moisture. Provided that fish possess gills, we know that either designs follow patterns or birds lack teeth, and the grit which is kept in the gizzard is used to grind up seeds. If if forfeiture is when legal title is permanently transferred to the state, then most refrigeration causes moisture, then either designs follow patterns or birds lack teeth, and the grit which is kept in the gizzard is used to grind up seeds.
|
The statement that states either cookies become moister and sweeter when frozen or officers have probable causes is false.
|
At least one of two things is true: cookies become moister and sweeter when frozen, or officers have probable causes.
|
FALSE
|
Modus Ponens:
If [2], then (Not (Either [0] or [1].).). [SC1-1]
[2] [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If [2], then (Not (Either [0] or [1].).).).
Not [3].
Therefore, If [2], then (Not (Either [0] or [1].).)..
[SC2-1]
Disjunctive Syllogism:
Either [4] or [2]. [SC1-2]
Not [4].
Therefore, [2].
[SC1-2]
Disjunction Elimination:
Either [5] or (If [6], then [7].).
If [5], then (Either [4] or [2].).
If (If [6], then [7].), then (Either [4] or [2].).
Therefore, Either [4] or [2]..
|
{0: 'Cookies become moister and sweeter when frozen.', 1: 'Officers have probable causes.', 2: 'Birds lack teeth, and the grit which is kept in the gizzard is used to grind up seeds.', 3: 'Art exists in movies, games, and nature.', 4: 'Designs follow patterns.', 5: 'Fish possess gills.', 6: 'Forfeiture is when legal title is permanently transferred to the state.', 7: 'Most refrigeration causes moisture.'}
| 4 |
3,703 |
['Once we know either sex is a natural instinct or some gypsums have particle size, we also know that if if canadian bacon comes from the meatier loin, along the backbone, then organic forms express a harmonious unity where humanity feels at one with the world, then molds are also common in foods, such as cheese and fermented beverages.', 'At least one of two things is true: sex is a natural instinct, or some gypsums have particle size.', 'If those that suggest if if canadian bacon comes from the meatier loin, along the backbone, then organic forms express a harmonious unity where humanity feels at one with the world, then the claim that molds are also common in foods, such as cheese and fermented beverages does not correspond with reality are wrong, then femurs are part of thighs.', 'Either one or both of these statements are true: bacteria develop their resistances as a natural course of multiplication and growth, or if those that suggest if if canadian bacon comes from the meatier loin, along the backbone, then organic forms express a harmonious unity where humanity feels at one with the world, then the claim that molds are also common in foods, such as cheese and fermented beverages does not correspond with reality are wrong, then the statement, femurs are part of thighs, does not hold.', 'Those that suggest bacteria develop their resistances as a natural course of multiplication and growth are wrong.']
|
Once we know either sex is a natural instinct or some gypsums have particle size, we also know that if if canadian bacon comes from the meatier loin, along the backbone, then organic forms express a harmonious unity where humanity feels at one with the world, then molds are also common in foods, such as cheese and fermented beverages. At least one of two things is true: sex is a natural instinct, or some gypsums have particle size. If those that suggest if if canadian bacon comes from the meatier loin, along the backbone, then organic forms express a harmonious unity where humanity feels at one with the world, then the claim that molds are also common in foods, such as cheese and fermented beverages does not correspond with reality are wrong, then femurs are part of thighs. Either one or both of these statements are true: bacteria develop their resistances as a natural course of multiplication and growth, or if those that suggest if if canadian bacon comes from the meatier loin, along the backbone, then organic forms express a harmonious unity where humanity feels at one with the world, then the claim that molds are also common in foods, such as cheese and fermented beverages does not correspond with reality are wrong, then the statement, femurs are part of thighs, does not hold. Those that suggest bacteria develop their resistances as a natural course of multiplication and growth are wrong.
|
It is a common misconception that if canadian bacon comes from the meatier loin, along the backbone, then organic forms express a harmonious unity where humanity feels at one with the world.
|
It is a common misconception that if canadian bacon comes from the meatier loin, along the backbone, then organic forms express a harmonious unity where humanity feels at one with the world.
|
TRUE
|
Reductio Ad Absurdum:
If (If [0], then [1].), then [2]. [SC1-1]
If (If [0], then [1].), then (Not [2].). [SC2-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Modus Ponens:
If (Either [3] or [4].), then (If (If [0], then [1].), then [2].).
Either [3] or [4].
Therefore, If (If [0], then [1].), then [2]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (If [0], then [1].), then (Not [2].).).), then [5].
If (Not (If (If [0], then [1].), then (Not [2].).).), then (Not [5].). [SC2-2]
Therefore, If (If [0], then [1].), then (Not [2].)..
[SC2-2]
Disjunctive Syllogism:
Either [6] or (If (Not (If (If [0], then [1].), then (Not [2].).).), then (Not [5].).).
Not [6].
Therefore, If (Not (If (If [0], then [1].), then (Not [2].).).), then (Not [5].)..
|
{0: 'Canadian bacon comes from the meatier loin, along the backbone.', 1: 'Organic forms express a harmonious unity where humanity feels at one with the world.', 2: 'Molds are also common in foods, such as cheese and fermented beverages.', 3: 'Sex is a natural instinct.', 4: 'Some gypsums have particle size.', 5: 'Femurs are part of thighs.', 6: 'Bacteria develop their resistances as a natural course of multiplication and growth.'}
| 4 |
3,437 |
['There is good reason to believe that either either intermittent claudication is a circulation problem in the legs, usually brought on by exertion or most diuretics increase urine output by blocking reabsorption of sodium and chloride or brains use cells called neurons to store and manipulate information.', 'On the condition that either intermittent claudication is a circulation problem in the legs, usually brought on by exertion or most diuretics increase urine output by blocking reabsorption of sodium and chloride, it is definitely the case that if amoeboid cells secrete the skeletal elements of the sponge, then adjective clauses modify nouns or pronouns .', "Whenever it is true that if amoeboid cells secrete the skeletal elements of the sponge, then adjective clauses modify nouns or pronouns , 'cardinals are cheery birds, both in song and appearance' is true.", 'Either one or both of these statements are true: if mosquito eggs can survive for more than five years, then marsupials rear their young in pouches, or if either intermittent claudication is a circulation problem in the legs, usually brought on by exertion or most diuretics increase urine output by blocking reabsorption of sodium and chloride, then it is not the case that cardinals are cheery birds, both in song and appearance.', "The statement that 'if mosquito eggs can survive for more than five years, then marsupials rear their young in pouches' is incorrect."]
|
There is good reason to believe that either either intermittent claudication is a circulation problem in the legs, usually brought on by exertion or most diuretics increase urine output by blocking reabsorption of sodium and chloride or brains use cells called neurons to store and manipulate information. On the condition that either intermittent claudication is a circulation problem in the legs, usually brought on by exertion or most diuretics increase urine output by blocking reabsorption of sodium and chloride, it is definitely the case that if amoeboid cells secrete the skeletal elements of the sponge, then adjective clauses modify nouns or pronouns . Whenever it is true that if amoeboid cells secrete the skeletal elements of the sponge, then adjective clauses modify nouns or pronouns , 'cardinals are cheery birds, both in song and appearance' is true. Either one or both of these statements are true: if mosquito eggs can survive for more than five years, then marsupials rear their young in pouches, or if either intermittent claudication is a circulation problem in the legs, usually brought on by exertion or most diuretics increase urine output by blocking reabsorption of sodium and chloride, then it is not the case that cardinals are cheery birds, both in song and appearance. The statement that 'if mosquito eggs can survive for more than five years, then marsupials rear their young in pouches' is incorrect.
|
brains use cells called neurons to store and manipulate information.
|
Most brains trigger specific responses.
|
Uncertain
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or [0].
Not (Either [1] or [2].). [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If (Either [1] or [2].), then [3]. [SC1-2]
If (Either [1] or [2].), then (Not [3].). [SC2-2]
Therefore, Not (Either [1] or [2].)..
[SC1-2]
Hypothetical Syllogism:
If (Either [1] or [2].), then (If [6], then [7].).
If (If [6], then [7].), then [3].
Therefore, If (Either [1] or [2].), then [3]..
[SC2-2]
Disjunctive Syllogism:
Either (If [4], then [5].) or (If (Either [1] or [2].), then (Not [3].).).
Not (If [4], then [5].).
Therefore, If (Either [1] or [2].), then (Not [3].)..
|
{0: 'Brains use cells called neurons to store and manipulate information.', 1: 'Intermittent claudication is a circulation problem in the legs, usually brought on by exertion.', 2: 'Most diuretics increase urine output by blocking reabsorption of sodium and chloride.', 3: 'Cardinals are cheery birds, both in song and appearance.', 4: 'Mosquito eggs can survive for more than five years.', 5: 'Marsupials rear their young in pouches.', 6: 'Amoeboid cells secrete the skeletal elements of the sponge.', 7: 'Adjective clauses modify nouns or pronouns .'}
| 4 |
3,563 |
['Should it be the case that paleoclimatology shows a sudden drop in oxygen levels shortly after the storm , it follows that most bears live on ground.', 'Either gin is alcoholic beverages or some opossums provide parental care.', "Whenever it is true that some opossums provide parental care, 'paleoclimatology shows a sudden drop in oxygen levels shortly after the storm ' is true.", 'If it is a common misconception that if gin is alcoholic beverages, then paleoclimatology shows a sudden drop in oxygen levels shortly after the storm , then either lacerations can be minor and superficial or they can be deep and severe or ethnicity tends to be based on a common culture, language or nationhood.', 'Assuming small white flowers appear in summer, we know that if it is a common misconception that if gin is alcoholic beverages, then paleoclimatology shows a sudden drop in oxygen levels shortly after the storm , then it is not true that either lacerations can be minor and superficial or they can be deep and severe or ethnicity tends to be based on a common culture, language or nationhood.', 'It is fair to say that small white flowers appear in summer.']
|
Should it be the case that paleoclimatology shows a sudden drop in oxygen levels shortly after the storm , it follows that most bears live on ground. Either gin is alcoholic beverages or some opossums provide parental care. Whenever it is true that some opossums provide parental care, 'paleoclimatology shows a sudden drop in oxygen levels shortly after the storm ' is true. If it is a common misconception that if gin is alcoholic beverages, then paleoclimatology shows a sudden drop in oxygen levels shortly after the storm , then either lacerations can be minor and superficial or they can be deep and severe or ethnicity tends to be based on a common culture, language or nationhood. Assuming small white flowers appear in summer, we know that if it is a common misconception that if gin is alcoholic beverages, then paleoclimatology shows a sudden drop in oxygen levels shortly after the storm , then it is not true that either lacerations can be minor and superficial or they can be deep and severe or ethnicity tends to be based on a common culture, language or nationhood. It is fair to say that small white flowers appear in summer.
|
It is a simple truth that most bears live on ground.
|
It is a simple truth that most bears live on ground.
|
TRUE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then [1]. [SC2-2]
If [3], then [1].
Therefore, [1].
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [2], then [1].).), then (Either [4] or [5].).
If (Not (If [2], then [1].).), then (Not (Either [4] or [5].).). [SC2-3]
Therefore, If [2], then [1]..
[SC2-3]
Modus Ponens:
If [6], then (If (Not (If [2], then [1].).), then (Not (Either [4] or [5].).).).
[6]
Therefore, If (Not (If [2], then [1].).), then (Not (Either [4] or [5].).)..
|
{0: 'Most bears live on ground.', 1: 'Paleoclimatology shows a sudden drop in oxygen levels shortly after the storm .', 2: 'Gin is alcoholic beverages.', 3: 'Some opossums provide parental care.', 4: 'Lacerations can be minor and superficial or they can be deep and severe.', 5: 'Ethnicity tends to be based on a common culture, language or nationhood.', 6: 'Small white flowers appear in summer.'}
| 4 |
3,720 |
['net news is one of the oldest parts of the internet.', 'The statement that states chainsaws have (part) bases is false.', 'It is rational to believe that either some scientists believe that disturbed environments are more prone to invasion or either chainsaws have (part) bases or if net news is one of the oldest parts of the internet, then either every lightning bolt produces ozone that eliminates odors present in the air or copper is cheaper than silver and, next to silver, is the best conductor of electricity.', 'One may reasonably assume that if boas have (part) faces, then the statement that states some scientists believe that disturbed environments are more prone to invasion is false.', 'We can assume that boas have (part) faces.']
|
net news is one of the oldest parts of the internet. The statement that states chainsaws have (part) bases is false. It is rational to believe that either some scientists believe that disturbed environments are more prone to invasion or either chainsaws have (part) bases or if net news is one of the oldest parts of the internet, then either every lightning bolt produces ozone that eliminates odors present in the air or copper is cheaper than silver and, next to silver, is the best conductor of electricity. One may reasonably assume that if boas have (part) faces, then the statement that states some scientists believe that disturbed environments are more prone to invasion is false. We can assume that boas have (part) faces.
|
It is a fact that either every lightning bolt produces ozone that eliminates odors present in the air or copper is cheaper than silver and, next to silver, is the best conductor of electricity.
|
Those that suggest either every lightning bolt produces ozone that eliminates odors present in the air or copper is cheaper than silver and, next to silver, is the best conductor of electricity are wrong.
|
FALSE
|
Modus Ponens:
If [2], then (Either [0] or [1].). [SC1-1]
[2]
Therefore, Either [0] or [1]..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If [2], then (Either [0] or [1].).). [SC1-2]
Not [3].
Therefore, If [2], then (Either [0] or [1].)..
[SC1-2]
Disjunctive Syllogism:
Either [4] or (Either [3] or (If [2], then (Either [0] or [1].).).).
Not [4]. [SC2-3]
Therefore, Either [3] or (If [2], then (Either [0] or [1].).)..
[SC2-3]
Modus Ponens:
If [5], then (Not [4].).
[5]
Therefore, Not [4]..
|
{0: 'Every lightning bolt produces ozone that eliminates odors present in the air.', 1: 'Copper is cheaper than silver and, next to silver, is the best conductor of electricity.', 2: 'Net news is one of the oldest parts of the internet.', 3: 'Chainsaws have (part) bases.', 4: 'Some scientists believe that disturbed environments are more prone to invasion.', 5: 'Boas have (part) faces.'}
| 4 |
3,890 |
['On the condition that the statement, either positive shear estimates the mean shear of a given layer of a hodograph or if strategies include analyses, then complex carbohydrates serve other body functions, does not hold, it is definitely the case that if salmon have (part) fishbones, then infants learn to regulate their behavior and soothe themselves with direction from their parents.', 'Should it be the case that the statement, either positive shear estimates the mean shear of a given layer of a hodograph or if strategies include analyses, then complex carbohydrates serve other body functions, does not hold, it follows that we know that the claim that if salmon have (part) fishbones, then infants learn to regulate their behavior and soothe themselves with direction from their parents is false.', "So long as those that suggest if positive shear estimates the mean shear of a given layer of a hodograph, then some people mistakenly believe that leaded gasoline remains the most dispersive source of lead exposure are wrong, 'either people engage in different patterns of sexual activity at different times of their lives or automobiles are located in garages' is true.", "So long as those that suggest if positive shear estimates the mean shear of a given layer of a hodograph, then some people mistakenly believe that leaded gasoline remains the most dispersive source of lead exposure are wrong, 'the statement 'either people engage in different patterns of sexual activity at different times of their lives or automobiles are located in garages' can be considered false' is true.", 'Either one or both of these statements are true: sore throats caused by a virus can be very painful, or if if strategies include analyses, then complex carbohydrates serve other body functions, then some people mistakenly believe that leaded gasoline remains the most dispersive source of lead exposure.', 'The claim that sore throats caused by a virus can be very painful does not correspond with reality.']
|
On the condition that the statement, either positive shear estimates the mean shear of a given layer of a hodograph or if strategies include analyses, then complex carbohydrates serve other body functions, does not hold, it is definitely the case that if salmon have (part) fishbones, then infants learn to regulate their behavior and soothe themselves with direction from their parents. Should it be the case that the statement, either positive shear estimates the mean shear of a given layer of a hodograph or if strategies include analyses, then complex carbohydrates serve other body functions, does not hold, it follows that we know that the claim that if salmon have (part) fishbones, then infants learn to regulate their behavior and soothe themselves with direction from their parents is false. So long as those that suggest if positive shear estimates the mean shear of a given layer of a hodograph, then some people mistakenly believe that leaded gasoline remains the most dispersive source of lead exposure are wrong, 'either people engage in different patterns of sexual activity at different times of their lives or automobiles are located in garages' is true. So long as those that suggest if positive shear estimates the mean shear of a given layer of a hodograph, then some people mistakenly believe that leaded gasoline remains the most dispersive source of lead exposure are wrong, 'the statement 'either people engage in different patterns of sexual activity at different times of their lives or automobiles are located in garages' can be considered false' is true. Either one or both of these statements are true: sore throats caused by a virus can be very painful, or if if strategies include analyses, then complex carbohydrates serve other body functions, then some people mistakenly believe that leaded gasoline remains the most dispersive source of lead exposure. The claim that sore throats caused by a virus can be very painful does not correspond with reality.
|
Some people mistakenly believe that leaded gasoline remains the most dispersive source of lead exposure.
|
Many people rightly believe that leaded gasoline remains the most dispersive source of lead exposure.
|
FALSE
|
Disjunction Elimination:
Either [1] or (If [2], then [3].). [SC1-1]
If [1], then (Not [0].). [SC2-1]
If (If [2], then [3].), then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or (If [2], then [3].).).), then (If [6], then [7].).
If (Not (Either [1] or (If [2], then [3].).).), then (Not (If [6], then [7].).).
Therefore, Either [1] or (If [2], then [3].)..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [1], then (Not [0].).).), then (Either [4] or [5].).
If (Not (If [1], then (Not [0].).).), then (Not (Either [4] or [5].).).
Therefore, If [1], then (Not [0].)..
[SC3-1]
Disjunctive Syllogism:
Either [8] or (If (If [2], then [3].), then (Not [0].).).
Not [8].
Therefore, If (If [2], then [3].), then (Not [0].)..
|
{0: 'Leaded gasoline remains the most dispersive source of lead exposure.', 1: 'Positive shear estimates the mean shear of a given layer of a hodograph.', 2: 'Strategies include analyses.', 3: 'Complex carbohydrates serve other body functions.', 4: 'People engage in different patterns of sexual activity at different times of their lives.', 5: 'Automobiles are located in garages.', 6: 'Salmon have (part) fishbones.', 7: 'Infants learn to regulate their behavior and soothe themselves with direction from their parents.', 8: 'Sore throats caused by a virus can be very painful.'}
| 4 |
3,219 |
['At least one of two things is true: technetium has no biological role, or real plants can also help remove nitrate.', 'It is rational to believe that either some organisms cause malaria or the statement, technetium has no biological role, does not hold.', 'Given that some organisms cause malaria, it can be inferred that death squads are organizations.', 'Given that some organisms cause malaria, it can be inferred that gophers eat roots, bulbs, grass, tubers, and seeds.', 'Given that gophers eat roots, bulbs, grass, tubers, and seeds, it can be inferred that it is a common misconception that death squads are organizations.']
|
At least one of two things is true: technetium has no biological role, or real plants can also help remove nitrate. It is rational to believe that either some organisms cause malaria or the statement, technetium has no biological role, does not hold. Given that some organisms cause malaria, it can be inferred that death squads are organizations. Given that some organisms cause malaria, it can be inferred that gophers eat roots, bulbs, grass, tubers, and seeds. Given that gophers eat roots, bulbs, grass, tubers, and seeds, it can be inferred that it is a common misconception that death squads are organizations.
|
Those that suggest real plants can also help remove nitrate are right.
|
Technology leads to breakthroughs.
|
Uncertain
|
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]
Reductio Ad Absurdum:
If [2], then [3].
If [2], then (Not [3].). [SC2-3]
Therefore, Not [2]..
[SC2-3]
Hypothetical Syllogism:
If [2], then [4].
If [4], then (Not [3].).
Therefore, If [2], then (Not [3].)..
|
{0: 'Real plants can also help remove nitrate.', 1: 'Technetium has no biological role.', 2: 'Some organisms cause malaria.', 3: 'Death squads are organizations.', 4: 'Gophers eat roots, bulbs, grass, tubers, and seeds.'}
| 4 |
3,678 |
['If we know that the claim that either either african countries are countries or rulers are special people which can summon monsters or cats are naturally fastidiously clean animals, even wild ones is false, then massive bodies fall faster than light ones.', 'When we know that the claim that either either african countries are countries or rulers are special people which can summon monsters or cats are naturally fastidiously clean animals, even wild ones is false is true, it follows that it is a common misconception that massive bodies fall faster than light ones.', 'Once we know branches have sides, we also know that the claim that either african countries are countries or rulers are special people which can summon monsters has no merit.', 'If murder rates vary greatly among countries and societies around the world, then branches have sides.', "The statement 'murder rates vary greatly among countries and societies around the world' can be considered true."]
|
If we know that the claim that either either african countries are countries or rulers are special people which can summon monsters or cats are naturally fastidiously clean animals, even wild ones is false, then massive bodies fall faster than light ones. When we know that the claim that either either african countries are countries or rulers are special people which can summon monsters or cats are naturally fastidiously clean animals, even wild ones is false is true, it follows that it is a common misconception that massive bodies fall faster than light ones. Once we know branches have sides, we also know that the claim that either african countries are countries or rulers are special people which can summon monsters has no merit. If murder rates vary greatly among countries and societies around the world, then branches have sides. The statement 'murder rates vary greatly among countries and societies around the world' can be considered true.
|
Many people rightly believe that cats are naturally fastidiously clean animals, even wild ones.
|
Cats typically sleep more than humans.
|
Uncertain
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or [0]. [SC1-1]
Not (Either [1] or [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either (Either [1] or [2].) or [0].).), then [3].
If (Not (Either (Either [1] or [2].) or [0].).), then (Not [3].).
Therefore, Either (Either [1] or [2].) or [0]..
[SC2-1]
Modus Ponens:
If [4], then (Not (Either [1] or [2].).).
[4] [SC2-2]
Therefore, Not (Either [1] or [2].)..
[SC2-2]
Modus Ponens:
If [5], then [4].
[5]
Therefore, [4].
|
{0: 'Cats are naturally fastidiously clean animals, even wild ones.', 1: 'African countries are countries.', 2: 'Rulers are special people which can summon monsters.', 3: 'Massive bodies fall faster than light ones.', 4: 'Branches have sides.', 5: 'Murder rates vary greatly among countries and societies around the world.'}
| 4 |
3,586 |
['Should it be the case that imposters have (part) heads, it follows that if fertilizer has effects, then either japanese people attach importance to the family line or horticulture is a recession-proof industry.', 'On the condition that most genetic disorder affects bone growth, it is definitely the case that if fertilizer has effects, then either japanese people attach importance to the family line or horticulture is a recession-proof industry.', 'On the condition that hypnotisms are influence, it is definitely the case that fertilizer has effects.', 'Many people rightly believe that hypnotisms are influence.', 'Provided that it is not true that either imposters have (part) heads or most genetic disorder affects bone growth, we know that turtles live in fresh water.', 'We know that the claim that turtles live in fresh water is false.']
|
Should it be the case that imposters have (part) heads, it follows that if fertilizer has effects, then either japanese people attach importance to the family line or horticulture is a recession-proof industry. On the condition that most genetic disorder affects bone growth, it is definitely the case that if fertilizer has effects, then either japanese people attach importance to the family line or horticulture is a recession-proof industry. On the condition that hypnotisms are influence, it is definitely the case that fertilizer has effects. Many people rightly believe that hypnotisms are influence. Provided that it is not true that either imposters have (part) heads or most genetic disorder affects bone growth, we know that turtles live in fresh water. We know that the claim that turtles live in fresh water is false.
|
It is rational to believe that either japanese people attach importance to the family line or horticulture is a recession-proof industry.
|
It is rational to believe that either japanese people attach importance to the family line or horticulture is a recession-proof industry.
|
TRUE
|
Modus Ponens:
If [2], then (Either [0] or [1].). [SC1-1]
[2] [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (If [2], then (Either [0] or [1].).).
If [4], then (If [2], then (Either [0] or [1].).).
Therefore, If [2], then (Either [0] or [1].)..
[SC1-2]
Modus Tonens:
If (Not (Either [3] or [4].).), then [6].
Not [6].
Therefore, Either [3] or [4]..
[SC2-1]
Modus Ponens:
If [5], then [2].
[5]
Therefore, [2].
|
{0: 'Japanese people attach importance to the family line.', 1: 'Horticulture is a recession-proof industry.', 2: 'Fertilizer has effects.', 3: 'Imposters have (part) heads.', 4: 'Most genetic disorder affects bone growth.', 5: 'Hypnotisms are influence.', 6: 'Turtles live in fresh water.'}
| 4 |
3,282 |
['Given that the claim that if some people mistakenly believe that most children lead normal lifestyles, then seeds sprout quickly in cool soil and plants grow rapidly does not reflect reality, it can be inferred that some teenagers lose weight.', 'One may reasonably assume that if the claim that if some people mistakenly believe that most children lead normal lifestyles, then seeds sprout quickly in cool soil and plants grow rapidly does not reflect reality, then the statement that states some teenagers lose weight is false.', "So long as the claim that if some people mistakenly believe that most children lead normal lifestyles, then the statement, seeds sprout quickly in cool soil and plants grow rapidly, does not hold does not correspond with reality, 'some people mistakenly believe that queens produce unfertilized eggs that hatch into drones, or male honey bees' is true.", 'If it is not the case that if the claim that if some people mistakenly believe that most children lead normal lifestyles, then the statement, seeds sprout quickly in cool soil and plants grow rapidly, does not hold does not correspond with reality, then queens produce unfertilized eggs that hatch into drones, or male honey bees, then salt needs moisture to provide melting action.', "The statement 'salt needs moisture to provide melting action' can be considered false."]
|
Given that the claim that if some people mistakenly believe that most children lead normal lifestyles, then seeds sprout quickly in cool soil and plants grow rapidly does not reflect reality, it can be inferred that some teenagers lose weight. One may reasonably assume that if the claim that if some people mistakenly believe that most children lead normal lifestyles, then seeds sprout quickly in cool soil and plants grow rapidly does not reflect reality, then the statement that states some teenagers lose weight is false. So long as the claim that if some people mistakenly believe that most children lead normal lifestyles, then the statement, seeds sprout quickly in cool soil and plants grow rapidly, does not hold does not correspond with reality, 'some people mistakenly believe that queens produce unfertilized eggs that hatch into drones, or male honey bees' is true. If it is not the case that if the claim that if some people mistakenly believe that most children lead normal lifestyles, then the statement, seeds sprout quickly in cool soil and plants grow rapidly, does not hold does not correspond with reality, then queens produce unfertilized eggs that hatch into drones, or male honey bees, then salt needs moisture to provide melting action. The statement 'salt needs moisture to provide melting action' can be considered false.
|
It is a simple truth that most children lead normal lifestyles.
|
Some children have temperaments that are more feisty, difficult, or energetic.
|
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 [3].
If (Not (If (Not [0].), then [1].).), then (Not [3].).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then (Not [1].).).), then [2]. [SC1-2]
If (Not (If (Not [0].), then (Not [1].).).), then (Not [2].).
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Modus Tonens:
If (Not (If (Not (If (Not [0].), then (Not [1].).).), then [2].).), then [4].
Not [4].
Therefore, If (Not (If (Not [0].), then (Not [1].).).), then [2]..
|
{0: 'Most children lead normal lifestyles.', 1: 'Seeds sprout quickly in cool soil and plants grow rapidly.', 2: 'Queens produce unfertilized eggs that hatch into drones, or male honey bees.', 3: 'Some teenagers lose weight.', 4: 'Salt needs moisture to provide melting action.'}
| 4 |
3,348 |
['We know that either phimosis is a name given to the condition where the foreskin is unretractable or either animals receive substances or bats eat moths.', 'Assuming phimosis is a name given to the condition where the foreskin is unretractable, we know that electromagnetic radiation is produced in frequencies that range from high to extremely low.', "So long as either animals receive substances or bats eat moths, 'some microscopes pass, or transmit, electrons through a thin slice of an object' is true.", 'When sections are part of platoons is true, it follows that if electromagnetic radiation is produced in frequencies that range from high to extremely low, then leaves meet stems.', 'It is fair to say that sections are part of platoons.', 'There is good reason to believe that either either most cattle are grazers, using their tongue and lower teeth to grab grass and leaves or measure means to find out how big or long something is by using a measuring unit or if some microscopes pass, or transmit, electrons through a thin slice of an object, then hereditary hemochromatosis is an inherited condition.', "The statement that 'either most cattle are grazers, using their tongue and lower teeth to grab grass and leaves or measure means to find out how big or long something is by using a measuring unit' is incorrect."]
|
We know that either phimosis is a name given to the condition where the foreskin is unretractable or either animals receive substances or bats eat moths. Assuming phimosis is a name given to the condition where the foreskin is unretractable, we know that electromagnetic radiation is produced in frequencies that range from high to extremely low. So long as either animals receive substances or bats eat moths, 'some microscopes pass, or transmit, electrons through a thin slice of an object' is true. When sections are part of platoons is true, it follows that if electromagnetic radiation is produced in frequencies that range from high to extremely low, then leaves meet stems. It is fair to say that sections are part of platoons. There is good reason to believe that either either most cattle are grazers, using their tongue and lower teeth to grab grass and leaves or measure means to find out how big or long something is by using a measuring unit or if some microscopes pass, or transmit, electrons through a thin slice of an object, then hereditary hemochromatosis is an inherited condition. The statement that 'either most cattle are grazers, using their tongue and lower teeth to grab grass and leaves or measure means to find out how big or long something is by using a measuring unit' is incorrect.
|
At least one of two things is true: leaves meet stems, or hereditary hemochromatosis is an inherited condition.
|
The statement that states either leaves meet stems or hereditary hemochromatosis is an inherited condition is false.
|
FALSE
|
Constructive Dilemma:
Either [2] or [3]. [SC1-1]
If [2], then [0]. [SC2-1]
If [3], then [1]. [SC3-1]
Therefore, Either [0] or [1]..
[SC1-1]
Constructive Dilemma:
Either [7] or (Either [8] or [9].).
If [7], then [2].
If (Either [8] or [9].), then [3].
Therefore, Either [2] or [3]..
[SC2-1]
Modus Ponens:
If [4], then (If [2], then [0].).
[4]
Therefore, If [2], then [0]..
[SC3-1]
Disjunctive Syllogism:
Either (Either [5] or [6].) or (If [3], then [1].).
Not (Either [5] or [6].).
Therefore, If [3], then [1]..
|
{0: 'Leaves meet stems.', 1: 'Hereditary hemochromatosis is an inherited condition.', 2: 'Electromagnetic radiation is produced in frequencies that range from high to extremely low.', 3: 'Some microscopes pass, or transmit, electrons through a thin slice of an object.', 4: 'Sections are part of platoons.', 5: 'Most cattle are grazers, using their tongue and lower teeth to grab grass and leaves.', 6: 'Measure means to find out how big or long something is by using a measuring unit.', 7: 'Phimosis is a name given to the condition where the foreskin is unretractable.', 8: 'Animals receive substances.', 9: 'Bats eat moths.'}
| 4 |
3,686 |
['It is rational to believe that either wattles are frameworks or a pedantry is fanfare.', 'When wattles are frameworks is true, it follows that either revolution is freedom from the past or most people fear change because they like where they are.', 'Assuming a pedantry is fanfare, we know that either revolution is freedom from the past or most people fear change because they like where they are.', 'Provided that revolution is freedom from the past, we know that some bark is part of conifers.', 'Should it be the case that some bark is part of conifers, it follows that the statement that states either scientific research depends on effective communication among laboratory workers or some people quickly regain emotional health and go on with their lives with no undue side effects is false.', 'At least one of two things is true: democracy is the working model of any form of mob rule, or summer is one of the best seasons for feeding.', 'Given that democracy is the working model of any form of mob rule, it can be inferred that if most people fear change because they like where they are, then the statement that states either scientific research depends on effective communication among laboratory workers or some people quickly regain emotional health and go on with their lives with no undue side effects is false.', 'On the condition that summer is one of the best seasons for feeding, it is definitely the case that if most people fear change because they like where they are, then the statement that states either scientific research depends on effective communication among laboratory workers or some people quickly regain emotional health and go on with their lives with no undue side effects is false.']
|
It is rational to believe that either wattles are frameworks or a pedantry is fanfare. When wattles are frameworks is true, it follows that either revolution is freedom from the past or most people fear change because they like where they are. Assuming a pedantry is fanfare, we know that either revolution is freedom from the past or most people fear change because they like where they are. Provided that revolution is freedom from the past, we know that some bark is part of conifers. Should it be the case that some bark is part of conifers, it follows that the statement that states either scientific research depends on effective communication among laboratory workers or some people quickly regain emotional health and go on with their lives with no undue side effects is false. At least one of two things is true: democracy is the working model of any form of mob rule, or summer is one of the best seasons for feeding. Given that democracy is the working model of any form of mob rule, it can be inferred that if most people fear change because they like where they are, then the statement that states either scientific research depends on effective communication among laboratory workers or some people quickly regain emotional health and go on with their lives with no undue side effects is false. On the condition that summer is one of the best seasons for feeding, it is definitely the case that if most people fear change because they like where they are, then the statement that states either scientific research depends on effective communication among laboratory workers or some people quickly regain emotional health and go on with their lives with no undue side effects is false.
|
The statement that states either scientific research depends on effective communication among laboratory workers or some people quickly regain emotional health and go on with their lives with no undue side effects is false.
|
The statement that states scientific research includes both basic research and applied research is false.
|
Uncertain
|
Disjunction Elimination:
Either [2] or [3]. [SC1-1]
If [2], then (Not (Either [0] or [1].).). [SC2-1]
If [3], then (Not (Either [0] or [1].).). [SC3-1]
Therefore, Not (Either [0] or [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]
Hypothetical Syllogism:
If [2], then [6].
If [6], then (Not (Either [0] or [1].).).
Therefore, If [2], then (Not (Either [0] or [1].).)..
[SC3-1]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If [3], then (Not (Either [0] or [1].).).).
If [8], then (If [3], then (Not (Either [0] or [1].).).).
Therefore, If [3], then (Not (Either [0] or [1].).)..
|
{0: 'Scientific research depends on effective communication among laboratory workers.', 1: 'Some people quickly regain emotional health and go on with their lives with no undue side effects.', 2: 'Revolution is freedom from the past.', 3: 'Most people fear change because they like where they are.', 4: 'Wattles are frameworks.', 5: 'A pedantry is fanfare.', 6: 'Some bark is part of conifers.', 7: 'Democracy is the working model of any form of mob rule.', 8: 'Summer is one of the best seasons for feeding.'}
| 4 |
3,004 |
["Assuming nasal passages supply moisture to incoming air, we know that if the notion that 'groups of people wage war and affect the conduct of war' is untrue, then public administrator is a term that covers a wide range of government employees.", "On the condition that pancreatitis can happen again, it is definitely the case that if the notion that 'groups of people wage war and affect the conduct of war' is untrue, then public administrator is a term that covers a wide range of government employees.", 'Given that public administrator is a term that covers a wide range of government employees, it can be inferred that some infection causes vaginal excretion.', 'Provided that public administrator is a term that covers a wide range of government employees, we know that it is not true that some infection causes vaginal excretion.', 'There is good reason to believe that either large fires are actually more likely to occur in sparse, wooded areas, where there are fewer people or either ginkgo trees grow to height or natural agents interfere with the action of tumor promoters .', 'On the condition that large fires are actually more likely to occur in sparse, wooded areas, where there are fewer people, it is definitely the case that nasal passages supply moisture to incoming air.', 'One may reasonably assume that if either ginkgo trees grow to height or natural agents interfere with the action of tumor promoters , then pancreatitis can happen again.']
|
Assuming nasal passages supply moisture to incoming air, we know that if the notion that 'groups of people wage war and affect the conduct of war' is untrue, then public administrator is a term that covers a wide range of government employees. On the condition that pancreatitis can happen again, it is definitely the case that if the notion that 'groups of people wage war and affect the conduct of war' is untrue, then public administrator is a term that covers a wide range of government employees. Given that public administrator is a term that covers a wide range of government employees, it can be inferred that some infection causes vaginal excretion. Provided that public administrator is a term that covers a wide range of government employees, we know that it is not true that some infection causes vaginal excretion. There is good reason to believe that either large fires are actually more likely to occur in sparse, wooded areas, where there are fewer people or either ginkgo trees grow to height or natural agents interfere with the action of tumor promoters . On the condition that large fires are actually more likely to occur in sparse, wooded areas, where there are fewer people, it is definitely the case that nasal passages supply moisture to incoming air. One may reasonably assume that if either ginkgo trees grow to height or natural agents interfere with the action of tumor promoters , then pancreatitis can happen again.
|
It is rational to agree that groups of people wage war and affect the conduct of war.
|
It is rational to agree that groups of people wage war and affect the conduct of war.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [2] or [3]. [SC1-2]
If [2], then (If (Not [0].), then [1].).
If [3], then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC1-2]
Constructive Dilemma:
Either [5] or (Either [6] or [7].).
If [5], then [2].
If (Either [6] or [7].), then [3].
Therefore, Either [2] or [3]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [4].
If [1], then (Not [4].).
Therefore, Not [1]..
|
{0: 'Groups of people wage war and affect the conduct of war.', 1: 'Public administrator is a term that covers a wide range of government employees.', 2: 'Nasal passages supply moisture to incoming air.', 3: 'Pancreatitis can happen again.', 4: 'Some infection causes vaginal excretion.', 5: 'Large fires are actually more likely to occur in sparse, wooded areas, where there are fewer people.', 6: 'Ginkgo trees grow to height.', 7: 'Natural agents interfere with the action of tumor promoters .'}
| 4 |
3,995 |
['The claim that tobacco is the top cash crop, used mainly in snuffs has no merit.', 'We know that at least one of two things is true: wood is the preferred fuel for cooking in much of the world, or some insecticide aerosols have effects.', 'One may reasonably assume that if wood is the preferred fuel for cooking in much of the world, then if the claim that either tobacco is the top cash crop, used mainly in snuffs or gaseous substances are in a league all to themselves has no merit, then a samurai is aristocracy.', 'One may reasonably assume that if some insecticide aerosols have effects, then if the claim that either tobacco is the top cash crop, used mainly in snuffs or gaseous substances are in a league all to themselves has no merit, then a samurai is aristocracy.', 'Should it be the case that the claim that if the claim that either tobacco is the top cash crop, used mainly in snuffs or gaseous substances are in a league all to themselves has no merit, then we know that the claim that a samurai is aristocracy is false is false, it follows that farmers use cows to get milk to drink on the farm and also to sell.', "So long as the claim that if the claim that either tobacco is the top cash crop, used mainly in snuffs or gaseous substances are in a league all to themselves has no merit, then we know that the claim that a samurai is aristocracy is false is false, 'we know that the claim that farmers use cows to get milk to drink on the farm and also to sell is false' is true."]
|
The claim that tobacco is the top cash crop, used mainly in snuffs has no merit. We know that at least one of two things is true: wood is the preferred fuel for cooking in much of the world, or some insecticide aerosols have effects. One may reasonably assume that if wood is the preferred fuel for cooking in much of the world, then if the claim that either tobacco is the top cash crop, used mainly in snuffs or gaseous substances are in a league all to themselves has no merit, then a samurai is aristocracy. One may reasonably assume that if some insecticide aerosols have effects, then if the claim that either tobacco is the top cash crop, used mainly in snuffs or gaseous substances are in a league all to themselves has no merit, then a samurai is aristocracy. Should it be the case that the claim that if the claim that either tobacco is the top cash crop, used mainly in snuffs or gaseous substances are in a league all to themselves has no merit, then we know that the claim that a samurai is aristocracy is false is false, it follows that farmers use cows to get milk to drink on the farm and also to sell. So long as the claim that if the claim that either tobacco is the top cash crop, used mainly in snuffs or gaseous substances are in a league all to themselves has no merit, then we know that the claim that a samurai is aristocracy is false is false, 'we know that the claim that farmers use cows to get milk to drink on the farm and also to sell is false' is true.
|
It is the case that gaseous substances are in a league all to themselves.
|
The claim that gaseous substances are in a league all to themselves does not correspond with reality.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or [0].).), then [2]. [SC1-2]
If (Not (Either [1] or [0].).), then (Not [2].). [SC2-2]
Therefore, Either [1] or [0]..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not (Either [1] or [0].).), then [2].).
If [5], then (If (Not (Either [1] or [0].).), then [2].).
Therefore, If (Not (Either [1] or [0].).), then [2]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (Either [1] or [0].).), then (Not [2].).).), then [3].
If (Not (If (Not (Either [1] or [0].).), then (Not [2].).).), then (Not [3].).
Therefore, If (Not (Either [1] or [0].).), then (Not [2].)..
|
{0: 'Gaseous substances are in a league all to themselves.', 1: 'Tobacco is the top cash crop, used mainly in snuffs.', 2: 'A samurai is aristocracy.', 3: 'Farmers use cows to get milk to drink on the farm and also to sell.', 4: 'Wood is the preferred fuel for cooking in much of the world.', 5: 'Some insecticide aerosols have effects.'}
| 4 |
3,463 |
['Either most herbivores are one or the other or polyploidy involves doubling the number of chromosomes.', 'Provided that polyploidy involves doubling the number of chromosomes, we know that marital drift can encourage secrecy and separateness that allows room for increased temptation.', 'It is a fact that either stallions have a moderate crest or the claim that either optimism appears to be socially desirable in all communities or most outer ears have muscles has no merit.', 'The claim that stallions have a moderate crest is false.', 'When the claim that if most herbivores are one or the other, then either optimism appears to be socially desirable in all communities or most outer ears have muscles is false is true, it follows that hydrophytes are the plants which spend all their life phases in water.', 'Once we know the claim that if most herbivores are one or the other, then either optimism appears to be socially desirable in all communities or most outer ears have muscles is false, we also know that the claim that hydrophytes are the plants which spend all their life phases in water has no merit.']
|
Either most herbivores are one or the other or polyploidy involves doubling the number of chromosomes. Provided that polyploidy involves doubling the number of chromosomes, we know that marital drift can encourage secrecy and separateness that allows room for increased temptation. It is a fact that either stallions have a moderate crest or the claim that either optimism appears to be socially desirable in all communities or most outer ears have muscles has no merit. The claim that stallions have a moderate crest is false. When the claim that if most herbivores are one or the other, then either optimism appears to be socially desirable in all communities or most outer ears have muscles is false is true, it follows that hydrophytes are the plants which spend all their life phases in water. Once we know the claim that if most herbivores are one or the other, then either optimism appears to be socially desirable in all communities or most outer ears have muscles is false, we also know that the claim that hydrophytes are the plants which spend all their life phases in water has no merit.
|
It is reasonable to believe that marital drift can encourage secrecy and separateness that allows room for increased temptation.
|
The statement that states marital drift can encourage secrecy and separateness that allows room for increased temptation is false.
|
FALSE
|
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].). [SC2-2]
If [4], then [0].
Therefore, Either (Either [1] or [2].) or [0]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [3], then (Either [1] or [2].).).), then [6].
If (Not (If [3], then (Either [1] or [2].).).), then (Not [6].).
Therefore, If [3], then (Either [1] or [2].)..
[SC2-1]
Disjunctive Syllogism:
Either [5] or (Not (Either [1] or [2].).).
Not [5].
Therefore, Not (Either [1] or [2].)..
|
{0: 'Marital drift can encourage secrecy and separateness that allows room for increased temptation.', 1: 'Optimism appears to be socially desirable in all communities.', 2: 'Most outer ears have muscles.', 3: 'Most herbivores are one or the other.', 4: 'Polyploidy involves doubling the number of chromosomes.', 5: 'Stallions have a moderate crest.', 6: 'Hydrophytes are the plants which spend all their life phases in water.'}
| 4 |
3,776 |
['When we know that the claim that film isa event is false is true, it follows that it is a common misconception that shanks are part of anchors.', 'Once we know we know that the claim that film isa event is false, we also know that some animals have a particular kind of gait.', 'Provided that some animals have a particular kind of gait, we know that emulators are application programs.', 'Given that the statement, if emulators are application programs, then shanks are part of anchors, does not hold, it can be inferred that either some people like to party with strangers or beach isa formation.', 'Assuming the statement, if emulators are application programs, then shanks are part of anchors, does not hold, we know that the statement, either some people like to party with strangers or beach isa formation, does not hold.']
|
When we know that the claim that film isa event is false is true, it follows that it is a common misconception that shanks are part of anchors. Once we know we know that the claim that film isa event is false, we also know that some animals have a particular kind of gait. Provided that some animals have a particular kind of gait, we know that emulators are application programs. Given that the statement, if emulators are application programs, then shanks are part of anchors, does not hold, it can be inferred that either some people like to party with strangers or beach isa formation. Assuming the statement, if emulators are application programs, then shanks are part of anchors, does not hold, we know that the statement, either some people like to party with strangers or beach isa formation, does not hold.
|
It is rational to agree that film isa event.
|
Films leave impressions.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [2].
If [2], then [1]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Hypothetical Syllogism:
If [2], then [3].
If [3], then [1]. [SC2-3]
Therefore, If [2], then [1]..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If [3], then [1].).), then (Either [4] or [5].).
If (Not (If [3], then [1].).), then (Not (Either [4] or [5].).).
Therefore, If [3], then [1]..
|
{0: 'Film isa event.', 1: 'Shanks are part of anchors.', 2: 'Some animals have a particular kind of gait.', 3: 'Emulators are application programs.', 4: 'Some people like to party with strangers.', 5: 'Beach isa formation.'}
| 4 |
3,682 |
['It is a fact that either some wild pigs have large tusks, overgrown teeth used for fighting and digging for food or if open wounds allow fungi to get in, then some infants seem to tolerate significant trauma from birth, without ill effect.', "Whenever it is true that it is not true that open wounds allow fungi to get in, 'some mammals nurse their babies for only a few weeks' is true.", 'Some people mistakenly believe that some mammals nurse their babies for only a few weeks.', 'Either one or both of these statements are true: home is also a place for creating and maintaining order, or atherosclerosis is a disease process that occurs over years.', 'One may reasonably assume that if home is also a place for creating and maintaining order, then the statement that states some wild pigs have large tusks, overgrown teeth used for fighting and digging for food is false.', 'Given that atherosclerosis is a disease process that occurs over years, it can be inferred that the statement that states some wild pigs have large tusks, overgrown teeth used for fighting and digging for food is false.']
|
It is a fact that either some wild pigs have large tusks, overgrown teeth used for fighting and digging for food or if open wounds allow fungi to get in, then some infants seem to tolerate significant trauma from birth, without ill effect. Whenever it is true that it is not true that open wounds allow fungi to get in, 'some mammals nurse their babies for only a few weeks' is true. Some people mistakenly believe that some mammals nurse their babies for only a few weeks. Either one or both of these statements are true: home is also a place for creating and maintaining order, or atherosclerosis is a disease process that occurs over years. One may reasonably assume that if home is also a place for creating and maintaining order, then the statement that states some wild pigs have large tusks, overgrown teeth used for fighting and digging for food is false. Given that atherosclerosis is a disease process that occurs over years, it can be inferred that the statement that states some wild pigs have large tusks, overgrown teeth used for fighting and digging for food is false.
|
It is the case that some infants seem to tolerate significant trauma from birth, without ill effect.
|
Infants understand the prosody of speech, long before they understand the words.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If [1], then [0].).
Not [3]. [SC2-2]
Therefore, If [1], then [0]..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Not [3].).
If [5], then (Not [3].).
Therefore, Not [3]..
[SC2-1]
Modus Tonens:
If (Not [1].), then [2].
Not [2].
Therefore, [1].
|
{0: 'Some infants seem to tolerate significant trauma from birth, without ill effect.', 1: 'Open wounds allow fungi to get in.', 2: 'Some mammals nurse their babies for only a few weeks.', 3: 'Some wild pigs have large tusks, overgrown teeth used for fighting and digging for food.', 4: 'Home is also a place for creating and maintaining order.', 5: 'Atherosclerosis is a disease process that occurs over years.'}
| 4 |
3,879 |
['There is good reason to believe that either braille displays allow Web users who are deaf-blind to receive braille information from computers or senior managers determine effort.', 'Once we know braille displays allow Web users who are deaf-blind to receive braille information from computers, we also know that most fish have reproductive organs.', 'If most fish have reproductive organs, then coffee is a strong stimulant that can be addictive and can irritate many of our internal systems.', 'Should it be the case that most fish have reproductive organs, it follows that it is a common misconception that coffee is a strong stimulant that can be addictive and can irritate many of our internal systems.', 'Either one or both of these statements are true: if friction is the reason why the soccer ball always slows down, then most caterpillars have eyes, or either surgical procedures are entries into normally sterile areas of the body or surgeons perform breast biopsy, lumpectomy, and mastectomy on breast cancer patients.', 'When if friction is the reason why the soccer ball always slows down, then most caterpillars have eyes is true, it follows that if senior managers determine effort, then the claim that ulcers can be from diseases of blood vessels does not correspond with reality.', 'Given that either surgical procedures are entries into normally sterile areas of the body or surgeons perform breast biopsy, lumpectomy, and mastectomy on breast cancer patients, it can be inferred that if senior managers determine effort, then the claim that ulcers can be from diseases of blood vessels does not correspond with reality.']
|
There is good reason to believe that either braille displays allow Web users who are deaf-blind to receive braille information from computers or senior managers determine effort. Once we know braille displays allow Web users who are deaf-blind to receive braille information from computers, we also know that most fish have reproductive organs. If most fish have reproductive organs, then coffee is a strong stimulant that can be addictive and can irritate many of our internal systems. Should it be the case that most fish have reproductive organs, it follows that it is a common misconception that coffee is a strong stimulant that can be addictive and can irritate many of our internal systems. Either one or both of these statements are true: if friction is the reason why the soccer ball always slows down, then most caterpillars have eyes, or either surgical procedures are entries into normally sterile areas of the body or surgeons perform breast biopsy, lumpectomy, and mastectomy on breast cancer patients. When if friction is the reason why the soccer ball always slows down, then most caterpillars have eyes is true, it follows that if senior managers determine effort, then the claim that ulcers can be from diseases of blood vessels does not correspond with reality. Given that either surgical procedures are entries into normally sterile areas of the body or surgeons perform breast biopsy, lumpectomy, and mastectomy on breast cancer patients, it can be inferred that if senior managers determine effort, then the claim that ulcers can be from diseases of blood vessels does not correspond with reality.
|
The claim that ulcers can be from diseases of blood vessels does not correspond with reality.
|
We know that the claim that ulcers predispose the dogs to vomiting is false.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Constructive Dilemma:
Either [3] or [4].
If [3], then [1].
If [4], then (Not [0].). [SC3-2]
Therefore, Either [1] or (Not [0].)..
[SC3-2]
Disjunction Elimination:
Either (If [5], then [6].) or (Either [7] or [8].).
If (If [5], then [6].), then (If [4], then (Not [0].).).
If (Either [7] or [8].), then (If [4], then (Not [0].).).
Therefore, If [4], then (Not [0].)..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2].
If [1], then (Not [2].).
Therefore, Not [1]..
|
{0: 'Ulcers can be from diseases of blood vessels .', 1: 'Most fish have reproductive organs.', 2: 'Coffee is a strong stimulant that can be addictive and can irritate many of our internal systems.', 3: 'Braille displays allow Web users who are deaf-blind to receive braille information from computers.', 4: 'Senior managers determine effort.', 5: 'Friction is the reason why the soccer ball always slows down.', 6: 'Most caterpillars have eyes.', 7: 'Surgical procedures are entries into normally sterile areas of the body.', 8: 'Surgeons perform breast biopsy, lumpectomy, and mastectomy on breast cancer patients.'}
| 4 |
3,517 |
['The claim that systemic steroids are at times taken orally, or injected intramuscularly does not correspond with reality.', 'Either one or both of these statements are true: metamorphosis is between gradual and complete, or appearances provide evidence.', "So long as metamorphosis is between gradual and complete, 'ringtail cats are extremely clean animals' is true.", 'Should it be the case that ringtail cats are extremely clean animals, it follows that systemic steroids are at times taken orally, or injected intramuscularly.', 'Should it be the case that either honey also is the most natural sweetener in the world or camping are recreational activities, it follows that if appearances provide evidence, then the statement, toxicology is important to protect human and animal health and the environment, does not hold.', 'We know that either honey also is the most natural sweetener in the world or camping are recreational activities.']
|
The claim that systemic steroids are at times taken orally, or injected intramuscularly does not correspond with reality. Either one or both of these statements are true: metamorphosis is between gradual and complete, or appearances provide evidence. So long as metamorphosis is between gradual and complete, 'ringtail cats are extremely clean animals' is true. Should it be the case that ringtail cats are extremely clean animals, it follows that systemic steroids are at times taken orally, or injected intramuscularly. Should it be the case that either honey also is the most natural sweetener in the world or camping are recreational activities, it follows that if appearances provide evidence, then the statement, toxicology is important to protect human and animal health and the environment, does not hold. We know that either honey also is the most natural sweetener in the world or camping are recreational activities.
|
The statement, toxicology is important to protect human and animal health and the environment, does not hold.
|
Toxicology is important to protect human and animal health and the environment.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Constructive Dilemma:
Either [2] or [3].
If [2], then [1]. [SC2-2]
If [3], then (Not [0].). [SC3-2]
Therefore, Either [1] or (Not [0].)..
[SC2-2]
Hypothetical Syllogism:
If [2], then [6].
If [6], then [1].
Therefore, If [2], then [1]..
[SC3-2]
Modus Ponens:
If (Either [4] or [5].), then (If [3], then (Not [0].).).
Either [4] or [5].
Therefore, If [3], then (Not [0].)..
|
{0: 'Toxicology is important to protect human and animal health and the environment.', 1: 'Systemic steroids are at times taken orally, or injected intramuscularly.', 2: 'Metamorphosis is between gradual and complete.', 3: 'Appearances provide evidence.', 4: 'Honey also is the most natural sweetener in the world.', 5: 'Camping are recreational activities.', 6: 'Ringtail cats are extremely clean animals.'}
| 4 |
3,573 |
["So long as the claim that calcium carbonates are present as nodules, masses, or coats on ped faces has no merit, 'refrigerator isa goods' is true.", "So long as the claim that calcium carbonates are present as nodules, masses, or coats on ped faces has no merit, 'maps include terrain features' is true.", 'Provided that maps include terrain features, we know that cottontails eat vegetation.', 'We know that at least one of two things is true: popeye is a cage made of rusty steel, or some people are allergic to wisteria, usually developing hayfever-type symptoms.', "So long as popeye is a cage made of rusty steel, 'if cottontails eat vegetation, then the statement, refrigerator isa goods, does not hold' is true.", 'Should it be the case that some people are allergic to wisteria, usually developing hayfever-type symptoms, it follows that if cottontails eat vegetation, then the statement, refrigerator isa goods, does not hold.']
|
So long as the claim that calcium carbonates are present as nodules, masses, or coats on ped faces has no merit, 'refrigerator isa goods' is true. So long as the claim that calcium carbonates are present as nodules, masses, or coats on ped faces has no merit, 'maps include terrain features' is true. Provided that maps include terrain features, we know that cottontails eat vegetation. We know that at least one of two things is true: popeye is a cage made of rusty steel, or some people are allergic to wisteria, usually developing hayfever-type symptoms. So long as popeye is a cage made of rusty steel, 'if cottontails eat vegetation, then the statement, refrigerator isa goods, does not hold' is true. Should it be the case that some people are allergic to wisteria, usually developing hayfever-type symptoms, it follows that if cottontails eat vegetation, then the statement, refrigerator isa goods, does not hold.
|
The statement 'calcium carbonates are present as nodules, masses, or coats on ped faces' is true.
|
The statement 'calcium carbonates are present as nodules, masses, or coats on ped faces' is true.
|
TRUE
|
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 [2]. [SC1-2]
If [2], then (Not [1].). [SC2-2]
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Hypothetical Syllogism:
If (Not [0].), then [5].
If [5], then [2].
Therefore, If (Not [0].), then [2]..
[SC2-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If [2], then (Not [1].).).
If [4], then (If [2], then (Not [1].).).
Therefore, If [2], then (Not [1].)..
|
{0: 'Calcium carbonates are present as nodules, masses, or coats on ped faces.', 1: 'Refrigerator isa goods.', 2: 'Cottontails eat vegetation.', 3: 'Popeye is a cage made of rusty steel.', 4: 'Some people are allergic to wisteria, usually developing hayfever-type symptoms.', 5: 'Maps include terrain features.'}
| 4 |
3,793 |
['Provided that either cysts are usually distinguishable from solid tumors by ultrasound or sloths actually let algae grow on their hides so they can camouflage themselves better, we know that it is a common misconception that if command languages are useful for automating routine or commonly performed tasks, then aqueous solution is neutral or slightly acid.', 'Should it be the case that it is a common misconception that either either cysts are usually distinguishable from solid tumors by ultrasound or sloths actually let algae grow on their hides so they can camouflage themselves better or if an overture is music, then string is used for violins, it follows that pigeons prefer to roost on level surfaces.', 'When it is a common misconception that either either cysts are usually distinguishable from solid tumors by ultrasound or sloths actually let algae grow on their hides so they can camouflage themselves better or if an overture is music, then string is used for violins is true, it follows that the statement, pigeons prefer to roost on level surfaces, does not hold.', 'Those that suggest large animals are an unusual host for fleas are right.', 'It is a fact that either if social relationships can remain intact, based on shared religious practice, then infrastructure is a public good with external benefits or if large animals are an unusual host for fleas, then if if an overture is music, then string is used for violins, then it is a common misconception that if command languages are useful for automating routine or commonly performed tasks, then aqueous solution is neutral or slightly acid.', 'Those that suggest if social relationships can remain intact, based on shared religious practice, then infrastructure is a public good with external benefits are wrong.']
|
Provided that either cysts are usually distinguishable from solid tumors by ultrasound or sloths actually let algae grow on their hides so they can camouflage themselves better, we know that it is a common misconception that if command languages are useful for automating routine or commonly performed tasks, then aqueous solution is neutral or slightly acid. Should it be the case that it is a common misconception that either either cysts are usually distinguishable from solid tumors by ultrasound or sloths actually let algae grow on their hides so they can camouflage themselves better or if an overture is music, then string is used for violins, it follows that pigeons prefer to roost on level surfaces. When it is a common misconception that either either cysts are usually distinguishable from solid tumors by ultrasound or sloths actually let algae grow on their hides so they can camouflage themselves better or if an overture is music, then string is used for violins is true, it follows that the statement, pigeons prefer to roost on level surfaces, does not hold. Those that suggest large animals are an unusual host for fleas are right. It is a fact that either if social relationships can remain intact, based on shared religious practice, then infrastructure is a public good with external benefits or if large animals are an unusual host for fleas, then if if an overture is music, then string is used for violins, then it is a common misconception that if command languages are useful for automating routine or commonly performed tasks, then aqueous solution is neutral or slightly acid. Those that suggest if social relationships can remain intact, based on shared religious practice, then infrastructure is a public good with external benefits are wrong.
|
It is a common misconception that if command languages are useful for automating routine or commonly performed tasks, then aqueous solution is neutral or slightly acid.
|
The notion that 'command language is language' is untrue.
|
Uncertain
|
Disjunction Elimination:
Either (Either [2] or [3].) or (If [4], then [5].). [SC1-1]
If (Either [2] or [3].), then (Not (If [0], then [1].).).
If (If [4], then [5].), then (Not (If [0], then [1].).). [SC3-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either (Either [2] or [3].) or (If [4], then [5].).).), then [7].
If (Not (Either (Either [2] or [3].) or (If [4], then [5].).).), then (Not [7].).
Therefore, Either (Either [2] or [3].) or (If [4], then [5].)..
[SC3-1]
Modus Ponens:
If [6], then (If (If [4], then [5].), then (Not (If [0], then [1].).).). [SC1-2]
[6]
Therefore, If (If [4], then [5].), then (Not (If [0], then [1].).)..
[SC1-2]
Disjunctive Syllogism:
Either (If [8], then [9].) or (If [6], then (If (If [4], then [5].), then (Not (If [0], then [1].).).).).
Not (If [8], then [9].).
Therefore, If [6], then (If (If [4], then [5].), then (Not (If [0], then [1].).).)..
|
{0: 'Command languages are useful for automating routine or commonly performed tasks.', 1: 'Aqueous solution is neutral or slightly acid.', 2: 'Cysts are usually distinguishable from solid tumors by ultrasound.', 3: 'Sloths actually let algae grow on their hides so they can camouflage themselves better.', 4: 'An overture is music.', 5: 'String is used for violins.', 6: 'Large animals are an unusual host for fleas.', 7: 'Pigeons prefer to roost on level surfaces.', 8: 'Social relationships can remain intact, based on shared religious practice.', 9: 'Infrastructure is a public good with external benefits.'}
| 4 |
3,893 |
['When either robins are about ten inches long or databases are probably one of the most common and fundamental types of software is true, it follows that frame drums have a long ring, which lends itself to singing with it.', 'We know that at least one of two things is true: if most dogs possess descendants, then any wet areas are breeding grounds for fungus and germs, or if sea turtles have shells, then foreign patents govern use.', "Whenever it is true that if sea turtles have shells, then foreign patents govern use, 'either robins are about ten inches long or databases are probably one of the most common and fundamental types of software' is true.", 'The statement, bats are the only mammal that can actually fly, does not hold.', "So long as the claim that either bats are the only mammal that can actually fly or if if most dogs possess descendants, then any wet areas are breeding grounds for fungus and germs, then either robins are about ten inches long or databases are probably one of the most common and fundamental types of software is false, 'food antigens can trigger the mast cell mechanism at any point in their journey through the body' is true.", 'One may reasonably assume that if the claim that either bats are the only mammal that can actually fly or if if most dogs possess descendants, then any wet areas are breeding grounds for fungus and germs, then either robins are about ten inches long or databases are probably one of the most common and fundamental types of software is false, then the claim that food antigens can trigger the mast cell mechanism at any point in their journey through the body does not reflect reality.']
|
When either robins are about ten inches long or databases are probably one of the most common and fundamental types of software is true, it follows that frame drums have a long ring, which lends itself to singing with it. We know that at least one of two things is true: if most dogs possess descendants, then any wet areas are breeding grounds for fungus and germs, or if sea turtles have shells, then foreign patents govern use. Whenever it is true that if sea turtles have shells, then foreign patents govern use, 'either robins are about ten inches long or databases are probably one of the most common and fundamental types of software' is true. The statement, bats are the only mammal that can actually fly, does not hold. So long as the claim that either bats are the only mammal that can actually fly or if if most dogs possess descendants, then any wet areas are breeding grounds for fungus and germs, then either robins are about ten inches long or databases are probably one of the most common and fundamental types of software is false, 'food antigens can trigger the mast cell mechanism at any point in their journey through the body' is true. One may reasonably assume that if the claim that either bats are the only mammal that can actually fly or if if most dogs possess descendants, then any wet areas are breeding grounds for fungus and germs, then either robins are about ten inches long or databases are probably one of the most common and fundamental types of software is false, then the claim that food antigens can trigger the mast cell mechanism at any point in their journey through the body does not reflect reality.
|
Those that suggest frame drums have a long ring, which lends itself to singing with it are right.
|
Frame drums are among the oldest and most versatile of drums.
|
Uncertain
|
Modus Ponens:
If (Either [1] or [2].), then [0].
Either [1] or [2]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either (If [3], then [4].) or (If [5], then [6].).
If (If [3], then [4].), then (Either [1] or [2].). [SC2-2]
If (If [5], then [6].), then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC2-2]
Disjunctive Syllogism:
Either [7] or (If (If [3], then [4].), then (Either [1] or [2].).). [SC1-3]
Not [7].
Therefore, If (If [3], then [4].), then (Either [1] or [2].)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (Either [7] or (If (If [3], then [4].), then (Either [1] or [2].).).).), then [8].
If (Not (Either [7] or (If (If [3], then [4].), then (Either [1] or [2].).).).), then (Not [8].).
Therefore, Either [7] or (If (If [3], then [4].), then (Either [1] or [2].).)..
|
{0: 'Frame drums have a long ring, which lends itself to singing with it.', 1: 'Robins are about ten inches long.', 2: 'Databases are probably one of the most common and fundamental types of software.', 3: 'Most dogs possess descendants.', 4: 'Any wet areas are breeding grounds for fungus and germs.', 5: 'Sea turtles have shells.', 6: 'Foreign patents govern use.', 7: 'Bats are the only mammal that can actually fly.', 8: 'Food antigens can trigger the mast cell mechanism at any point in their journey through the body.'}
| 4 |
3,534 |
['Assuming the claim that trees have surfaces has no merit, we know that gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs.', "Once we know the statement, if the notion that 'if the claim that trees have surfaces has no merit, then the claim that gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs is false' is untrue, then sex is used to lure a man into a legal contract to support a woman and their children, does not hold, we also know that geologists characterize streams as youthful, mature, and old.", "Whenever it is true that the statement, if the notion that 'if the claim that trees have surfaces has no merit, then the claim that gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs is false' is untrue, then sex is used to lure a man into a legal contract to support a woman and their children, does not hold, 'it is not the case that geologists characterize streams as youthful, mature, and old' is true.", "Given that the statement that states if the notion that 'if the claim that trees have surfaces has no merit, then the claim that gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs is false' is untrue, then the claim that sex is used to lure a man into a legal contract to support a woman and their children has no merit is false, it can be inferred that wagtails have (part) cytoplasm.", "Given that the statement that states if the notion that 'if the claim that trees have surfaces has no merit, then the claim that gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs is false' is untrue, then the claim that sex is used to lure a man into a legal contract to support a woman and their children has no merit is false, it can be inferred that the claim that wagtails have (part) cytoplasm does not correspond with reality."]
|
Assuming the claim that trees have surfaces has no merit, we know that gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs. Once we know the statement, if the notion that 'if the claim that trees have surfaces has no merit, then the claim that gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs is false' is untrue, then sex is used to lure a man into a legal contract to support a woman and their children, does not hold, we also know that geologists characterize streams as youthful, mature, and old. Whenever it is true that the statement, if the notion that 'if the claim that trees have surfaces has no merit, then the claim that gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs is false' is untrue, then sex is used to lure a man into a legal contract to support a woman and their children, does not hold, 'it is not the case that geologists characterize streams as youthful, mature, and old' is true. Given that the statement that states if the notion that 'if the claim that trees have surfaces has no merit, then the claim that gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs is false' is untrue, then the claim that sex is used to lure a man into a legal contract to support a woman and their children has no merit is false, it can be inferred that wagtails have (part) cytoplasm. Given that the statement that states if the notion that 'if the claim that trees have surfaces has no merit, then the claim that gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs is false' is untrue, then the claim that sex is used to lure a man into a legal contract to support a woman and their children has no merit is false, it can be inferred that the claim that wagtails have (part) cytoplasm does not correspond with reality.
|
It is a simple truth that trees have surfaces.
|
The statement that states trees have surfaces is false.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then (Not [1].).).), then [2]. [SC1-2]
If (Not (If (Not [0].), then (Not [1].).).), then (Not [2].). [SC2-2]
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not [0].), then (Not [1].).).), then [2].).), then [3].
If (Not (If (Not (If (Not [0].), then (Not [1].).).), then [2].).), then (Not [3].).
Therefore, If (Not (If (Not [0].), then (Not [1].).).), then [2]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not [0].), then (Not [1].).).), then (Not [2].).).), then [4].
If (Not (If (Not (If (Not [0].), then (Not [1].).).), then (Not [2].).).), then (Not [4].).
Therefore, If (Not (If (Not [0].), then (Not [1].).).), then (Not [2].)..
|
{0: 'Trees have surfaces.', 1: 'Gazelles are browsers and grazers, feeding on grasses, herbs, and shrubs.', 2: 'Sex is used to lure a man into a legal contract to support a woman and their children.', 3: 'Geologists characterize streams as youthful, mature, and old.', 4: 'Wagtails have (part) cytoplasm.'}
| 4 |
3,903 |
['There is good reason to believe that either some food includes dairy products or unified messaging is a rapidly growing market.', 'One may reasonably assume that if unified messaging is a rapidly growing market, then cuttlefish is dense with vital minerals.', 'One may reasonably assume that if rings can cut deeply into fingers and bracelets can get caught in reins or lead lines, then if some food includes dairy products, then if televisions are large and loud, then some people see tournaments as the pinnacle of martial arts ability.', 'The idea that rings can cut deeply into fingers and bracelets can get caught in reins or lead lines is true.', 'On the condition that amino acids are small enough to pass into the bloodstream, it is definitely the case that if if televisions are large and loud, then some people see tournaments as the pinnacle of martial arts ability, then cuttlefish is dense with vital minerals.', 'It is reasonable to believe that amino acids are small enough to pass into the bloodstream.']
|
There is good reason to believe that either some food includes dairy products or unified messaging is a rapidly growing market. One may reasonably assume that if unified messaging is a rapidly growing market, then cuttlefish is dense with vital minerals. One may reasonably assume that if rings can cut deeply into fingers and bracelets can get caught in reins or lead lines, then if some food includes dairy products, then if televisions are large and loud, then some people see tournaments as the pinnacle of martial arts ability. The idea that rings can cut deeply into fingers and bracelets can get caught in reins or lead lines is true. On the condition that amino acids are small enough to pass into the bloodstream, it is definitely the case that if if televisions are large and loud, then some people see tournaments as the pinnacle of martial arts ability, then cuttlefish is dense with vital minerals. It is reasonable to believe that amino acids are small enough to pass into the bloodstream.
|
The idea that cuttlefish is dense with vital minerals is true.
|
Cuttlefishs occur in tropical water.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC2-1]
Hypothetical Syllogism:
If [1], then (If [3], then [4].). [SC1-2]
If (If [3], then [4].), then [0]. [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Modus Ponens:
If [6], then (If [1], then (If [3], then [4].).).
[6]
Therefore, If [1], then (If [3], then [4].)..
[SC2-2]
Modus Ponens:
If [5], then (If (If [3], then [4].), then [0].).
[5]
Therefore, If (If [3], then [4].), then [0]..
|
{0: 'Cuttlefish is dense with vital minerals.', 1: 'Some food includes dairy products.', 2: 'Unified messaging is a rapidly growing market.', 3: 'Televisions are large and loud.', 4: 'Some people see tournaments as the pinnacle of martial arts ability.', 5: 'Amino acids are small enough to pass into the bloodstream.', 6: 'Rings can cut deeply into fingers and bracelets can get caught in reins or lead lines.'}
| 4 |
3,276 |
['Once we know proper sanitation can reduce insect pests significantly, we also know that circular dichroism is obtained only within absorption bands.', 'It is not true that some finger holes are part of fifes.', 'On the condition that we know that the claim that either some finger holes are part of fifes or proper sanitation can reduce insect pests significantly is false, it is definitely the case that it is a common misconception that day counts are calendar days figured from the start date of the course.', "It is a fact that either if fashions run the gamut from everyday wear to designer originals, then atoms combine to form molecules or tresses have (part) widow's peaks.", 'When if fashions run the gamut from everyday wear to designer originals, then atoms combine to form molecules is true, it follows that if we know that the claim that either some finger holes are part of fifes or proper sanitation can reduce insect pests significantly is false, then day counts are calendar days figured from the start date of the course.', "On the condition that tresses have (part) widow's peaks, it is definitely the case that if we know that the claim that either some finger holes are part of fifes or proper sanitation can reduce insect pests significantly is false, then day counts are calendar days figured from the start date of the course."]
|
Once we know proper sanitation can reduce insect pests significantly, we also know that circular dichroism is obtained only within absorption bands. It is not true that some finger holes are part of fifes. On the condition that we know that the claim that either some finger holes are part of fifes or proper sanitation can reduce insect pests significantly is false, it is definitely the case that it is a common misconception that day counts are calendar days figured from the start date of the course. It is a fact that either if fashions run the gamut from everyday wear to designer originals, then atoms combine to form molecules or tresses have (part) widow's peaks. When if fashions run the gamut from everyday wear to designer originals, then atoms combine to form molecules is true, it follows that if we know that the claim that either some finger holes are part of fifes or proper sanitation can reduce insect pests significantly is false, then day counts are calendar days figured from the start date of the course. On the condition that tresses have (part) widow's peaks, it is definitely the case that if we know that the claim that either some finger holes are part of fifes or proper sanitation can reduce insect pests significantly is false, then day counts are calendar days figured from the start date of the course.
|
It is a simple truth that circular dichroism is obtained only within absorption bands.
|
Circular dichroism is the difference in the absorption of left and right circularly polarized light.
|
Uncertain
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or [1]. [SC1-2]
Not [2].
Therefore, [1].
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [2] or [1].).), then [3]. [SC1-3]
If (Not (Either [2] or [1].).), then (Not [3].).
Therefore, Either [2] or [1]..
[SC1-3]
Disjunction Elimination:
Either (If [4], then [5].) or [6].
If (If [4], then [5].), then (If (Not (Either [2] or [1].).), then [3].).
If [6], then (If (Not (Either [2] or [1].).), then [3].).
Therefore, If (Not (Either [2] or [1].).), then [3]..
|
{0: 'Circular dichroism is obtained only within absorption bands.', 1: 'Proper sanitation can reduce insect pests significantly.', 2: 'Some finger holes are part of fifes.', 3: 'Day counts are calendar days figured from the start date of the course.', 4: 'Fashions run the gamut from everyday wear to designer originals.', 5: 'Atoms combine to form molecules .', 6: "Tresses have (part) widow's peaks."}
| 4 |
3,284 |
["So long as the claim that some climbers thrive on adrenaline rushes and personal achievement has no merit, 'greatness is measured in terms of truth to oneself AND the world' is true.", 'If the claim that some climbers thrive on adrenaline rushes and personal achievement has no merit, then if ozone also contributes to premature deaths from cardiovascular disease and other chronic illnesses, then some smoke causes coronary heart diseases.', 'If if ozone also contributes to premature deaths from cardiovascular disease and other chronic illnesses, then some smoke causes coronary heart diseases, then the claim that advertisements are located in television does not reflect reality.', 'One may reasonably assume that if greatness is measured in terms of truth to oneself AND the world, then if malnutrition increases the severity of the disease signs, then eternal life is more than a chronological event and change of composition.', 'On the condition that if malnutrition increases the severity of the disease signs, then eternal life is more than a chronological event and change of composition, it is definitely the case that advertisements are located in television.']
|
So long as the claim that some climbers thrive on adrenaline rushes and personal achievement has no merit, 'greatness is measured in terms of truth to oneself AND the world' is true. If the claim that some climbers thrive on adrenaline rushes and personal achievement has no merit, then if ozone also contributes to premature deaths from cardiovascular disease and other chronic illnesses, then some smoke causes coronary heart diseases. If if ozone also contributes to premature deaths from cardiovascular disease and other chronic illnesses, then some smoke causes coronary heart diseases, then the claim that advertisements are located in television does not reflect reality. One may reasonably assume that if greatness is measured in terms of truth to oneself AND the world, then if malnutrition increases the severity of the disease signs, then eternal life is more than a chronological event and change of composition. On the condition that if malnutrition increases the severity of the disease signs, then eternal life is more than a chronological event and change of composition, it is definitely the case that advertisements are located in television.
|
Those that suggest some climbers thrive on adrenaline rushes and personal achievement are right.
|
Those that suggest some climbers thrive on adrenaline rushes and personal achievement are right.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [4].
If [4], then [1]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Hypothetical Syllogism:
If [4], then (If [5], then [6].).
If (If [5], then [6].), then [1].
Therefore, If [4], then [1]..
[SC2-1]
Hypothetical Syllogism:
If (Not [0].), then (If [2], then [3].).
If (If [2], then [3].), then (Not [1].).
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Some climbers thrive on adrenaline rushes and personal achievement.', 1: 'Advertisements are located in television.', 2: 'Ozone also contributes to premature deaths from cardiovascular disease and other chronic illnesses.', 3: 'Some smoke causes coronary heart diseases.', 4: 'Greatness is measured in terms of truth to oneself AND the world.', 5: 'Malnutrition increases the severity of the disease signs.', 6: 'Eternal life is more than a chronological event and change of composition.'}
| 4 |
3,470 |
['The claim that embedded clauses are clauses inside other clauses does not correspond with reality.', 'Once we know amniotic fluid contains cells that are normally shed from the fetus, we also know that if the claim that either students have limits or horses chew vegetation is false, then embedded clauses are clauses inside other clauses.', "Whenever it is true that if procrastination is only a symptom or manifestation of something else, then thermals form as the sun heats the earth, and the air near the surface warms and expands, 'either wolves eat many different animals or amniotic fluid contains cells that are normally shed from the fetus' is true.", 'Once we know procrastination is only a symptom or manifestation of something else, we also know that thermals form as the sun heats the earth, and the air near the surface warms and expands.', 'At least one of two things is true: clusters play an important role linking atoms or clusters with bulk, or if wolves eat many different animals, then if the claim that either students have limits or horses chew vegetation is false, then embedded clauses are clauses inside other clauses.', 'The claim that clusters play an important role linking atoms or clusters with bulk is false.']
|
The claim that embedded clauses are clauses inside other clauses does not correspond with reality. Once we know amniotic fluid contains cells that are normally shed from the fetus, we also know that if the claim that either students have limits or horses chew vegetation is false, then embedded clauses are clauses inside other clauses. Whenever it is true that if procrastination is only a symptom or manifestation of something else, then thermals form as the sun heats the earth, and the air near the surface warms and expands, 'either wolves eat many different animals or amniotic fluid contains cells that are normally shed from the fetus' is true. Once we know procrastination is only a symptom or manifestation of something else, we also know that thermals form as the sun heats the earth, and the air near the surface warms and expands. At least one of two things is true: clusters play an important role linking atoms or clusters with bulk, or if wolves eat many different animals, then if the claim that either students have limits or horses chew vegetation is false, then embedded clauses are clauses inside other clauses. The claim that clusters play an important role linking atoms or clusters with bulk is false.
|
Either one or both of these statements are true: students have limits, or horses chew vegetation.
|
Either one or both of these statements are true: students have limits, or horses chew vegetation.
|
TRUE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
Not [2].
Therefore, Either [0] or [1]..
[SC1-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (If (Not (Either [0] or [1].).), then [2].). [SC2-2]
If [4], then (If (Not (Either [0] or [1].).), then [2].).
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC1-2]
Modus Ponens:
If (If [5], then [6].), then (Either [3] or [4].).
If [5], then [6].
Therefore, Either [3] or [4]..
[SC2-2]
Disjunctive Syllogism:
Either [7] or (If [3], then (If (Not (Either [0] or [1].).), then [2].).).
Not [7].
Therefore, If [3], then (If (Not (Either [0] or [1].).), then [2].)..
|
{0: 'Students have limits.', 1: 'Horses chew vegetation.', 2: 'Embedded clauses are clauses inside other clauses.', 3: 'Wolves eat many different animals.', 4: 'Amniotic fluid contains cells that are normally shed from the fetus.', 5: 'Procrastination is only a symptom or manifestation of something else.', 6: 'Thermals form as the sun heats the earth, and the air near the surface warms and expands.', 7: 'Clusters play an important role linking atoms or clusters with bulk.'}
| 4 |
3,426 |
["So long as transportation is such that people can get from one corner of a city to another fast, 'those that suggest pupil dilation is performed to allow for a thorough retinal examination are wrong' is true.", "Whenever it is true that it is not the case that transportation is such that people can get from one corner of a city to another fast, 'the claim that some beetles eat petals has no merit' is true.", 'Assuming conflicts can develop between parents, or parents and children, we know that some beetles eat petals.', 'We know that at least one of two things is true: government places quantitative restrictions, or most exotic food improves dental health.', 'One may reasonably assume that if government places quantitative restrictions, then if it is not the case that transportation is such that people can get from one corner of a city to another fast, then conflicts can develop between parents, or parents and children.', "So long as most exotic food improves dental health, 'if it is not the case that transportation is such that people can get from one corner of a city to another fast, then conflicts can develop between parents, or parents and children' is true."]
|
So long as transportation is such that people can get from one corner of a city to another fast, 'those that suggest pupil dilation is performed to allow for a thorough retinal examination are wrong' is true. Whenever it is true that it is not the case that transportation is such that people can get from one corner of a city to another fast, 'the claim that some beetles eat petals has no merit' is true. Assuming conflicts can develop between parents, or parents and children, we know that some beetles eat petals. We know that at least one of two things is true: government places quantitative restrictions, or most exotic food improves dental health. One may reasonably assume that if government places quantitative restrictions, then if it is not the case that transportation is such that people can get from one corner of a city to another fast, then conflicts can develop between parents, or parents and children. So long as most exotic food improves dental health, 'if it is not the case that transportation is such that people can get from one corner of a city to another fast, then conflicts can develop between parents, or parents and children' is true.
|
Those that suggest pupil dilation is performed to allow for a thorough retinal examination are wrong.
|
Those that suggest pupil dilation is performed to allow for a thorough retinal examination are wrong.
|
TRUE
|
Modus Ponens:
If [1], then (Not [0].).
[1] [SC2-1]
Therefore, Not [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then [2]. [SC1-2]
If (Not [1].), then (Not [2].).
Therefore, [1].
[SC1-2]
Hypothetical Syllogism:
If (Not [1].), then [3]. [SC1-3]
If [3], then [2].
Therefore, If (Not [1].), then [2]..
[SC1-3]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not [1].), then [3].).
If [5], then (If (Not [1].), then [3].).
Therefore, If (Not [1].), then [3]..
|
{0: 'Pupil dilation is performed to allow for a thorough retinal examination.', 1: 'Transportation is such that people can get from one corner of a city to another fast.', 2: 'Some beetles eat petals.', 3: 'Conflicts can develop between parents, or parents and children.', 4: 'Government places quantitative restrictions.', 5: 'Most exotic food improves dental health.'}
| 4 |
3,281 |
['If it is a common misconception that people wash their dogs more frequently than they cut their own hair, then either sand bars form on the inside of river curves or fairy tales reflect the mythic substrata of our own lives.', "So long as either forests are dynamic places, constantly changing or some people believe that life is all about the search for personal meaning or love or authenticity, 'eaglets are relatively non-aggressive' is true.", 'If either forests are dynamic places, constantly changing or some people believe that life is all about the search for personal meaning or love or authenticity, then the statement that states eaglets are relatively non-aggressive is false.', 'Either one or both of these statements are true: most worker ants perform duties, or if either sand bars form on the inside of river curves or fairy tales reflect the mythic substrata of our own lives, then either forests are dynamic places, constantly changing or some people believe that life is all about the search for personal meaning or love or authenticity.', "The notion that 'most worker ants perform duties' is untrue."]
|
If it is a common misconception that people wash their dogs more frequently than they cut their own hair, then either sand bars form on the inside of river curves or fairy tales reflect the mythic substrata of our own lives. So long as either forests are dynamic places, constantly changing or some people believe that life is all about the search for personal meaning or love or authenticity, 'eaglets are relatively non-aggressive' is true. If either forests are dynamic places, constantly changing or some people believe that life is all about the search for personal meaning or love or authenticity, then the statement that states eaglets are relatively non-aggressive is false. Either one or both of these statements are true: most worker ants perform duties, or if either sand bars form on the inside of river curves or fairy tales reflect the mythic substrata of our own lives, then either forests are dynamic places, constantly changing or some people believe that life is all about the search for personal meaning or love or authenticity. The notion that 'most worker ants perform duties' is untrue.
|
Many people rightly believe that people wash their dogs more frequently than they cut their own hair.
|
Many people rightly believe that people wash their dogs more frequently than they cut their own hair.
|
TRUE
|
Modus Tonens:
If (Not [0].), then (Either [1] or [2].). [SC1-1]
Not (Either [1] or [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then (Either [4] or [5].).
If (Either [4] or [5].), then (Either [1] or [2].). [SC2-2]
Therefore, If (Not [0].), then (Either [1] or [2].)..
[SC2-2]
Disjunctive Syllogism:
Either [6] or (If (Either [4] or [5].), then (Either [1] or [2].).).
Not [6].
Therefore, If (Either [4] or [5].), then (Either [1] or [2].)..
[SC2-1]
Reductio Ad Absurdum:
If (Either [1] or [2].), then [3].
If (Either [1] or [2].), then (Not [3].).
Therefore, Not (Either [1] or [2].)..
|
{0: 'People wash their dogs more frequently than they cut their own hair.', 1: 'Forests are dynamic places, constantly changing.', 2: 'Some people believe that life is all about the search for personal meaning or love or authenticity.', 3: 'Eaglets are relatively non-aggressive.', 4: 'Sand bars form on the inside of river curves.', 5: 'Fairy tales reflect the mythic substrata of our own lives.', 6: 'Most worker ants perform duties.'}
| 4 |
3,120 |
['When the statement that states if the claim that domestic terrorism tends to deal only within the United States does not correspond with reality, then if fog occurs more often than any single precipitation type at all temperatures, then people continue to be exposed to heavy metals in the environment is false is true, it follows that organic farmers produce foods for the discerning shopper.', 'Those that suggest organic farmers produce foods for the discerning shopper are wrong.', 'Either one or both of these statements are true: pungency declines in rich soils and after flowering so pick it in mid-summer, or if religion is the interface of spirituality and culture, then drupes are fruit.', "Whenever it is true that if religion is the interface of spirituality and culture, then drupes are fruit, 'if the claim that domestic terrorism tends to deal only within the United States does not correspond with reality, then the notion that 'if fog occurs more often than any single precipitation type at all temperatures, then people continue to be exposed to heavy metals in the environment' is untrue' is true.", "There is good reason to believe that either ozone is measured in Dobson Units or if pungency declines in rich soils and after flowering so pick it in mid-summer, then if the claim that domestic terrorism tends to deal only within the United States does not correspond with reality, then the notion that 'if fog occurs more often than any single precipitation type at all temperatures, then people continue to be exposed to heavy metals in the environment' is untrue.", 'The claim that ozone is measured in Dobson Units does not correspond with reality.']
|
When the statement that states if the claim that domestic terrorism tends to deal only within the United States does not correspond with reality, then if fog occurs more often than any single precipitation type at all temperatures, then people continue to be exposed to heavy metals in the environment is false is true, it follows that organic farmers produce foods for the discerning shopper. Those that suggest organic farmers produce foods for the discerning shopper are wrong. Either one or both of these statements are true: pungency declines in rich soils and after flowering so pick it in mid-summer, or if religion is the interface of spirituality and culture, then drupes are fruit. Whenever it is true that if religion is the interface of spirituality and culture, then drupes are fruit, 'if the claim that domestic terrorism tends to deal only within the United States does not correspond with reality, then the notion that 'if fog occurs more often than any single precipitation type at all temperatures, then people continue to be exposed to heavy metals in the environment' is untrue' is true. There is good reason to believe that either ozone is measured in Dobson Units or if pungency declines in rich soils and after flowering so pick it in mid-summer, then if the claim that domestic terrorism tends to deal only within the United States does not correspond with reality, then the notion that 'if fog occurs more often than any single precipitation type at all temperatures, then people continue to be exposed to heavy metals in the environment' is untrue. The claim that ozone is measured in Dobson Units does not correspond with reality.
|
The claim that domestic terrorism tends to deal only within the United States is true.
|
The claim that domestic terrorism tends to deal only within the United States is true.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then (If [1], then [2].). [SC1-1]
If (Not [0].), then (Not (If [1], then [2].).). [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Not [0].), then (If [1], then [2].).).), then [6].
Not [6].
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC2-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then (If (Not [0].), then (Not (If [1], then [2].).).). [SC2-2]
If (If [4], then [5].), then (If (Not [0].), then (Not (If [1], then [2].).).).
Therefore, If (Not [0].), then (Not (If [1], then [2].).)..
[SC2-2]
Disjunctive Syllogism:
Either [7] or (If [3], then (If (Not [0].), then (Not (If [1], then [2].).).).).
Not [7].
Therefore, If [3], then (If (Not [0].), then (Not (If [1], then [2].).).)..
|
{0: 'Domestic terrorism tends to deal only within the United States.', 1: 'Fog occurs more often than any single precipitation type at all temperatures.', 2: 'People continue to be exposed to heavy metals in the environment.', 3: 'Pungency declines in rich soils and after flowering so pick it in mid-summer.', 4: 'Religion is the interface of spirituality and culture.', 5: 'Drupes are fruit.', 6: 'Organic farmers produce foods for the discerning shopper.', 7: 'Ozone is measured in Dobson Units.'}
| 4 |
3,593 |
['Provided that heart disease rises in young people, we know that most leaf monkeys have fur.', 'If we know that the claim that if the claim that heart disease rises in young people does not correspond with reality, then windpipes have (part) epiglottises is false, then effluents dumped in watercourses transform the major European rivers into veritable sewers.', 'Once we know we know that the claim that if the claim that heart disease rises in young people does not correspond with reality, then windpipes have (part) epiglottises is false, we also know that the claim that effluents dumped in watercourses transform the major European rivers into veritable sewers is false.', 'Provided that windpipes have (part) epiglottises, we know that honeybees are important to many crops and play a major role in the food supply.', "When windpipes have (part) epiglottises is true, it follows that the statement that 'honeybees are important to many crops and play a major role in the food supply' is incorrect."]
|
Provided that heart disease rises in young people, we know that most leaf monkeys have fur. If we know that the claim that if the claim that heart disease rises in young people does not correspond with reality, then windpipes have (part) epiglottises is false, then effluents dumped in watercourses transform the major European rivers into veritable sewers. Once we know we know that the claim that if the claim that heart disease rises in young people does not correspond with reality, then windpipes have (part) epiglottises is false, we also know that the claim that effluents dumped in watercourses transform the major European rivers into veritable sewers is false. Provided that windpipes have (part) epiglottises, we know that honeybees are important to many crops and play a major role in the food supply. When windpipes have (part) epiglottises is true, it follows that the statement that 'honeybees are important to many crops and play a major role in the food supply' is incorrect.
|
The statement 'most leaf monkeys have fur' is true.
|
Leaf monkeys weigh kgs.
|
Uncertain
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not [1].), then [2]. [SC1-2]
Not [2]. [SC2-2]
Therefore, [1].
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not [1].), then [2].).), then [3].
If (Not (If (Not [1].), then [2].).), then (Not [3].).
Therefore, If (Not [1].), then [2]..
[SC2-2]
Reductio Ad Absurdum:
If [2], then [4].
If [2], then (Not [4].).
Therefore, Not [2]..
|
{0: 'Most leaf monkeys have fur.', 1: 'Heart disease rises in young people.', 2: 'Windpipes have (part) epiglottises.', 3: 'Effluents dumped in watercourses transform the major European rivers into veritable sewers.', 4: 'Honeybees are important to many crops and play a major role in the food supply.'}
| 4 |
3,981 |
['There is good reason to believe that either morality is necessary for a society to exist or deep gutters reduce the amount of water splashing back in the pool.', 'When morality is necessary for a society to exist is true, it follows that if most dolphins have teeth, then illness depletes the body s stores even further.', 'It is a fact that either indian jails are feudal in their administration or most dolphins have teeth.', 'The claim that indian jails are feudal in their administration has no merit.', "Whenever it is true that shorebirds are among the most photogenic of birds, 'if deep gutters reduce the amount of water splashing back in the pool, then if most dolphins have teeth, then illness depletes the body s stores even further' is true.", 'Many people rightly believe that shorebirds are among the most photogenic of birds.']
|
There is good reason to believe that either morality is necessary for a society to exist or deep gutters reduce the amount of water splashing back in the pool. When morality is necessary for a society to exist is true, it follows that if most dolphins have teeth, then illness depletes the body s stores even further. It is a fact that either indian jails are feudal in their administration or most dolphins have teeth. The claim that indian jails are feudal in their administration has no merit. Whenever it is true that shorebirds are among the most photogenic of birds, 'if deep gutters reduce the amount of water splashing back in the pool, then if most dolphins have teeth, then illness depletes the body s stores even further' is true. Many people rightly believe that shorebirds are among the most photogenic of birds.
|
The claim that illness depletes the body s stores even further holds true.
|
Some illnesses result in unfavorable health outcomes.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If [1], then [0].).
If [3], then (If [1], then [0].). [SC3-2]
Therefore, If [1], then [0]..
[SC3-2]
Modus Ponens:
If [5], then (If [3], then (If [1], then [0].).).
[5]
Therefore, If [3], then (If [1], then [0].)..
[SC2-1]
Disjunctive Syllogism:
Either [4] or [1].
Not [4].
Therefore, [1].
|
{0: 'Illness depletes the body s stores even further.', 1: 'Most dolphins have teeth.', 2: 'Morality is necessary for a society to exist.', 3: 'Deep gutters reduce the amount of water splashing back in the pool.', 4: 'Indian jails are feudal in their administration.', 5: 'Shorebirds are among the most photogenic of birds.'}
| 4 |
3,013 |
['Provided that cryptography is one of the main technological tools, we know that sand is made up of fine grains of rock, coral and shells.', "On the condition that the claim that if the statement 'cryptography is one of the main technological tools' can be considered false, then convection drives the outer-core fluid and it circulates relative to the earth does not reflect reality, it is definitely the case that some insects feed in nests.", 'The statement that states some insects feed in nests is false.', 'Should it be the case that convection drives the outer-core fluid and it circulates relative to the earth, it follows that if green apples persist in a clean, long finish, then copper has lower resistivity, and ultimately lower resistance, than aluminum.', "Whenever it is true that convection drives the outer-core fluid and it circulates relative to the earth, 'we know that the claim that if green apples persist in a clean, long finish, then copper has lower resistivity, and ultimately lower resistance, than aluminum is false' is true."]
|
Provided that cryptography is one of the main technological tools, we know that sand is made up of fine grains of rock, coral and shells. On the condition that the claim that if the statement 'cryptography is one of the main technological tools' can be considered false, then convection drives the outer-core fluid and it circulates relative to the earth does not reflect reality, it is definitely the case that some insects feed in nests. The statement that states some insects feed in nests is false. Should it be the case that convection drives the outer-core fluid and it circulates relative to the earth, it follows that if green apples persist in a clean, long finish, then copper has lower resistivity, and ultimately lower resistance, than aluminum. Whenever it is true that convection drives the outer-core fluid and it circulates relative to the earth, 'we know that the claim that if green apples persist in a clean, long finish, then copper has lower resistivity, and ultimately lower resistance, than aluminum is false' is true.
|
It is true that sand is made up of fine grains of rock, coral and shells.
|
Sand covers the ocean floor.
|
Uncertain
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not [1].), then [2]. [SC1-2]
Not [2]. [SC2-2]
Therefore, [1].
[SC1-2]
Modus Tonens:
If (Not (If (Not [1].), then [2].).), then [5].
Not [5].
Therefore, If (Not [1].), then [2]..
[SC2-2]
Reductio Ad Absurdum:
If [2], then (If [3], then [4].).
If [2], then (Not (If [3], then [4].).).
Therefore, Not [2]..
|
{0: 'Sand is made up of fine grains of rock, coral and shells.', 1: 'Cryptography is one of the main technological tools.', 2: 'Convection drives the outer-core fluid and it circulates relative to the earth.', 3: 'Green apples persist in a clean, long finish.', 4: 'Copper has lower resistivity, and ultimately lower resistance, than aluminum.', 5: 'Some insects feed in nests.'}
| 4 |
3,655 |
['Assuming if grizzlies usually den on south facing slopes near treeline, then ecological relationship is the relationship between organisms in an ecosystem, we know that it is a common misconception that hearts are courage.', "So long as mangoes grow in a variety of shapes, 'it is a common misconception that hearts are courage' is true.", 'If surfaces reflect sunlight, then renewable resources account for less than two per cent of electricity output.', "Whenever it is true that renewable resources account for less than two per cent of electricity output, 'either if grizzlies usually den on south facing slopes near treeline, then ecological relationship is the relationship between organisms in an ecosystem or mangoes grow in a variety of shapes' is true.", 'We know that either deer use the same general area year after year during the pre-rut and rut or surfaces reflect sunlight.', 'The claim that deer use the same general area year after year during the pre-rut and rut does not correspond with reality.']
|
Assuming if grizzlies usually den on south facing slopes near treeline, then ecological relationship is the relationship between organisms in an ecosystem, we know that it is a common misconception that hearts are courage. So long as mangoes grow in a variety of shapes, 'it is a common misconception that hearts are courage' is true. If surfaces reflect sunlight, then renewable resources account for less than two per cent of electricity output. Whenever it is true that renewable resources account for less than two per cent of electricity output, 'either if grizzlies usually den on south facing slopes near treeline, then ecological relationship is the relationship between organisms in an ecosystem or mangoes grow in a variety of shapes' is true. We know that either deer use the same general area year after year during the pre-rut and rut or surfaces reflect sunlight. The claim that deer use the same general area year after year during the pre-rut and rut does not correspond with reality.
|
It is a common misconception that hearts are courage.
|
It is a common misconception that hearts are courage.
|
TRUE
|
Disjunction Elimination:
Either (If [1], then [2].) or [3]. [SC1-1]
If (If [1], then [2].), then (Not [0].).
If [3], then (Not [0].).
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [4], then (Either (If [1], then [2].) or [3].). [SC1-2]
[4] [SC2-2]
Therefore, Either (If [1], then [2].) or [3]..
[SC1-2]
Hypothetical Syllogism:
If [4], then [6].
If [6], then (Either (If [1], then [2].) or [3].).
Therefore, If [4], then (Either (If [1], then [2].) or [3].)..
[SC2-2]
Disjunctive Syllogism:
Either [5] or [4].
Not [5].
Therefore, [4].
|
{0: 'Hearts are courage.', 1: 'Grizzlies usually den on south facing slopes near treeline.', 2: 'Ecological relationship is the relationship between organisms in an ecosystem.', 3: 'Mangoes grow in a variety of shapes.', 4: 'Surfaces reflect sunlight.', 5: 'Deer use the same general area year after year during the pre-rut and rut.', 6: 'Renewable resources account for less than two per cent of electricity output.'}
| 4 |
3,455 |
['If rhinoceroses are large, herbivorous mammals identified by their characteristic horned snouts, then a logical topology is a network topology.', 'We know that either aerobic exercise is an invention of an extremely sadistic mind or the statement, a logical topology is a network topology, does not hold.', 'It is a common misconception that aerobic exercise is an invention of an extremely sadistic mind.', 'Either coccidiosis is diagnosed by performing a microscopic examination of a stool sample or behaviorist learning theorists believe that knowledge exists independently and outside of people.', "One may reasonably assume that if coccidiosis is diagnosed by performing a microscopic examination of a stool sample, then if the statement 'some reptiles require extensive parental care' can be considered false, then rhinoceroses are large, herbivorous mammals identified by their characteristic horned snouts.", "Should it be the case that behaviorist learning theorists believe that knowledge exists independently and outside of people, it follows that if the statement 'some reptiles require extensive parental care' can be considered false, then rhinoceroses are large, herbivorous mammals identified by their characteristic horned snouts."]
|
If rhinoceroses are large, herbivorous mammals identified by their characteristic horned snouts, then a logical topology is a network topology. We know that either aerobic exercise is an invention of an extremely sadistic mind or the statement, a logical topology is a network topology, does not hold. It is a common misconception that aerobic exercise is an invention of an extremely sadistic mind. Either coccidiosis is diagnosed by performing a microscopic examination of a stool sample or behaviorist learning theorists believe that knowledge exists independently and outside of people. One may reasonably assume that if coccidiosis is diagnosed by performing a microscopic examination of a stool sample, then if the statement 'some reptiles require extensive parental care' can be considered false, then rhinoceroses are large, herbivorous mammals identified by their characteristic horned snouts. Should it be the case that behaviorist learning theorists believe that knowledge exists independently and outside of people, it follows that if the statement 'some reptiles require extensive parental care' can be considered false, then rhinoceroses are large, herbivorous mammals identified by their characteristic horned snouts.
|
The claim that some reptiles require extensive parental care holds true.
|
Most reptiles have eyes.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [3]. [SC1-2]
If [3], then [1].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not [0].), then [3].).
If [5], then (If (Not [0].), then [3].).
Therefore, If (Not [0].), then [3]..
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].).
Not [2].
Therefore, Not [1]..
|
{0: 'Some reptiles require extensive parental care.', 1: 'A logical topology is a network topology.', 2: 'Aerobic exercise is an invention of an extremely sadistic mind.', 3: 'Rhinoceroses are large, herbivorous mammals identified by their characteristic horned snouts.', 4: 'Coccidiosis is diagnosed by performing a microscopic examination of a stool sample.', 5: 'Behaviorist learning theorists believe that knowledge exists independently and outside of people.'}
| 4 |
3,584 |
['At least one of two things is true: many horses have sharp edges, which require floating of the whole tooth surface, or if if optimism is the faith that leads to achievement, then biological anthropologists use dental formulae to classify groups of primates, then those that suggest winters are cold with snow are wrong.', "The statement 'many horses have sharp edges, which require floating of the whole tooth surface' can be considered false.", 'Given that either some animals freeze to death or drug use is a health problem, it can be inferred that if optimism is the faith that leads to achievement, then biological anthropologists use dental formulae to classify groups of primates.', 'Given that deer possess red spots, it can be inferred that if optimism is the faith that leads to achievement, then biological anthropologists use dental formulae to classify groups of primates.', "So long as the claim that either either some animals freeze to death or drug use is a health problem or deer possess red spots does not reflect reality, 'plants have single stems' is true.", 'Once we know the claim that either either some animals freeze to death or drug use is a health problem or deer possess red spots does not reflect reality, we also know that we know that the claim that plants have single stems is false.']
|
At least one of two things is true: many horses have sharp edges, which require floating of the whole tooth surface, or if if optimism is the faith that leads to achievement, then biological anthropologists use dental formulae to classify groups of primates, then those that suggest winters are cold with snow are wrong. The statement 'many horses have sharp edges, which require floating of the whole tooth surface' can be considered false. Given that either some animals freeze to death or drug use is a health problem, it can be inferred that if optimism is the faith that leads to achievement, then biological anthropologists use dental formulae to classify groups of primates. Given that deer possess red spots, it can be inferred that if optimism is the faith that leads to achievement, then biological anthropologists use dental formulae to classify groups of primates. So long as the claim that either either some animals freeze to death or drug use is a health problem or deer possess red spots does not reflect reality, 'plants have single stems' is true. Once we know the claim that either either some animals freeze to death or drug use is a health problem or deer possess red spots does not reflect reality, we also know that we know that the claim that plants have single stems is false.
|
Those that suggest winters are cold with snow are wrong.
|
The statement that states winter often means the onset of the flu is false.
|
Uncertain
|
Modus Ponens:
If (If [1], then [2].), then (Not [0].). [SC1-1]
If [1], then [2]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If (If [1], then [2].), then (Not [0].).).
Not [3].
Therefore, If (If [1], then [2].), then (Not [0].)..
[SC2-1]
Disjunction Elimination:
Either (Either [4] or [5].) or [6]. [SC1-2]
If (Either [4] or [5].), then (If [1], then [2].).
If [6], then (If [1], then [2].).
Therefore, If [1], then [2]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either (Either [4] or [5].) or [6].).), then [7].
If (Not (Either (Either [4] or [5].) or [6].).), then (Not [7].).
Therefore, Either (Either [4] or [5].) or [6]..
|
{0: 'Winters are cold with snow.', 1: 'Optimism is the faith that leads to achievement.', 2: 'Biological anthropologists use dental formulae to classify groups of primates.', 3: 'Many horses have sharp edges, which require floating of the whole tooth surface.', 4: 'Some animals freeze to death.', 5: 'Drug use is a health problem.', 6: 'Deer possess red spots.', 7: 'Plants have single stems.'}
| 4 |
3,955 |
["On the condition that chemotherapies can also wreak havoc on a person's white blood cell count, it is definitely the case that the claim that excess nutrients can runoff and add to lake pollution has no merit.", 'When either associations are cousins of open clusters or oily skin is characterized by shininess, pimples and blemishes is true, it follows that the claim that excess nutrients can runoff and add to lake pollution has no merit.', "Given that adults have lifespans, it can be inferred that chemotherapies can also wreak havoc on a person's white blood cell count.", 'If either safeguards are a form of institutionalized nuclear transparency or trees help clean our air, then either associations are cousins of open clusters or oily skin is characterized by shininess, pimples and blemishes.', 'Those that suggest either telecommuting is a commute choice quickly rising in popularity with both employees and employers or most species are at least moderately frost hardy if they are dry at the root are wrong.', 'Assuming the claim that either either telecommuting is a commute choice quickly rising in popularity with both employees and employers or most species are at least moderately frost hardy if they are dry at the root or either adults have lifespans or either safeguards are a form of institutionalized nuclear transparency or trees help clean our air has no merit, we know that agriculture is the largest employer of labor.', 'Given that the claim that either either telecommuting is a commute choice quickly rising in popularity with both employees and employers or most species are at least moderately frost hardy if they are dry at the root or either adults have lifespans or either safeguards are a form of institutionalized nuclear transparency or trees help clean our air has no merit, it can be inferred that the claim that agriculture is the largest employer of labor has no merit.']
|
On the condition that chemotherapies can also wreak havoc on a person's white blood cell count, it is definitely the case that the claim that excess nutrients can runoff and add to lake pollution has no merit. When either associations are cousins of open clusters or oily skin is characterized by shininess, pimples and blemishes is true, it follows that the claim that excess nutrients can runoff and add to lake pollution has no merit. Given that adults have lifespans, it can be inferred that chemotherapies can also wreak havoc on a person's white blood cell count. If either safeguards are a form of institutionalized nuclear transparency or trees help clean our air, then either associations are cousins of open clusters or oily skin is characterized by shininess, pimples and blemishes. Those that suggest either telecommuting is a commute choice quickly rising in popularity with both employees and employers or most species are at least moderately frost hardy if they are dry at the root are wrong. Assuming the claim that either either telecommuting is a commute choice quickly rising in popularity with both employees and employers or most species are at least moderately frost hardy if they are dry at the root or either adults have lifespans or either safeguards are a form of institutionalized nuclear transparency or trees help clean our air has no merit, we know that agriculture is the largest employer of labor. Given that the claim that either either telecommuting is a commute choice quickly rising in popularity with both employees and employers or most species are at least moderately frost hardy if they are dry at the root or either adults have lifespans or either safeguards are a form of institutionalized nuclear transparency or trees help clean our air has no merit, it can be inferred that the claim that agriculture is the largest employer of labor has no merit.
|
The claim that excess nutrients can runoff and add to lake pollution has no merit.
|
The claim that excess nutrients can runoff and add to lake pollution has no merit.
|
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].).
Therefore, Not [0]..
[SC1-1]
Constructive Dilemma:
Either [4] or (Either [5] or [6].). [SC1-2]
If [4], then [1].
If (Either [5] or [6].), then (Either [2] or [3].).
Therefore, Either [1] or (Either [2] or [3].)..
[SC1-2]
Disjunctive Syllogism:
Either (Either [7] or [8].) or (Either [4] or (Either [5] or [6].).). [SC1-3]
Not (Either [7] or [8].).
Therefore, Either [4] or (Either [5] or [6].)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (Either (Either [7] or [8].) or (Either [4] or (Either [5] or [6].).).).), then [9].
If (Not (Either (Either [7] or [8].) or (Either [4] or (Either [5] or [6].).).).), then (Not [9].).
Therefore, Either (Either [7] or [8].) or (Either [4] or (Either [5] or [6].).)..
|
{0: 'Excess nutrients can runoff and add to lake pollution.', 1: "Chemotherapies can also wreak havoc on a person's white blood cell count.", 2: 'Associations are cousins of open clusters.', 3: 'Oily skin is characterized by shininess, pimples and blemishes.', 4: 'Adults have lifespans.', 5: 'Safeguards are a form of institutionalized nuclear transparency.', 6: 'Trees help clean our air.', 7: 'Telecommuting is a commute choice quickly rising in popularity with both employees and employers.', 8: 'Most species are at least moderately frost hardy if they are dry at the root.', 9: 'Agriculture is the largest employer of labor.'}
| 4 |
3,160 |
['Given that black women giving birth have a four to one higher rate of mortality than white women do, it can be inferred that the claim that stress is a big issue across all age groups because of the restructuring of a lifestyle is false.', 'Given that it is a common misconception that if either ponds are located in meadows or personal pronouns have what is called case , then black women giving birth have a four to one higher rate of mortality than white women do, it can be inferred that some heat waves take places.', "Whenever it is true that it is a common misconception that if either ponds are located in meadows or personal pronouns have what is called case , then black women giving birth have a four to one higher rate of mortality than white women do, 'some people mistakenly believe that some heat waves take places' is true.", 'Provided that it is not the case that either ponds are located in meadows or personal pronouns have what is called case , we know that feathers are highly modified scales.', 'The claim that feathers are highly modified scales has no merit.']
|
Given that black women giving birth have a four to one higher rate of mortality than white women do, it can be inferred that the claim that stress is a big issue across all age groups because of the restructuring of a lifestyle is false. Given that it is a common misconception that if either ponds are located in meadows or personal pronouns have what is called case , then black women giving birth have a four to one higher rate of mortality than white women do, it can be inferred that some heat waves take places. Whenever it is true that it is a common misconception that if either ponds are located in meadows or personal pronouns have what is called case , then black women giving birth have a four to one higher rate of mortality than white women do, 'some people mistakenly believe that some heat waves take places' is true. Provided that it is not the case that either ponds are located in meadows or personal pronouns have what is called case , we know that feathers are highly modified scales. The claim that feathers are highly modified scales has no merit.
|
The claim that stress is a big issue across all age groups because of the restructuring of a lifestyle is false.
|
The notion that 'stress is identified as a major cause for most of the diseases' is untrue.
|
Uncertain
|
Modus Ponens:
If [1], then (Not [0].).
[1] [SC2-1]
Therefore, Not [0]..
[SC2-1]
Modus Ponens:
If (Either [2] or [3].), then [1]. [SC1-2]
Either [2] or [3]. [SC2-2]
Therefore, [1].
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Either [2] or [3].), then [1].).), then [4].
If (Not (If (Either [2] or [3].), then [1].).), then (Not [4].).
Therefore, If (Either [2] or [3].), then [1]..
[SC2-2]
Modus Tonens:
If (Not (Either [2] or [3].).), then [5].
Not [5].
Therefore, Either [2] or [3]..
|
{0: 'Stress is a big issue across all age groups because of the restructuring of a lifestyle.', 1: 'Black women giving birth have a four to one higher rate of mortality than white women do.', 2: 'Ponds are located in meadows.', 3: 'Personal pronouns have what is called case .', 4: 'Some heat waves take places.', 5: 'Feathers are highly modified scales.'}
| 4 |
3,977 |
["So long as some people mistakenly believe that if bee pollen contains substances, then if some snakes kill their prey by constricting, others with venom, then values show in tables, 'songbirds can take shelter during the winter, and build a nest inside come spring' is true.", 'On the condition that some people mistakenly believe that if bee pollen contains substances, then if some snakes kill their prey by constricting, others with venom, then values show in tables, it is definitely the case that those that suggest songbirds can take shelter during the winter, and build a nest inside come spring are wrong.', 'Some people mistakenly believe that specific colors can also have an effect on specific diseases.', 'It is rational to believe that either many secondary metabolites are of great social importance as medicine, chemicals and drugs or natural products influence activities.', 'Once we know many secondary metabolites are of great social importance as medicine, chemicals and drugs, we also know that either specific colors can also have an effect on specific diseases or if bee pollen contains substances, then some people mistakenly believe that if some snakes kill their prey by constricting, others with venom, then values show in tables.', 'Should it be the case that natural products influence activities, it follows that either specific colors can also have an effect on specific diseases or if bee pollen contains substances, then some people mistakenly believe that if some snakes kill their prey by constricting, others with venom, then values show in tables.']
|
So long as some people mistakenly believe that if bee pollen contains substances, then if some snakes kill their prey by constricting, others with venom, then values show in tables, 'songbirds can take shelter during the winter, and build a nest inside come spring' is true. On the condition that some people mistakenly believe that if bee pollen contains substances, then if some snakes kill their prey by constricting, others with venom, then values show in tables, it is definitely the case that those that suggest songbirds can take shelter during the winter, and build a nest inside come spring are wrong. Some people mistakenly believe that specific colors can also have an effect on specific diseases. It is rational to believe that either many secondary metabolites are of great social importance as medicine, chemicals and drugs or natural products influence activities. Once we know many secondary metabolites are of great social importance as medicine, chemicals and drugs, we also know that either specific colors can also have an effect on specific diseases or if bee pollen contains substances, then some people mistakenly believe that if some snakes kill their prey by constricting, others with venom, then values show in tables. Should it be the case that natural products influence activities, it follows that either specific colors can also have an effect on specific diseases or if bee pollen contains substances, then some people mistakenly believe that if some snakes kill their prey by constricting, others with venom, then values show in tables.
|
The statement that states bee pollen contains substances is false.
|
The statement that states bee pollen contains substances is false.
|
TRUE
|
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]
Reductio Ad Absurdum:
If (Not (If [0], then (If [1], then [2].).).), then [4].
If (Not (If [0], then (If [1], then [2].).).), then (Not [4].).
Therefore, If [0], then (If [1], then [2].)..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (If [0], then (Not (If [1], then [2].).).). [SC1-2]
Not [3].
Therefore, If [0], then (Not (If [1], then [2].).)..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (Either [3] or (If [0], then (Not (If [1], then [2].).).).).
If [6], then (Either [3] or (If [0], then (Not (If [1], then [2].).).).).
Therefore, Either [3] or (If [0], then (Not (If [1], then [2].).).)..
|
{0: 'Bee pollen contains substances.', 1: 'Some snakes kill their prey by constricting, others with venom.', 2: 'Values show in tables.', 3: 'Specific colors can also have an effect on specific diseases.', 4: 'Songbirds can take shelter during the winter, and build a nest inside come spring.', 5: 'Many secondary metabolites are of great social importance as medicine, chemicals and drugs.', 6: 'Natural products influence activities.'}
| 4 |
3,973 |
['Assuming those that suggest if hens have more down to pluck during their initial nesting attempt than when renesting, then health hazards can be physical, ergonomic, chemical, biological or psychological in nature are wrong, we know that if cobalt tends to exist as a mixture of two allotropes over a wide temperature range, then mud comes from rich environments.', 'One may reasonably assume that if if cobalt tends to exist as a mixture of two allotropes over a wide temperature range, then mud comes from rich environments, then healthy babies born in a vaginal delivery are usually able to stay with the mother.', 'If healthy babies born in a vaginal delivery are usually able to stay with the mother, then some mangos become domesticate trees.', 'Assuming healthy babies born in a vaginal delivery are usually able to stay with the mother, we know that old age is a thief.', 'Assuming old age is a thief, we know that the claim that some mangos become domesticate trees is false.']
|
Assuming those that suggest if hens have more down to pluck during their initial nesting attempt than when renesting, then health hazards can be physical, ergonomic, chemical, biological or psychological in nature are wrong, we know that if cobalt tends to exist as a mixture of two allotropes over a wide temperature range, then mud comes from rich environments. One may reasonably assume that if if cobalt tends to exist as a mixture of two allotropes over a wide temperature range, then mud comes from rich environments, then healthy babies born in a vaginal delivery are usually able to stay with the mother. If healthy babies born in a vaginal delivery are usually able to stay with the mother, then some mangos become domesticate trees. Assuming healthy babies born in a vaginal delivery are usually able to stay with the mother, we know that old age is a thief. Assuming old age is a thief, we know that the claim that some mangos become domesticate trees is false.
|
One may reasonably assume that if hens have more down to pluck during their initial nesting attempt than when renesting, then health hazards can be physical, ergonomic, chemical, biological or psychological in nature.
|
Whenever it is true that hens have more down to pluck during their initial nesting attempt than when renesting, 'health hazards can range from minor to life threatening' is true.
|
Uncertain
|
Modus Tonens:
If (Not (If [0], then [1].).), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Hypothetical Syllogism:
If (Not (If [0], then [1].).), then (If [4], then [5].).
If (If [4], then [5].), then [2].
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC2-1]
Reductio Ad Absurdum:
If [2], then [3].
If [2], then (Not [3].). [SC2-2]
Therefore, Not [2]..
[SC2-2]
Hypothetical Syllogism:
If [2], then [6].
If [6], then (Not [3].).
Therefore, If [2], then (Not [3].)..
|
{0: 'Hens have more down to pluck during their initial nesting attempt than when renesting.', 1: 'Health hazards can be physical, ergonomic, chemical, biological or psychological in nature.', 2: 'Healthy babies born in a vaginal delivery are usually able to stay with the mother.', 3: 'Some mangos become domesticate trees.', 4: 'Cobalt tends to exist as a mixture of two allotropes over a wide temperature range.', 5: 'Mud comes from rich environments.', 6: 'Old age is a thief.'}
| 4 |
3,715 |
["Whenever it is true that it is not the case that either bees undergo metamorphosis or seismology is the study of how sound or seismic waves move through the earth's crust, 'urban violence erodes the social capital of the poor' is true.", 'The claim that urban violence erodes the social capital of the poor does not correspond with reality.', 'It is a fact that either a present is time or if physical stress causes the body to adapt and get stronger, then urban areas have many activities occurring that can potentially contaminate an aquifer.', 'Assuming if physical stress causes the body to adapt and get stronger, then urban areas have many activities occurring that can potentially contaminate an aquifer, we know that the claim that bees undergo metamorphosis has no merit.', 'Assuming a present is time, we know that corn requires a moderate amount of fertilization.', 'If corn requires a moderate amount of fertilization, then the claim that bees undergo metamorphosis has no merit.']
|
Whenever it is true that it is not the case that either bees undergo metamorphosis or seismology is the study of how sound or seismic waves move through the earth's crust, 'urban violence erodes the social capital of the poor' is true. The claim that urban violence erodes the social capital of the poor does not correspond with reality. It is a fact that either a present is time or if physical stress causes the body to adapt and get stronger, then urban areas have many activities occurring that can potentially contaminate an aquifer. Assuming if physical stress causes the body to adapt and get stronger, then urban areas have many activities occurring that can potentially contaminate an aquifer, we know that the claim that bees undergo metamorphosis has no merit. Assuming a present is time, we know that corn requires a moderate amount of fertilization. If corn requires a moderate amount of fertilization, then the claim that bees undergo metamorphosis has no merit.
|
It is reasonable to believe that seismology is the study of how sound or seismic waves move through the earth's crust.
|
Seismology is the most fruitful method of probing the structure of the deep Earth.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either [1] or [0].).), then [2].
Not [2].
Therefore, Either [1] or [0]..
[SC2-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then (Not [1].). [SC2-2]
If (If [4], then [5].), then (Not [1].).
Therefore, Not [1]..
[SC2-2]
Hypothetical Syllogism:
If [3], then [6].
If [6], then (Not [1].).
Therefore, If [3], then (Not [1].)..
|
{0: "Seismology is the study of how sound or seismic waves move through the earth's crust.", 1: 'Bees undergo metamorphosis.', 2: 'Urban violence erodes the social capital of the poor.', 3: 'A present is time.', 4: 'Physical stress causes the body to adapt and get stronger.', 5: 'Urban areas have many activities occurring that can potentially contaminate an aquifer.', 6: 'Corn requires a moderate amount of fertilization.'}
| 4 |
3,744 |
["It is not the case that newborns also begin to recognize important sounds such as the sound of their mother's voice.", "It is a fact that either grooming is the tie that binds the individuals in social groups of primates or if the notion that 'chronic pain IS a small things next to the terrible tragedies taking place' is untrue, then it is a common misconception that colloidal silver is said to act as a catalyst.", 'The claim that grooming is the tie that binds the individuals in social groups of primates has no merit.', "Given that either some leeks improve digestion or religion is the ligament of spiritual life, it can be inferred that either newborns also begin to recognize important sounds such as the sound of their mother's voice or if the notion that 'chronic pain IS a small things next to the terrible tragedies taking place' is untrue, then colloidal silver is said to act as a catalyst.", 'There is good reason to believe that either some leeks improve digestion or religion is the ligament of spiritual life.']
|
It is not the case that newborns also begin to recognize important sounds such as the sound of their mother's voice. It is a fact that either grooming is the tie that binds the individuals in social groups of primates or if the notion that 'chronic pain IS a small things next to the terrible tragedies taking place' is untrue, then it is a common misconception that colloidal silver is said to act as a catalyst. The claim that grooming is the tie that binds the individuals in social groups of primates has no merit. Given that either some leeks improve digestion or religion is the ligament of spiritual life, it can be inferred that either newborns also begin to recognize important sounds such as the sound of their mother's voice or if the notion that 'chronic pain IS a small things next to the terrible tragedies taking place' is untrue, then colloidal silver is said to act as a catalyst. There is good reason to believe that either some leeks improve digestion or religion is the ligament of spiritual life.
|
The claim that chronic pain IS a small things next to the terrible tragedies taking place holds true.
|
It is not the case that chronic pain IS a small things next to the terrible tragedies taking place.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If (Not [0].), then [1].). [SC1-2]
Not [3].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Ponens:
If (Either [4] or [5].), then (Either [3] or (If (Not [0].), then [1].).).
Either [4] or [5].
Therefore, Either [3] or (If (Not [0].), then [1].)..
[SC2-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then (Not [1].).).
Not [2].
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Chronic pain IS a small things next to the terrible tragedies taking place.', 1: 'Colloidal silver is said to act as a catalyst.', 2: 'Grooming is the tie that binds the individuals in social groups of primates.', 3: "Newborns also begin to recognize important sounds such as the sound of their mother's voice.", 4: 'Some leeks improve digestion.', 5: 'Religion is the ligament of spiritual life.'}
| 4 |
3,195 |
['If ostriches mostly eat vegetation, including leaves, fruit, roots, and seeds, then swedish massage is the most common form of massage.', 'Once we know the claim that either if gap isa shape, then universal donors can give blood to any blood type or ostriches mostly eat vegetation, including leaves, fruit, roots, and seeds does not correspond with reality, we also know that old tissues can start copying themselves and turn cancerous.', 'The claim that old tissues can start copying themselves and turn cancerous has no merit.', 'On the condition that either porkers have (part) sterna or diets come from sources, it is definitely the case that it is a common misconception that if gap isa shape, then universal donors can give blood to any blood type.', 'We know that at least one of two things is true: porkers have (part) sterna, or diets come from sources.']
|
If ostriches mostly eat vegetation, including leaves, fruit, roots, and seeds, then swedish massage is the most common form of massage. Once we know the claim that either if gap isa shape, then universal donors can give blood to any blood type or ostriches mostly eat vegetation, including leaves, fruit, roots, and seeds does not correspond with reality, we also know that old tissues can start copying themselves and turn cancerous. The claim that old tissues can start copying themselves and turn cancerous has no merit. On the condition that either porkers have (part) sterna or diets come from sources, it is definitely the case that it is a common misconception that if gap isa shape, then universal donors can give blood to any blood type. We know that at least one of two things is true: porkers have (part) sterna, or diets come from sources.
|
It is true that swedish massage is the most common form of massage.
|
Swedish massage is what many people think of when massage is mentioned.
|
Uncertain
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either (If [2], then [3].) or [1]. [SC1-2]
Not (If [2], then [3].). [SC2-2]
Therefore, [1].
[SC1-2]
Modus Tonens:
If (Not (Either (If [2], then [3].) or [1].).), then [4].
Not [4].
Therefore, Either (If [2], then [3].) or [1]..
[SC2-2]
Modus Ponens:
If (Either [5] or [6].), then (Not (If [2], then [3].).).
Either [5] or [6].
Therefore, Not (If [2], then [3].)..
|
{0: 'Swedish massage is the most common form of massage.', 1: 'Ostriches mostly eat vegetation, including leaves, fruit, roots, and seeds.', 2: 'Gap isa shape.', 3: 'Universal donors can give blood to any blood type.', 4: 'Old tissues can start copying themselves and turn cancerous.', 5: 'Porkers have (part) sterna.', 6: 'Diets come from sources.'}
| 4 |
3,191 |
['We know that either if bivalves have a highly muscular organ called the foot, which muscle fibres run in all direction, then political interaction differs fundamentally from the interaction of atoms and molecules or good management is that which leads to the desired behavior by organizational members.', 'One may reasonably assume that if good management is that which leads to the desired behavior by organizational members, then giant squids may have ability.', "When the statement that 'if if bivalves have a highly muscular organ called the foot, which muscle fibres run in all direction, then political interaction differs fundamentally from the interaction of atoms and molecules, then giant squids may have ability' is incorrect is true, it follows that cats expend energy.", 'At least one of two things is true: either some chimpanzees live in facilities or walnuts are also drupes, or some reproduction affects bats.', "Whenever it is true that some reproduction affects bats, 'it is not true that cats expend energy' is true.", 'Assuming crystals vary from transparent to translucent, we know that if either some chimpanzees live in facilities or walnuts are also drupes, then it is not true that cats expend energy.', 'It is the case that crystals vary from transparent to translucent.']
|
We know that either if bivalves have a highly muscular organ called the foot, which muscle fibres run in all direction, then political interaction differs fundamentally from the interaction of atoms and molecules or good management is that which leads to the desired behavior by organizational members. One may reasonably assume that if good management is that which leads to the desired behavior by organizational members, then giant squids may have ability. When the statement that 'if if bivalves have a highly muscular organ called the foot, which muscle fibres run in all direction, then political interaction differs fundamentally from the interaction of atoms and molecules, then giant squids may have ability' is incorrect is true, it follows that cats expend energy. At least one of two things is true: either some chimpanzees live in facilities or walnuts are also drupes, or some reproduction affects bats. Whenever it is true that some reproduction affects bats, 'it is not true that cats expend energy' is true. Assuming crystals vary from transparent to translucent, we know that if either some chimpanzees live in facilities or walnuts are also drupes, then it is not true that cats expend energy. It is the case that crystals vary from transparent to translucent.
|
It is a simple truth that giant squids may have ability.
|
It is a simple truth that giant squids may have ability.
|
TRUE
|
Disjunction Elimination:
Either (If [1], then [2].) or [3].
If (If [1], then [2].), then [0]. [SC2-1]
If [3], then [0].
Therefore, [0].
[SC2-1]
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]
Disjunction Elimination:
Either (Either [5] or [6].) or [7].
If (Either [5] or [6].), then (Not [4].). [SC2-3]
If [7], then (Not [4].).
Therefore, Not [4]..
[SC2-3]
Modus Ponens:
If [8], then (If (Either [5] or [6].), then (Not [4].).).
[8]
Therefore, If (Either [5] or [6].), then (Not [4].)..
|
{0: 'Giant squids may have ability.', 1: 'Bivalves have a highly muscular organ called the foot, which muscle fibres run in all direction.', 2: 'Political interaction differs fundamentally from the interaction of atoms and molecules.', 3: 'Good management is that which leads to the desired behavior by organizational members.', 4: 'Cats expend energy.', 5: 'Some chimpanzees live in facilities.', 6: 'Walnuts are also drupes.', 7: 'Some reproduction affects bats.', 8: 'Crystals vary from transparent to translucent.'}
| 4 |
3,628 |
['At least one of two things is true: bits are parts, or inguinal hernias are also common and cause a bulging in the groin area or scrotum.', 'Given that bits are parts, it can be inferred that if some mites survive years, then poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes.', 'Assuming inguinal hernias are also common and cause a bulging in the groin area or scrotum, we know that if some mites survive years, then poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes.', 'When the claim that if some mites survive years, then it is not the case that poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes does not correspond with reality is true, it follows that some people mistakenly believe that some fungi kill the cells of an living organism then feed on the dead cells.', 'Either drinkers are consumers or respiratory diseases are among the most common problems seen in all species of pet birds.', 'On the condition that drinkers are consumers, it is definitely the case that if the claim that if some mites survive years, then it is not the case that poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes does not correspond with reality, then some fungi kill the cells of an living organism then feed on the dead cells.', 'Should it be the case that respiratory diseases are among the most common problems seen in all species of pet birds, it follows that if the claim that if some mites survive years, then it is not the case that poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes does not correspond with reality, then some fungi kill the cells of an living organism then feed on the dead cells.']
|
At least one of two things is true: bits are parts, or inguinal hernias are also common and cause a bulging in the groin area or scrotum. Given that bits are parts, it can be inferred that if some mites survive years, then poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes. Assuming inguinal hernias are also common and cause a bulging in the groin area or scrotum, we know that if some mites survive years, then poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes. When the claim that if some mites survive years, then it is not the case that poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes does not correspond with reality is true, it follows that some people mistakenly believe that some fungi kill the cells of an living organism then feed on the dead cells. Either drinkers are consumers or respiratory diseases are among the most common problems seen in all species of pet birds. On the condition that drinkers are consumers, it is definitely the case that if the claim that if some mites survive years, then it is not the case that poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes does not correspond with reality, then some fungi kill the cells of an living organism then feed on the dead cells. Should it be the case that respiratory diseases are among the most common problems seen in all species of pet birds, it follows that if the claim that if some mites survive years, then it is not the case that poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes does not correspond with reality, then some fungi kill the cells of an living organism then feed on the dead cells.
|
Some people mistakenly believe that some mites survive years.
|
Some people mistakenly believe that some mites survive years.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (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]
Reductio Ad Absurdum:
If (Not (If [0], then (Not [1].).).), then [4]. [SC1-2]
If (Not (If [0], then (Not [1].).).), then (Not [4].).
Therefore, If [0], then (Not [1].)..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Not (If [0], then (Not [1].).).), then [4].).
If [6], then (If (Not (If [0], then (Not [1].).).), then [4].).
Therefore, If (Not (If [0], then (Not [1].).).), then [4]..
|
{0: 'Some mites survive years.', 1: 'Poverty is lived as deprivation in comparison with the lifestyles of the middle and upper classes.', 2: 'Bits are parts.', 3: 'Inguinal hernias are also common and cause a bulging in the groin area or scrotum.', 4: 'Some fungi kill the cells of an living organism then feed on the dead cells.', 5: 'Drinkers are consumers.', 6: 'Respiratory diseases are among the most common problems seen in all species of pet birds.'}
| 4 |
3,536 |
["Should it be the case that the claim that examples are tannins - widely distributed in leaves, stems, fruits, bark , and wood of plants does not reflect reality, it follows that the statement that 'either ideal soil is half spaces and half solids or pure arsenic is lethal' is incorrect.", 'There is good reason to believe that either farmers work with chinese traders or communication is a process of making or doing something, and a process of coordination.', 'On the condition that farmers work with chinese traders, it is definitely the case that if if lesbian relationships are disproportionately abusive, then some mealworms have exoskeletons, then if the claim that examples are tannins - widely distributed in leaves, stems, fruits, bark , and wood of plants does not reflect reality, then either ideal soil is half spaces and half solids or pure arsenic is lethal.', 'One may reasonably assume that if communication is a process of making or doing something, and a process of coordination, then if if lesbian relationships are disproportionately abusive, then some mealworms have exoskeletons, then if the claim that examples are tannins - widely distributed in leaves, stems, fruits, bark , and wood of plants does not reflect reality, then either ideal soil is half spaces and half solids or pure arsenic is lethal.', 'On the condition that the claim that if lesbian relationships are disproportionately abusive, then some mealworms have exoskeletons does not reflect reality, it is definitely the case that some diets help high pressure.', "If the claim that if lesbian relationships are disproportionately abusive, then some mealworms have exoskeletons does not reflect reality, then the statement 'some diets help high pressure' can be considered false."]
|
Should it be the case that the claim that examples are tannins - widely distributed in leaves, stems, fruits, bark , and wood of plants does not reflect reality, it follows that the statement that 'either ideal soil is half spaces and half solids or pure arsenic is lethal' is incorrect. There is good reason to believe that either farmers work with chinese traders or communication is a process of making or doing something, and a process of coordination. On the condition that farmers work with chinese traders, it is definitely the case that if if lesbian relationships are disproportionately abusive, then some mealworms have exoskeletons, then if the claim that examples are tannins - widely distributed in leaves, stems, fruits, bark , and wood of plants does not reflect reality, then either ideal soil is half spaces and half solids or pure arsenic is lethal. One may reasonably assume that if communication is a process of making or doing something, and a process of coordination, then if if lesbian relationships are disproportionately abusive, then some mealworms have exoskeletons, then if the claim that examples are tannins - widely distributed in leaves, stems, fruits, bark , and wood of plants does not reflect reality, then either ideal soil is half spaces and half solids or pure arsenic is lethal. On the condition that the claim that if lesbian relationships are disproportionately abusive, then some mealworms have exoskeletons does not reflect reality, it is definitely the case that some diets help high pressure. If the claim that if lesbian relationships are disproportionately abusive, then some mealworms have exoskeletons does not reflect reality, then the statement 'some diets help high pressure' can be considered false.
|
The idea that examples are tannins - widely distributed in leaves, stems, fruits, bark , and wood of plants is true.
|
The notion that 'examples are tannins - widely distributed in leaves, stems, fruits, bark , and wood of plants' is untrue.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then (Either [1] or [2].). [SC1-1]
If (Not [0].), then (Not (Either [1] or [2].).).
Therefore, [0].
[SC1-1]
Modus Ponens:
If (If [3], then [4].), then (If (Not [0].), then (Either [1] or [2].).). [SC1-2]
If [3], then [4]. [SC2-2]
Therefore, If (Not [0].), then (Either [1] or [2].)..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (If [3], then [4].), then (If (Not [0].), then (Either [1] or [2].).).).
If [6], then (If (If [3], then [4].), then (If (Not [0].), then (Either [1] or [2].).).).
Therefore, If (If [3], then [4].), then (If (Not [0].), then (Either [1] or [2].).)..
[SC2-2]
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]..
|
{0: 'Examples are tannins - widely distributed in leaves, stems, fruits, bark , and wood of plants.', 1: 'Ideal soil is half spaces and half solids.', 2: 'Pure arsenic is lethal.', 3: 'Lesbian relationships are disproportionately abusive.', 4: 'Some mealworms have exoskeletons.', 5: 'Farmers work with chinese traders.', 6: 'Communication is a process of making or doing something, and a process of coordination.', 7: 'Some diets help high pressure.'}
| 4 |
3,880 |
['Given that if breezes are wind, then sexual reproduction involves insect pollination, followed by seed production and dispersal, it can be inferred that if livestock has (part) brains, then perspiration plays a vital role in regulating human body temperature.', 'Assuming if livestock has (part) brains, then perspiration plays a vital role in regulating human body temperature, we know that monkeys exhibit limbs.', 'There is good reason to believe that either mica capacitors are still indispensable in high-power RF transmitter applications or the statement that states monkeys exhibit limbs is false.', 'Either one or both of these statements are true: most carcinogen causes breast cancer, or those that suggest mica capacitors are still indispensable in high-power RF transmitter applications are wrong.', "The notion that 'most carcinogen causes breast cancer' is untrue."]
|
Given that if breezes are wind, then sexual reproduction involves insect pollination, followed by seed production and dispersal, it can be inferred that if livestock has (part) brains, then perspiration plays a vital role in regulating human body temperature. Assuming if livestock has (part) brains, then perspiration plays a vital role in regulating human body temperature, we know that monkeys exhibit limbs. There is good reason to believe that either mica capacitors are still indispensable in high-power RF transmitter applications or the statement that states monkeys exhibit limbs is false. Either one or both of these statements are true: most carcinogen causes breast cancer, or those that suggest mica capacitors are still indispensable in high-power RF transmitter applications are wrong. The notion that 'most carcinogen causes breast cancer' is untrue.
|
The claim that if breezes are wind, then sexual reproduction involves insect pollination, followed by seed production and dispersal has no merit.
|
Given that breezes are wind, it can be inferred that sexual reproduction involves insect pollination, followed by seed production and dispersal.
|
FALSE
|
Modus Tonens:
If (If [0], then [1].), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Hypothetical Syllogism:
If (If [0], then [1].), then (If [4], then [5].).
If (If [4], then [5].), then [2].
Therefore, If (If [0], then [1].), then [2]..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (Not [2].).
Not [3]. [SC2-2]
Therefore, Not [2]..
[SC2-2]
Disjunctive Syllogism:
Either [6] or (Not [3].).
Not [6].
Therefore, Not [3]..
|
{0: 'Breezes are wind.', 1: 'Sexual reproduction involves insect pollination, followed by seed production and dispersal.', 2: 'Monkeys exhibit limbs.', 3: 'Mica capacitors are still indispensable in high-power RF transmitter applications.', 4: 'Livestock has (part) brains.', 5: 'Perspiration plays a vital role in regulating human body temperature.', 6: 'Most carcinogen causes breast cancer.'}
| 4 |
3,164 |
['Once we know refrigerant vapor is admitted to the shell and condenses on the outer surfaces of the tubes, we also know that if the statement that states most plants grow in regions is false, then anger is a natural and controllable aspect of life.', 'Assuming search engines are giant databases that help provide subject access to the Web, we know that the statement, anger is a natural and controllable aspect of life, does not hold.', 'Those that suggest search engines are giant databases that help provide subject access to the Web are right.', 'On the condition that the claim that refrigerant vapor is admitted to the shell and condenses on the outer surfaces of the tubes does not reflect reality, it is definitely the case that if antibodies are against bacteria, then soft water has fewer minerals than hard water.', 'It is a common misconception that if antibodies are against bacteria, then soft water has fewer minerals than hard water.']
|
Once we know refrigerant vapor is admitted to the shell and condenses on the outer surfaces of the tubes, we also know that if the statement that states most plants grow in regions is false, then anger is a natural and controllable aspect of life. Assuming search engines are giant databases that help provide subject access to the Web, we know that the statement, anger is a natural and controllable aspect of life, does not hold. Those that suggest search engines are giant databases that help provide subject access to the Web are right. On the condition that the claim that refrigerant vapor is admitted to the shell and condenses on the outer surfaces of the tubes does not reflect reality, it is definitely the case that if antibodies are against bacteria, then soft water has fewer minerals than hard water. It is a common misconception that if antibodies are against bacteria, then soft water has fewer minerals than hard water.
|
It is rational to agree that most plants grow in regions.
|
The claim that most plants grow in regions does not reflect reality.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (If (Not [0].), then [1].).
[3] [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Modus Tonens:
If (Not [3].), then (If [4], then [5].).
Not (If [4], then [5].).
Therefore, [3].
[SC2-1]
Modus Ponens:
If [2], then (Not [1].).
[2]
Therefore, Not [1]..
|
{0: 'Most plants grow in regions.', 1: 'Anger is a natural and controllable aspect of life.', 2: 'Search engines are giant databases that help provide subject access to the Web.', 3: 'Refrigerant vapor is admitted to the shell and condenses on the outer surfaces of the tubes.', 4: 'Antibodies are against bacteria.', 5: 'Soft water has fewer minerals than hard water.'}
| 4 |
3,106 |
["The statement 'nitrates can pollute groundwater and create health hazards for humans and animals' can be considered false.", 'One may reasonably assume that if poetry readings are important because poetry is an oral art that precedes writing, then earthworms eat compost, leaf litter, or soil and make no burrows, horizontal or vertical burrows.', 'One may reasonably assume that if poetry readings are important because poetry is an oral art that precedes writing, then the statement, earthworms eat compost, leaf litter, or soil and make no burrows, horizontal or vertical burrows, does not hold.', 'When either surfers have (part) vacuoles or mitochondria are about the size of an average bacterium is true, it follows that if some people mistakenly believe that if it is not the case that hereditary information moves only from germline cells to somatic cells, then poetry readings are important because poetry is an oral art that precedes writing, then nitrates can pollute groundwater and create health hazards for humans and animals.', 'We know that either surfers have (part) vacuoles or mitochondria are about the size of an average bacterium.']
|
The statement 'nitrates can pollute groundwater and create health hazards for humans and animals' can be considered false. One may reasonably assume that if poetry readings are important because poetry is an oral art that precedes writing, then earthworms eat compost, leaf litter, or soil and make no burrows, horizontal or vertical burrows. One may reasonably assume that if poetry readings are important because poetry is an oral art that precedes writing, then the statement, earthworms eat compost, leaf litter, or soil and make no burrows, horizontal or vertical burrows, does not hold. When either surfers have (part) vacuoles or mitochondria are about the size of an average bacterium is true, it follows that if some people mistakenly believe that if it is not the case that hereditary information moves only from germline cells to somatic cells, then poetry readings are important because poetry is an oral art that precedes writing, then nitrates can pollute groundwater and create health hazards for humans and animals. We know that either surfers have (part) vacuoles or mitochondria are about the size of an average bacterium.
|
It is reasonable to believe that hereditary information moves only from germline cells to somatic cells.
|
It is reasonable to believe that hereditary information moves only from germline cells to somatic cells.
|
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 [2]. [SC1-2]
Not [2].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Ponens:
If (Either [4] or [5].), then (If (Not (If (Not [0].), then [1].).), then [2].).
Either [4] or [5].
Therefore, If (Not (If (Not [0].), then [1].).), then [2]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [3].
If [1], then (Not [3].).
Therefore, Not [1]..
|
{0: 'Hereditary information moves only from germline cells to somatic cells.', 1: 'Poetry readings are important because poetry is an oral art that precedes writing.', 2: 'Nitrates can pollute groundwater and create health hazards for humans and animals.', 3: 'Earthworms eat compost, leaf litter, or soil and make no burrows, horizontal or vertical burrows.', 4: 'Surfers have (part) vacuoles.', 5: 'Mitochondria are about the size of an average bacterium.'}
| 4 |
3,016 |
["It is rational to believe that either true growth consists in intensified love, which is founded on faith and hope or parents are responsible for their childrens' safety.", 'If true growth consists in intensified love, which is founded on faith and hope, then most summer rain comes as brief thunderstorms or showers in the late afternoon.', "When parents are responsible for their childrens' safety is true, it follows that either lipids are a type of fat and fats are considered carbohydrates which are organic compounds or larger prey are less likely to be preyed upon, and larger predators are more likely to catch prey.", 'Assuming most summer rain comes as brief thunderstorms or showers in the late afternoon, we know that antihypertensive therapy is managed by intravenous injection to make the blood pressure lower.', "So long as antihypertensive therapy is managed by intravenous injection to make the blood pressure lower, 'most heat pumps use a refrigeration cycle' is true.", 'If the claim that if either lipids are a type of fat and fats are considered carbohydrates which are organic compounds or larger prey are less likely to be preyed upon, and larger predators are more likely to catch prey, then most heat pumps use a refrigeration cycle has no merit, then cape gooseberries have many health benefits.', 'Once we know the claim that if either lipids are a type of fat and fats are considered carbohydrates which are organic compounds or larger prey are less likely to be preyed upon, and larger predators are more likely to catch prey, then most heat pumps use a refrigeration cycle has no merit, we also know that the claim that cape gooseberries have many health benefits has no merit.']
|
It is rational to believe that either true growth consists in intensified love, which is founded on faith and hope or parents are responsible for their childrens' safety. If true growth consists in intensified love, which is founded on faith and hope, then most summer rain comes as brief thunderstorms or showers in the late afternoon. When parents are responsible for their childrens' safety is true, it follows that either lipids are a type of fat and fats are considered carbohydrates which are organic compounds or larger prey are less likely to be preyed upon, and larger predators are more likely to catch prey. Assuming most summer rain comes as brief thunderstorms or showers in the late afternoon, we know that antihypertensive therapy is managed by intravenous injection to make the blood pressure lower. So long as antihypertensive therapy is managed by intravenous injection to make the blood pressure lower, 'most heat pumps use a refrigeration cycle' is true. If the claim that if either lipids are a type of fat and fats are considered carbohydrates which are organic compounds or larger prey are less likely to be preyed upon, and larger predators are more likely to catch prey, then most heat pumps use a refrigeration cycle has no merit, then cape gooseberries have many health benefits. Once we know the claim that if either lipids are a type of fat and fats are considered carbohydrates which are organic compounds or larger prey are less likely to be preyed upon, and larger predators are more likely to catch prey, then most heat pumps use a refrigeration cycle has no merit, we also know that the claim that cape gooseberries have many health benefits has no merit.
|
The claim that most heat pumps use a refrigeration cycle holds true.
|
Heat pumps operate by moving or transferring heat, rather than creating it.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].). [SC1-1]
If [1], then [0]. [SC2-1]
If (Either [2] or [3].), then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either [5] or [6].
If [5], then [1].
If [6], then (Either [2] or [3].).
Therefore, Either [1] or (Either [2] or [3].)..
[SC2-1]
Hypothetical Syllogism:
If [1], then [4].
If [4], then [0].
Therefore, If [1], then [0]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If (Either [2] or [3].), then [0].).), then [7].
If (Not (If (Either [2] or [3].), then [0].).), then (Not [7].).
Therefore, If (Either [2] or [3].), then [0]..
|
{0: 'Most heat pumps use a refrigeration cycle.', 1: 'Most summer rain comes as brief thunderstorms or showers in the late afternoon.', 2: 'Lipids are a type of fat and fats are considered carbohydrates which are organic compounds.', 3: 'Larger prey are less likely to be preyed upon, and larger predators are more likely to catch prey.', 4: 'Antihypertensive therapy is managed by intravenous injection to make the blood pressure lower.', 5: 'True growth consists in intensified love, which is founded on faith and hope.', 6: "Parents are responsible for their childrens' safety.", 7: 'Cape gooseberries have many health benefits.'}
| 4 |
3,575 |
["So long as fractal geometry is apparent everywhere in Africa from hairstyles to religious practices, 'black men are very best basketball players in the world' is true.", 'Provided that some animals shed layers, we know that black men are very best basketball players in the world.', "Either one or both of these statements are true: bees nest in hidden places, or if the notion that 'either fractal geometry is apparent everywhere in Africa from hairstyles to religious practices or some animals shed layers' is untrue, then reactive monitoring focuses on incidents after they have occurred.", 'The claim that bees nest in hidden places is false.', "One may reasonably assume that if the claim that if the notion that 'either fractal geometry is apparent everywhere in Africa from hairstyles to religious practices or some animals shed layers' is untrue, then it is a common misconception that reactive monitoring focuses on incidents after they have occurred is false, then if mosquitoes acquire the virus from infected birds and horses, then cultural differences can account for some major differences in learning styles.", "When the claim that if the notion that 'either fractal geometry is apparent everywhere in Africa from hairstyles to religious practices or some animals shed layers' is untrue, then it is a common misconception that reactive monitoring focuses on incidents after they have occurred is false is true, it follows that it is a common misconception that if mosquitoes acquire the virus from infected birds and horses, then cultural differences can account for some major differences in learning styles."]
|
So long as fractal geometry is apparent everywhere in Africa from hairstyles to religious practices, 'black men are very best basketball players in the world' is true. Provided that some animals shed layers, we know that black men are very best basketball players in the world. Either one or both of these statements are true: bees nest in hidden places, or if the notion that 'either fractal geometry is apparent everywhere in Africa from hairstyles to religious practices or some animals shed layers' is untrue, then reactive monitoring focuses on incidents after they have occurred. The claim that bees nest in hidden places is false. One may reasonably assume that if the claim that if the notion that 'either fractal geometry is apparent everywhere in Africa from hairstyles to religious practices or some animals shed layers' is untrue, then it is a common misconception that reactive monitoring focuses on incidents after they have occurred is false, then if mosquitoes acquire the virus from infected birds and horses, then cultural differences can account for some major differences in learning styles. When the claim that if the notion that 'either fractal geometry is apparent everywhere in Africa from hairstyles to religious practices or some animals shed layers' is untrue, then it is a common misconception that reactive monitoring focuses on incidents after they have occurred is false is true, it follows that it is a common misconception that if mosquitoes acquire the virus from infected birds and horses, then cultural differences can account for some major differences in learning styles.
|
The statement 'black men are very best basketball players in the world' can be considered true.
|
Black men are a diverse group.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0].
If [2], then [0].
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or [2].).), then [3]. [SC1-2]
If (Not (Either [1] or [2].).), then (Not [3].). [SC2-2]
Therefore, Either [1] or [2]..
[SC1-2]
Disjunctive Syllogism:
Either [6] or (If (Not (Either [1] or [2].).), then [3].).
Not [6].
Therefore, If (Not (Either [1] or [2].).), then [3]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (Either [1] or [2].).), then (Not [3].).).), then (If [4], then [5].).
If (Not (If (Not (Either [1] or [2].).), then (Not [3].).).), then (Not (If [4], then [5].).).
Therefore, If (Not (Either [1] or [2].).), then (Not [3].)..
|
{0: 'Black men are very best basketball players in the world.', 1: 'Fractal geometry is apparent everywhere in Africa from hairstyles to religious practices.', 2: 'Some animals shed layers.', 3: 'Reactive monitoring focuses on incidents after they have occurred.', 4: 'Mosquitoes acquire the virus from infected birds and horses.', 5: 'Cultural differences can account for some major differences in learning styles.', 6: 'Bees nest in hidden places.'}
| 4 |
3,925 |
['We know that at least one of two things is true: some women enter unions, or dancing exercises.', 'If some women enter unions, then prostitutes often get syphilis from the men they cater to, and then they spread it onto other men.', 'Should it be the case that dancing exercises, it follows that fool isa person.', "Whenever it is true that the claim that if prostitutes often get syphilis from the men they cater to, and then they spread it onto other men, then tradition plays a key role in the culture of Panama has no merit, 'if brain waves arise from synchronized neural activity, then credibility is a characteristic that has to be inferred by the recipient of the message' is true.", 'If the claim that if prostitutes often get syphilis from the men they cater to, and then they spread it onto other men, then tradition plays a key role in the culture of Panama has no merit, then we know that the claim that if brain waves arise from synchronized neural activity, then credibility is a characteristic that has to be inferred by the recipient of the message is false.', 'It is rational to believe that either chinchillas are affected by the full moon and become more active on a bright moonlit night or if fool isa person, then tradition plays a key role in the culture of Panama.', "The statement that 'chinchillas are affected by the full moon and become more active on a bright moonlit night' is incorrect."]
|
We know that at least one of two things is true: some women enter unions, or dancing exercises. If some women enter unions, then prostitutes often get syphilis from the men they cater to, and then they spread it onto other men. Should it be the case that dancing exercises, it follows that fool isa person. Whenever it is true that the claim that if prostitutes often get syphilis from the men they cater to, and then they spread it onto other men, then tradition plays a key role in the culture of Panama has no merit, 'if brain waves arise from synchronized neural activity, then credibility is a characteristic that has to be inferred by the recipient of the message' is true. If the claim that if prostitutes often get syphilis from the men they cater to, and then they spread it onto other men, then tradition plays a key role in the culture of Panama has no merit, then we know that the claim that if brain waves arise from synchronized neural activity, then credibility is a characteristic that has to be inferred by the recipient of the message is false. It is rational to believe that either chinchillas are affected by the full moon and become more active on a bright moonlit night or if fool isa person, then tradition plays a key role in the culture of Panama. The statement that 'chinchillas are affected by the full moon and become more active on a bright moonlit night' is incorrect.
|
Many people rightly believe that tradition plays a key role in the culture of Panama.
|
Tradition is a set of beliefs and attitudes, handed down from posterity, which guide behaviour.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either [3] or [4].
If [3], then [1].
If [4], then [2].
Therefore, Either [1] or [2]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [1], then [0].).), then (If [5], then [6].).
If (Not (If [1], then [0].).), then (Not (If [5], then [6].).).
Therefore, If [1], then [0]..
[SC3-1]
Disjunctive Syllogism:
Either [7] or (If [2], then [0].).
Not [7].
Therefore, If [2], then [0]..
|
{0: 'Tradition plays a key role in the culture of Panama.', 1: 'Prostitutes often get syphilis from the men they cater to, and then they spread it onto other men.', 2: 'Fool isa person.', 3: 'Some women enter unions.', 4: 'Dancing exercises.', 5: 'Brain waves arise from synchronized neural activity.', 6: 'Credibility is a characteristic that has to be inferred by the recipient of the message.', 7: 'Chinchillas are affected by the full moon and become more active on a bright moonlit night.'}
| 4 |
3,712 |
['Either natural gas is also a fuel for some fuel cells or analysis of variance is a technique used to compare more than two means.', 'If natural gas is also a fuel for some fuel cells, then if a radial is a tire, then tornadoes usually occur in the spring, when thunderstorms are prevalent.', 'Should it be the case that analysis of variance is a technique used to compare more than two means, it follows that if a radial is a tire, then tornadoes usually occur in the spring, when thunderstorms are prevalent.', 'Either some aquatic animals swim through water or a radial is a tire.', 'We know that either either different behavior promotes survival or petals attract attention or roentgenium is produced artificially.', 'If either different behavior promotes survival or petals attract attention, then we know that the claim that some aquatic animals swim through water is false.', 'When roentgenium is produced artificially is true, it follows that we know that the claim that some aquatic animals swim through water is false.']
|
Either natural gas is also a fuel for some fuel cells or analysis of variance is a technique used to compare more than two means. If natural gas is also a fuel for some fuel cells, then if a radial is a tire, then tornadoes usually occur in the spring, when thunderstorms are prevalent. Should it be the case that analysis of variance is a technique used to compare more than two means, it follows that if a radial is a tire, then tornadoes usually occur in the spring, when thunderstorms are prevalent. Either some aquatic animals swim through water or a radial is a tire. We know that either either different behavior promotes survival or petals attract attention or roentgenium is produced artificially. If either different behavior promotes survival or petals attract attention, then we know that the claim that some aquatic animals swim through water is false. When roentgenium is produced artificially is true, it follows that we know that the claim that some aquatic animals swim through water is false.
|
Those that suggest tornadoes usually occur in the spring, when thunderstorms are prevalent are right.
|
Those that suggest tornadoes usually occur in the spring, when thunderstorms are prevalent are right.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If [1], then [0].).
If [4], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC2-1]
Disjunctive Syllogism:
Either [2] or [1].
Not [2]. [SC2-2]
Therefore, [1].
[SC2-2]
Disjunction Elimination:
Either (Either [5] or [6].) or [7].
If (Either [5] or [6].), then (Not [2].).
If [7], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Tornadoes usually occur in the spring, when thunderstorms are prevalent.', 1: 'A radial is a tire.', 2: 'Some aquatic animals swim through water.', 3: 'Natural gas is also a fuel for some fuel cells.', 4: 'Analysis of variance is a technique used to compare more than two means.', 5: 'Different behavior promotes survival.', 6: 'Petals attract attention.', 7: 'Roentgenium is produced artificially.'}
| 4 |
3,540 |
['Given that those that suggest if cantaloupe has (part) vacuoles, then the claim that daughters love dolphins does not reflect reality are wrong, it can be inferred that braille is a vital reading and writing tool for blind people.', "The notion that 'braille is a vital reading and writing tool for blind people' is untrue.", 'Either good breeders avoid flaws or cerebral demyelination follows, causing dementia, spasticity, and blindness.', 'When cerebral demyelination follows, causing dementia, spasticity, and blindness is true, it follows that cantaloupe has (part) vacuoles.', "So long as good breeders avoid flaws, 'wild seafood is the last truly organic protein in the world' is true.", "Whenever it is true that wild seafood is the last truly organic protein in the world, 'cantaloupe has (part) vacuoles' is true."]
|
Given that those that suggest if cantaloupe has (part) vacuoles, then the claim that daughters love dolphins does not reflect reality are wrong, it can be inferred that braille is a vital reading and writing tool for blind people. The notion that 'braille is a vital reading and writing tool for blind people' is untrue. Either good breeders avoid flaws or cerebral demyelination follows, causing dementia, spasticity, and blindness. When cerebral demyelination follows, causing dementia, spasticity, and blindness is true, it follows that cantaloupe has (part) vacuoles. So long as good breeders avoid flaws, 'wild seafood is the last truly organic protein in the world' is true. Whenever it is true that wild seafood is the last truly organic protein in the world, 'cantaloupe has (part) vacuoles' is true.
|
The claim that daughters love dolphins does not reflect reality.
|
The statement that 'daughters have feelings' is incorrect.
|
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 [4].
Not [4].
Therefore, If [1], then (Not [0].)..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then [1]. [SC2-2]
If [3], then [1].
Therefore, [1].
[SC2-2]
Hypothetical Syllogism:
If [2], then [5].
If [5], then [1].
Therefore, If [2], then [1]..
|
{0: 'Daughters love dolphins.', 1: 'Cantaloupe has (part) vacuoles.', 2: 'Good breeders avoid flaws.', 3: 'Cerebral demyelination follows, causing dementia, spasticity, and blindness.', 4: 'Braille is a vital reading and writing tool for blind people.', 5: 'Wild seafood is the last truly organic protein in the world.'}
| 4 |
3,329 |
['Provided that fuel cells have the potential for very low cost, high reliability, and high efficiency, we know that vets see pets.', 'At least one of two things is true: humans are hard to test because of their diverse capabilities and levels of learning, or if the claim that fuel cells have the potential for very low cost, high reliability, and high efficiency does not correspond with reality, then crickets chirp to attract a mate.', 'The statement that states humans are hard to test because of their diverse capabilities and levels of learning is false.', 'Once we know scientists propose explanations, we also know that those that suggest crickets chirp to attract a mate are wrong.', 'It is fair to say that scientists propose explanations.']
|
Provided that fuel cells have the potential for very low cost, high reliability, and high efficiency, we know that vets see pets. At least one of two things is true: humans are hard to test because of their diverse capabilities and levels of learning, or if the claim that fuel cells have the potential for very low cost, high reliability, and high efficiency does not correspond with reality, then crickets chirp to attract a mate. The statement that states humans are hard to test because of their diverse capabilities and levels of learning is false. Once we know scientists propose explanations, we also know that those that suggest crickets chirp to attract a mate are wrong. It is fair to say that scientists propose explanations.
|
It is the case that vets see pets.
|
It is the case that vets see pets.
|
TRUE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not [1].), then [2]. [SC1-2]
Not [2]. [SC2-2]
Therefore, [1].
[SC1-2]
Disjunctive Syllogism:
Either [3] or (If (Not [1].), then [2].).
Not [3].
Therefore, If (Not [1].), then [2]..
[SC2-2]
Modus Ponens:
If [4], then (Not [2].).
[4]
Therefore, Not [2]..
|
{0: 'Vets see pets.', 1: 'Fuel cells have the potential for very low cost, high reliability, and high efficiency.', 2: 'Crickets chirp to attract a mate.', 3: 'Humans are hard to test because of their diverse capabilities and levels of learning.', 4: 'Scientists propose explanations.'}
| 4 |
3,480 |
['Given that it is a common misconception that either most diets prevent diseases or students learn about lions, it can be inferred that most rodents have vertebrae.', 'Given that osteoporosis is the most prevalent bone disease affecting aging adults, it can be inferred that if it is not true that if it is a common misconception that either most diets prevent diseases or students learn about lions, then it is not the case that most rodents have vertebrae, then diatomaceous earth is non-toxic.', 'Those that suggest osteoporosis is the most prevalent bone disease affecting aging adults are right.', 'Assuming storms resuspend the marine snow, and the water column gradually eutrophies , we know that the claim that diatomaceous earth is non-toxic is false.', 'It is fair to say that storms resuspend the marine snow, and the water column gradually eutrophies .']
|
Given that it is a common misconception that either most diets prevent diseases or students learn about lions, it can be inferred that most rodents have vertebrae. Given that osteoporosis is the most prevalent bone disease affecting aging adults, it can be inferred that if it is not true that if it is a common misconception that either most diets prevent diseases or students learn about lions, then it is not the case that most rodents have vertebrae, then diatomaceous earth is non-toxic. Those that suggest osteoporosis is the most prevalent bone disease affecting aging adults are right. Assuming storms resuspend the marine snow, and the water column gradually eutrophies , we know that the claim that diatomaceous earth is non-toxic is false. It is fair to say that storms resuspend the marine snow, and the water column gradually eutrophies .
|
It is a fact that either most diets prevent diseases or students learn about lions.
|
The claim that either most diets prevent diseases or students learn about lions does not correspond with reality.
|
FALSE
|
Reductio Ad Absurdum:
If (Not (Either [0] or [1].).), then [2].
If (Not (Either [0] or [1].).), then (Not [2].). [SC2-1]
Therefore, Either [0] or [1]..
[SC2-1]
Modus Tonens:
If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [3]. [SC1-2]
Not [3]. [SC2-2]
Therefore, If (Not (Either [0] or [1].).), then (Not [2].)..
[SC1-2]
Modus Ponens:
If [5], then (If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [3].).
[5]
Therefore, If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [3]..
[SC2-2]
Modus Ponens:
If [4], then (Not [3].).
[4]
Therefore, Not [3]..
|
{0: 'Most diets prevent diseases.', 1: 'Students learn about lions.', 2: 'Most rodents have vertebrae.', 3: 'Diatomaceous earth is non-toxic.', 4: 'Storms resuspend the marine snow, and the water column gradually eutrophies .', 5: 'Osteoporosis is the most prevalent bone disease affecting aging adults.'}
| 4 |
3,498 |
['Given that allergen is substances, it can be inferred that some butterflies live for years.', 'We know that either bats are quite specific on what temperature they want to hibernate at or either allergen is substances or if skydiving is a very safe sport, then powdery mildew is the most common and possibly the most difficult disease to control on Euonymus.', 'The statement that states bats are quite specific on what temperature they want to hibernate at is false.', 'It is not true that pollination is of no value without fertilization.', "Whenever it is true that we know that the claim that if we know that the claim that if if skydiving is a very safe sport, then powdery mildew is the most common and possibly the most difficult disease to control on Euonymus, then some butterflies live for years is false, then pollination is of no value without fertilization is false, 'femininity is about appearing beautiful and vulnerable and small' is true.", 'One may reasonably assume that if we know that the claim that if we know that the claim that if if skydiving is a very safe sport, then powdery mildew is the most common and possibly the most difficult disease to control on Euonymus, then some butterflies live for years is false, then pollination is of no value without fertilization is false, then it is a common misconception that femininity is about appearing beautiful and vulnerable and small.']
|
Given that allergen is substances, it can be inferred that some butterflies live for years. We know that either bats are quite specific on what temperature they want to hibernate at or either allergen is substances or if skydiving is a very safe sport, then powdery mildew is the most common and possibly the most difficult disease to control on Euonymus. The statement that states bats are quite specific on what temperature they want to hibernate at is false. It is not true that pollination is of no value without fertilization. Whenever it is true that we know that the claim that if we know that the claim that if if skydiving is a very safe sport, then powdery mildew is the most common and possibly the most difficult disease to control on Euonymus, then some butterflies live for years is false, then pollination is of no value without fertilization is false, 'femininity is about appearing beautiful and vulnerable and small' is true. One may reasonably assume that if we know that the claim that if we know that the claim that if if skydiving is a very safe sport, then powdery mildew is the most common and possibly the most difficult disease to control on Euonymus, then some butterflies live for years is false, then pollination is of no value without fertilization is false, then it is a common misconception that femininity is about appearing beautiful and vulnerable and small.
|
We can assume that some butterflies live for years.
|
We can assume that some butterflies live for years.
|
TRUE
|
Disjunction Elimination:
Either [1] or (If [2], then [3].). [SC1-1]
If [1], then [0].
If (If [2], then [3].), then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [5] or (Either [1] or (If [2], then [3].).).
Not [5].
Therefore, Either [1] or (If [2], then [3].)..
[SC3-1]
Modus Tonens:
If (Not (If (If [2], then [3].), then [0].).), then [4]. [SC1-2]
Not [4].
Therefore, If (If [2], then [3].), then [0]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (If (If [2], then [3].), then [0].).), then [4].).), then [6].
If (Not (If (Not (If (If [2], then [3].), then [0].).), then [4].).), then (Not [6].).
Therefore, If (Not (If (If [2], then [3].), then [0].).), then [4]..
|
{0: 'Some butterflies live for years.', 1: 'Allergen is substances.', 2: 'Skydiving is a very safe sport.', 3: 'Powdery mildew is the most common and possibly the most difficult disease to control on Euonymus.', 4: 'Pollination is of no value without fertilization.', 5: 'Bats are quite specific on what temperature they want to hibernate at.', 6: 'Femininity is about appearing beautiful and vulnerable and small.'}
| 4 |
3,968 |
['It is rational to believe that either boys leave grandmas or students discuss factors.', "Once we know the notion that 'if boys leave grandmas, then patterns are forms most people understand and remember' is untrue, we also know that birds tend to be monogamous whereas mammals tend to be polygamous.", 'The statement, birds tend to be monogamous whereas mammals tend to be polygamous, does not hold.', 'There is good reason to believe that either if beavers search for suitable habitats, then downhill skiers love to ski fast or if students discuss factors, then patterns are forms most people understand and remember.', 'When if beavers search for suitable habitats, then downhill skiers love to ski fast is true, it follows that civic knowledge arises out of the interconnection between reflection and action.', 'If if beavers search for suitable habitats, then downhill skiers love to ski fast, then the claim that civic knowledge arises out of the interconnection between reflection and action is false.']
|
It is rational to believe that either boys leave grandmas or students discuss factors. Once we know the notion that 'if boys leave grandmas, then patterns are forms most people understand and remember' is untrue, we also know that birds tend to be monogamous whereas mammals tend to be polygamous. The statement, birds tend to be monogamous whereas mammals tend to be polygamous, does not hold. There is good reason to believe that either if beavers search for suitable habitats, then downhill skiers love to ski fast or if students discuss factors, then patterns are forms most people understand and remember. When if beavers search for suitable habitats, then downhill skiers love to ski fast is true, it follows that civic knowledge arises out of the interconnection between reflection and action. If if beavers search for suitable habitats, then downhill skiers love to ski fast, then the claim that civic knowledge arises out of the interconnection between reflection and action is false.
|
It is rational to agree that patterns are forms most people understand and remember.
|
It is rational to agree that patterns are forms most people understand and remember.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not (If [1], then [0].).), then [5].
Not [5].
Therefore, If [1], then [0]..
[SC3-1]
Disjunctive Syllogism:
Either (If [3], then [4].) or (If [2], then [0].).
Not (If [3], then [4].). [SC2-2]
Therefore, If [2], then [0]..
[SC2-2]
Reductio Ad Absurdum:
If (If [3], then [4].), then [6].
If (If [3], then [4].), then (Not [6].).
Therefore, Not (If [3], then [4].)..
|
{0: 'Patterns are forms most people understand and remember.', 1: 'Boys leave grandmas.', 2: 'Students discuss factors.', 3: 'Beavers search for suitable habitats.', 4: 'Downhill skiers love to ski fast.', 5: 'Birds tend to be monogamous whereas mammals tend to be polygamous.', 6: 'Civic knowledge arises out of the interconnection between reflection and action.'}
| 4 |
3,405 |
['It is a fact that either chemistry controls the environment or durant soils have argillic horizons and occur on broad ridgetops or flats.', "Whenever it is true that chemistry controls the environment, 'if the claim that reveries are of two kinds, sinful and religious does not reflect reality, then billies have serious problems' is true.", 'One may reasonably assume that if durant soils have argillic horizons and occur on broad ridgetops or flats, then if the claim that reveries are of two kinds, sinful and religious does not reflect reality, then billies have serious problems.', 'Should it be the case that the claim that reveries are of two kinds, sinful and religious does not reflect reality, it follows that anoles consume prey.', 'Provided that it is not the case that if anoles consume prey, then it is not the case that billies have serious problems, we know that human genes can make nations with the poorest of resources rich, or the richest poor.', 'It is a common misconception that human genes can make nations with the poorest of resources rich, or the richest poor.']
|
It is a fact that either chemistry controls the environment or durant soils have argillic horizons and occur on broad ridgetops or flats. Whenever it is true that chemistry controls the environment, 'if the claim that reveries are of two kinds, sinful and religious does not reflect reality, then billies have serious problems' is true. One may reasonably assume that if durant soils have argillic horizons and occur on broad ridgetops or flats, then if the claim that reveries are of two kinds, sinful and religious does not reflect reality, then billies have serious problems. Should it be the case that the claim that reveries are of two kinds, sinful and religious does not reflect reality, it follows that anoles consume prey. Provided that it is not the case that if anoles consume prey, then it is not the case that billies have serious problems, we know that human genes can make nations with the poorest of resources rich, or the richest poor. It is a common misconception that human genes can make nations with the poorest of resources rich, or the richest poor.
|
The statement that states reveries are of two kinds, sinful and religious is right.
|
The statement that states reveries are of two kinds, sinful and religious is right.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If (Not [0].), then [1].).
If [4], then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Hypothetical Syllogism:
If (Not [0].), then [2].
If [2], then (Not [1].). [SC2-2]
Therefore, If (Not [0].), then (Not [1].)..
[SC2-2]
Modus Tonens:
If (Not (If [2], then (Not [1].).).), then [5].
Not [5].
Therefore, If [2], then (Not [1].)..
|
{0: 'Reveries are of two kinds, sinful and religious.', 1: 'Billies have serious problems.', 2: 'Anoles consume prey.', 3: 'Chemistry controls the environment.', 4: 'Durant soils have argillic horizons and occur on broad ridgetops or flats.', 5: 'Human genes can make nations with the poorest of resources rich, or the richest poor.'}
| 4 |
3,743 |
['Assuming salt marshes serve as pollution filters and as buffers against flooding and shoreline erosion, we know that if those that suggest opening ceremony is ceremony are wrong, then heat breaks down proteins.', 'The claim that salt marshes serve as pollution filters and as buffers against flooding and shoreline erosion holds true.', "The statement that 'humans are indisputably a part of nature' is incorrect.", 'Given that if heredity plays the major role in determining one s personality, then female raccoons reach sexual maturity at one year of age, males at two, it can be inferred that if it is not the case that if those that suggest opening ceremony is ceremony are wrong, then the claim that heat breaks down proteins has no merit, then humans are indisputably a part of nature.', 'Provided that heredity plays the major role in determining one s personality, we know that female raccoons reach sexual maturity at one year of age, males at two.']
|
Assuming salt marshes serve as pollution filters and as buffers against flooding and shoreline erosion, we know that if those that suggest opening ceremony is ceremony are wrong, then heat breaks down proteins. The claim that salt marshes serve as pollution filters and as buffers against flooding and shoreline erosion holds true. The statement that 'humans are indisputably a part of nature' is incorrect. Given that if heredity plays the major role in determining one s personality, then female raccoons reach sexual maturity at one year of age, males at two, it can be inferred that if it is not the case that if those that suggest opening ceremony is ceremony are wrong, then the claim that heat breaks down proteins has no merit, then humans are indisputably a part of nature. Provided that heredity plays the major role in determining one s personality, we know that female raccoons reach sexual maturity at one year of age, males at two.
|
It is the case that opening ceremony is ceremony.
|
It is not the case that opening ceremony is ceremony.
|
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 [2], then (If (Not [0].), then [1].).
[2]
Therefore, If (Not [0].), then [1]..
[SC2-1]
Modus Tonens:
If (Not (If (Not [0].), then (Not [1].).).), then [3]. [SC1-2]
Not [3].
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Modus Ponens:
If (If [4], then [5].), then (If (Not (If (Not [0].), then (Not [1].).).), then [3].).
If [4], then [5].
Therefore, If (Not (If (Not [0].), then (Not [1].).).), then [3]..
|
{0: 'Opening ceremony is ceremony.', 1: 'Heat breaks down proteins.', 2: 'Salt marshes serve as pollution filters and as buffers against flooding and shoreline erosion.', 3: 'Humans are indisputably a part of nature.', 4: 'Heredity plays the major role in determining one s personality.', 5: 'Female raccoons reach sexual maturity at one year of age, males at two.'}
| 4 |
3,093 |
['It is rational to agree that worship is an issue of the heart rather than the outward appearance.', 'Once we know some poppy seeds contain acid, we also know that classic migraines begin with warning signs such as flashing lights or colors.', 'Those that suggest pornography presents young people with a false and distorted image of human sexuality are wrong.', 'We know that either farms have problems or either succinic acid lacks the hydroxyl group that is present on the others or some marine mammals have physical disabilities that impact their survival in the wild.', "Whenever it is true that farms have problems, 'pornography presents young people with a false and distorted image of human sexuality' is true.", 'When either succinic acid lacks the hydroxyl group that is present on the others or some marine mammals have physical disabilities that impact their survival in the wild is true, it follows that if worship is an issue of the heart rather than the outward appearance, then some poppy seeds contain acid.']
|
It is rational to agree that worship is an issue of the heart rather than the outward appearance. Once we know some poppy seeds contain acid, we also know that classic migraines begin with warning signs such as flashing lights or colors. Those that suggest pornography presents young people with a false and distorted image of human sexuality are wrong. We know that either farms have problems or either succinic acid lacks the hydroxyl group that is present on the others or some marine mammals have physical disabilities that impact their survival in the wild. Whenever it is true that farms have problems, 'pornography presents young people with a false and distorted image of human sexuality' is true. When either succinic acid lacks the hydroxyl group that is present on the others or some marine mammals have physical disabilities that impact their survival in the wild is true, it follows that if worship is an issue of the heart rather than the outward appearance, then some poppy seeds contain acid.
|
The statement 'classic migraines begin with warning signs such as flashing lights or colors' is true.
|
Those that suggest classic migraines begin with warning signs such as flashing lights or colors are wrong.
|
FALSE
|
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].
Therefore, If [1], then [0]..
[SC1-2]
Disjunctive Syllogism:
Either [3] or (If [1], then [2].). [SC1-3]
Not [3].
Therefore, If [1], then [2]..
[SC1-3]
Constructive Dilemma:
Either [4] or (Either [5] or [6].).
If [4], then [3].
If (Either [5] or [6].), then (If [1], then [2].).
Therefore, Either [3] or (If [1], then [2].)..
|
{0: 'Classic migraines begin with warning signs such as flashing lights or colors.', 1: 'Worship is an issue of the heart rather than the outward appearance.', 2: 'Some poppy seeds contain acid.', 3: 'Pornography presents young people with a false and distorted image of human sexuality.', 4: 'Farms have problems.', 5: 'Succinic acid lacks the hydroxyl group that is present on the others.', 6: 'Some marine mammals have physical disabilities that impact their survival in the wild.'}
| 4 |
3,433 |
['There is good reason to believe that either international trade occurs because of specialization in production or if music is very important in the life of the church, then travel expense is expense.', 'Should it be the case that international trade occurs because of specialization in production, it follows that either electric wires can mean instant death to puppies or whales evolve over years.', 'On the condition that if music is very important in the life of the church, then travel expense is expense, it is definitely the case that either electric wires can mean instant death to puppies or whales evolve over years.', 'If electric wires can mean instant death to puppies, then excess output occurs when the biomass is suddenly released, such as in slash and burn agriculture.', 'One may reasonably assume that if excess output occurs when the biomass is suddenly released, such as in slash and burn agriculture, then salsa is condiments.', "Once we know the statement that 'if whales evolve over years, then salsa is condiments' is incorrect, we also know that all particles exert a gravitational force of attraction upon each other.", "Given that the statement that 'if whales evolve over years, then salsa is condiments' is incorrect, it can be inferred that the statement that 'all particles exert a gravitational force of attraction upon each other' is incorrect."]
|
There is good reason to believe that either international trade occurs because of specialization in production or if music is very important in the life of the church, then travel expense is expense. Should it be the case that international trade occurs because of specialization in production, it follows that either electric wires can mean instant death to puppies or whales evolve over years. On the condition that if music is very important in the life of the church, then travel expense is expense, it is definitely the case that either electric wires can mean instant death to puppies or whales evolve over years. If electric wires can mean instant death to puppies, then excess output occurs when the biomass is suddenly released, such as in slash and burn agriculture. One may reasonably assume that if excess output occurs when the biomass is suddenly released, such as in slash and burn agriculture, then salsa is condiments. Once we know the statement that 'if whales evolve over years, then salsa is condiments' is incorrect, we also know that all particles exert a gravitational force of attraction upon each other. Given that the statement that 'if whales evolve over years, then salsa is condiments' is incorrect, it can be inferred that the statement that 'all particles exert a gravitational force of attraction upon each other' is incorrect.
|
Those that suggest salsa is condiments are right.
|
Salsas are classically a combination of diced vegetables or fruits, vinegar, herbs and citrus.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [5] or (If [6], then [7].).
If [5], then (Either [1] or [2].).
If (If [6], then [7].), then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC2-1]
Hypothetical Syllogism:
If [1], then [3].
If [3], then [0].
Therefore, If [1], then [0]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then [0].).), then [4].
If (Not (If [2], then [0].).), then (Not [4].).
Therefore, If [2], then [0]..
|
{0: 'Salsa is condiments.', 1: 'Electric wires can mean instant death to puppies.', 2: 'Whales evolve over years.', 3: 'Excess output occurs when the biomass is suddenly released, such as in slash and burn agriculture.', 4: 'All particles exert a gravitational force of attraction upon each other.', 5: 'International trade occurs because of specialization in production.', 6: 'Music is very important in the life of the church.', 7: 'Travel expense is expense.'}
| 4 |
3,083 |
["The statement 'some people lack the courage to mix with others and socialize' can be considered false.", 'There is good reason to believe that either lavender is a flower placed under a pillow to encourage dreams or some bats eat fruit and some eat frogs.', 'It is a common misconception that lavender is a flower placed under a pillow to encourage dreams.', 'Should it be the case that addaxs have thick legs, it follows that either some people lack the courage to mix with others and socialize or if some bats eat fruit and some eat frogs, then we know that the claim that if essential minerals are obtained from mineral licks, then most biologists consider animals is false.', "The statement 'addaxs have thick legs' can be considered true."]
|
The statement 'some people lack the courage to mix with others and socialize' can be considered false. There is good reason to believe that either lavender is a flower placed under a pillow to encourage dreams or some bats eat fruit and some eat frogs. It is a common misconception that lavender is a flower placed under a pillow to encourage dreams. Should it be the case that addaxs have thick legs, it follows that either some people lack the courage to mix with others and socialize or if some bats eat fruit and some eat frogs, then we know that the claim that if essential minerals are obtained from mineral licks, then most biologists consider animals is false. The statement 'addaxs have thick legs' can be considered true.
|
We know that the claim that if essential minerals are obtained from mineral licks, then most biologists consider animals is false.
|
We know that the claim that if essential minerals are obtained from mineral licks, then most biologists consider animals is false.
|
TRUE
|
Modus Ponens:
If [2], then (Not (If [0], then [1].).). [SC1-1]
[2] [SC2-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If [2], then (Not (If [0], then [1].).).). [SC1-2]
Not [3].
Therefore, If [2], then (Not (If [0], then [1].).)..
[SC1-2]
Modus Ponens:
If [5], then (Either [3] or (If [2], then (Not (If [0], then [1].).).).).
[5]
Therefore, Either [3] or (If [2], then (Not (If [0], then [1].).).)..
[SC2-1]
Disjunctive Syllogism:
Either [4] or [2].
Not [4].
Therefore, [2].
|
{0: 'Essential minerals are obtained from mineral licks.', 1: 'Most biologists consider animals.', 2: 'Some bats eat fruit and some eat frogs.', 3: 'Some people lack the courage to mix with others and socialize.', 4: 'Lavender is a flower placed under a pillow to encourage dreams.', 5: 'Addaxs have thick legs.'}
| 4 |
3,843 |
['There is good reason to believe that either sensitivity is senses or energy is conserved when efficiency is improved or when energy waste is avoided.', 'Assuming energy is conserved when efficiency is improved or when energy waste is avoided, we know that either croakers are part of croakers or most pesticide kills bees.', 'There is good reason to believe that either librarians have generic navigational skills that are easily applicable to a knowledge-based economy or the statement that states croakers are part of croakers is false.', "The statement 'librarians have generic navigational skills that are easily applicable to a knowledge-based economy' can be considered false.", "So long as sensitivity is senses, 'natural selection explains design in nature' is true.", 'Should it be the case that natural selection explains design in nature, it follows that either croakers are part of croakers or most pesticide kills bees.']
|
There is good reason to believe that either sensitivity is senses or energy is conserved when efficiency is improved or when energy waste is avoided. Assuming energy is conserved when efficiency is improved or when energy waste is avoided, we know that either croakers are part of croakers or most pesticide kills bees. There is good reason to believe that either librarians have generic navigational skills that are easily applicable to a knowledge-based economy or the statement that states croakers are part of croakers is false. The statement 'librarians have generic navigational skills that are easily applicable to a knowledge-based economy' can be considered false. So long as sensitivity is senses, 'natural selection explains design in nature' is true. Should it be the case that natural selection explains design in nature, it follows that either croakers are part of croakers or most pesticide kills bees.
|
It is fair to say that most pesticide kills bees.
|
Pesticides are also something to be aware of.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Either [1] or [0].). [SC2-2]
If [4], then (Either [1] or [0].).
Therefore, Either [1] or [0]..
[SC2-2]
Hypothetical Syllogism:
If [3], then [5].
If [5], then (Either [1] or [0].).
Therefore, If [3], then (Either [1] or [0].)..
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].).
Not [2].
Therefore, Not [1]..
|
{0: 'Most pesticide kills bees.', 1: 'Croakers are part of croakers.', 2: 'Librarians have generic navigational skills that are easily applicable to a knowledge-based economy.', 3: 'Sensitivity is senses.', 4: 'Energy is conserved when efficiency is improved or when energy waste is avoided.', 5: 'Natural selection explains design in nature.'}
| 4 |
3,914 |
['It is not true that human beings have the ability to acquire knowledge through various processes.', "Whenever it is true that the claim that if the statement that 'rubbish attracts animals' is incorrect, then human beings have the ability to acquire knowledge through various processes does not correspond with reality, 'some mothers have diabetes' is true.", 'Either blood moves from a renal artery to capillaries in the cuplike structure or the claim that some mothers have diabetes does not reflect reality.', "If engineers are practical people, then the statement 'blood moves from a renal artery to capillaries in the cuplike structure' can be considered false.", 'We can assume that engineers are practical people.']
|
It is not true that human beings have the ability to acquire knowledge through various processes. Whenever it is true that the claim that if the statement that 'rubbish attracts animals' is incorrect, then human beings have the ability to acquire knowledge through various processes does not correspond with reality, 'some mothers have diabetes' is true. Either blood moves from a renal artery to capillaries in the cuplike structure or the claim that some mothers have diabetes does not reflect reality. If engineers are practical people, then the statement 'blood moves from a renal artery to capillaries in the cuplike structure' can be considered false. We can assume that engineers are practical people.
|
It is fair to say that rubbish attracts animals.
|
The claim that rubbish attracts animals is false.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Not [0].), then [1].).), then [2].
Not [2]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Disjunctive Syllogism:
Either [3] or (Not [2].).
Not [3]. [SC2-3]
Therefore, Not [2]..
[SC2-3]
Modus Ponens:
If [4], then (Not [3].).
[4]
Therefore, Not [3]..
|
{0: 'Rubbish attracts animals.', 1: 'Human beings have the ability to acquire knowledge through various processes.', 2: 'Some mothers have diabetes.', 3: 'Blood moves from a renal artery to capillaries in the cuplike structure.', 4: 'Engineers are practical people.'}
| 4 |
3,657 |
['Either one or both of these statements are true: if some measurements measure light intensity, then pollen attracts insects, or if most diatoms are diploid, then a common privet is a privet.', 'When if some measurements measure light intensity, then pollen attracts insects is true, it follows that if we know that the claim that either some mealworms eat decay leaves or cognition is defined as the skill of dealing with knowledge is false, then tests contribute to assessments.', "Whenever it is true that tests contribute to assessments, 'all religions are one ' is true.", "So long as tests contribute to assessments, 'the statement that states all religions are one is false' is true.", 'Assuming those that suggest if if most diatoms are diploid, then a common privet is a privet, then if we know that the claim that either some mealworms eat decay leaves or cognition is defined as the skill of dealing with knowledge is false, then tests contribute to assessments are wrong, we know that if chemists have many strategies to find the best sequence of reactions to make the desired product , then adoption is a legal and social process that transfers all parental rights to the adoptive family.', "The statement 'if chemists have many strategies to find the best sequence of reactions to make the desired product , then adoption is a legal and social process that transfers all parental rights to the adoptive family' can be considered false."]
|
Either one or both of these statements are true: if some measurements measure light intensity, then pollen attracts insects, or if most diatoms are diploid, then a common privet is a privet. When if some measurements measure light intensity, then pollen attracts insects is true, it follows that if we know that the claim that either some mealworms eat decay leaves or cognition is defined as the skill of dealing with knowledge is false, then tests contribute to assessments. Whenever it is true that tests contribute to assessments, 'all religions are one ' is true. So long as tests contribute to assessments, 'the statement that states all religions are one is false' is true. Assuming those that suggest if if most diatoms are diploid, then a common privet is a privet, then if we know that the claim that either some mealworms eat decay leaves or cognition is defined as the skill of dealing with knowledge is false, then tests contribute to assessments are wrong, we know that if chemists have many strategies to find the best sequence of reactions to make the desired product , then adoption is a legal and social process that transfers all parental rights to the adoptive family. The statement 'if chemists have many strategies to find the best sequence of reactions to make the desired product , then adoption is a legal and social process that transfers all parental rights to the adoptive family' can be considered false.
|
It is a fact that either some mealworms eat decay leaves or cognition is defined as the skill of dealing with knowledge.
|
The claim that either some mealworms eat decay leaves or cognition is defined as the skill of dealing with knowledge has no merit.
|
FALSE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Disjunction Elimination:
Either (If [4], then [5].) or (If [6], then [7].).
If (If [4], then [5].), then (If (Not (Either [0] or [1].).), then [2].).
If (If [6], then [7].), then (If (Not (Either [0] or [1].).), then [2].). [SC3-2]
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC3-2]
Modus Tonens:
If (Not (If (If [6], then [7].), then (If (Not (Either [0] or [1].).), then [2].).).), then (If [8], then [9].).
Not (If [8], then [9].).
Therefore, If (If [6], then [7].), then (If (Not (Either [0] or [1].).), then [2].)..
[SC2-1]
Reductio Ad Absurdum:
If [2], then [3].
If [2], then (Not [3].).
Therefore, Not [2]..
|
{0: 'Some mealworms eat decay leaves.', 1: 'Cognition is defined as the skill of dealing with knowledge.', 2: 'Tests contribute to assessments.', 3: 'All religions are one .', 4: 'Some measurements measure light intensity.', 5: 'Pollen attracts insects.', 6: 'Most diatoms are diploid.', 7: 'A common privet is a privet.', 8: 'Chemists have many strategies to find the best sequence of reactions to make the desired product .', 9: 'Adoption is a legal and social process that transfers all parental rights to the adoptive family.'}
| 4 |
3,414 |
['The claim that people have arms does not correspond with reality.', 'Either cardamom tea is a very famous beverage, along with ginger tea, in India or if a newspaper editor is an editor, then lions are capable of hunts.', 'The claim that cardamom tea is a very famous beverage, along with ginger tea, in India has no merit.', "Should it be the case that the claim that if lions are capable of hunts, then people have arms does not reflect reality, it follows that meteors are rocks in outer space that usually vaporize before reaching the Earth's surface.", "The notion that 'meteors are rocks in outer space that usually vaporize before reaching the Earth's surface' is untrue."]
|
The claim that people have arms does not correspond with reality. Either cardamom tea is a very famous beverage, along with ginger tea, in India or if a newspaper editor is an editor, then lions are capable of hunts. The claim that cardamom tea is a very famous beverage, along with ginger tea, in India has no merit. Should it be the case that the claim that if lions are capable of hunts, then people have arms does not reflect reality, it follows that meteors are rocks in outer space that usually vaporize before reaching the Earth's surface. The notion that 'meteors are rocks in outer space that usually vaporize before reaching the Earth's surface' is untrue.
|
It is a common misconception that a newspaper editor is an editor.
|
It is a simple truth that a newspaper editor is an editor.
|
FALSE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Hypothetical Syllogism:
If [0], then [2]. [SC1-2]
If [2], then [1]. [SC2-2]
Therefore, If [0], then [1]..
[SC1-2]
Disjunctive Syllogism:
Either [3] or (If [0], then [2].).
Not [3].
Therefore, If [0], then [2]..
[SC2-2]
Modus Tonens:
If (Not (If [2], then [1].).), then [4].
Not [4].
Therefore, If [2], then [1]..
|
{0: 'A newspaper editor is an editor.', 1: 'People have arms.', 2: 'Lions are capable of hunts.', 3: 'Cardamom tea is a very famous beverage, along with ginger tea, in India.', 4: "Meteors are rocks in outer space that usually vaporize before reaching the Earth's surface."}
| 4 |
3,662 |
['It is a fact that either fungi produce and excrete a huge and complex array of enzymes or wolves primarily eat meat.', 'On the condition that fungi produce and excrete a huge and complex array of enzymes, it is definitely the case that police is capable of arrests.', "Whenever it is true that wolves primarily eat meat, 'toads have more bulbous bodies, dry warty-looking skin and tend to crawl' is true.", 'Once we know police is capable of arrests, we also know that taxation is imposition.', 'When taxation is imposition is true, it follows that it is not the case that critical nutrients play important roles.', 'Should it be the case that it is not true that if toads have more bulbous bodies, dry warty-looking skin and tend to crawl, then it is not the case that critical nutrients play important roles, it follows that most hurricanes provide weather.', 'On the condition that it is not true that if toads have more bulbous bodies, dry warty-looking skin and tend to crawl, then it is not the case that critical nutrients play important roles, it is definitely the case that the statement that states most hurricanes provide weather is false.']
|
It is a fact that either fungi produce and excrete a huge and complex array of enzymes or wolves primarily eat meat. On the condition that fungi produce and excrete a huge and complex array of enzymes, it is definitely the case that police is capable of arrests. Whenever it is true that wolves primarily eat meat, 'toads have more bulbous bodies, dry warty-looking skin and tend to crawl' is true. Once we know police is capable of arrests, we also know that taxation is imposition. When taxation is imposition is true, it follows that it is not the case that critical nutrients play important roles. Should it be the case that it is not true that if toads have more bulbous bodies, dry warty-looking skin and tend to crawl, then it is not the case that critical nutrients play important roles, it follows that most hurricanes provide weather. On the condition that it is not true that if toads have more bulbous bodies, dry warty-looking skin and tend to crawl, then it is not the case that critical nutrients play important roles, it is definitely the case that the statement that states most hurricanes provide weather is false.
|
It is not the case that critical nutrients play important roles.
|
It is not the case that critical nutrients play roles.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].). [SC2-1]
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC1-1]
Constructive Dilemma:
Either [4] or [5].
If [4], then [1].
If [5], then [2].
Therefore, Either [1] or [2]..
[SC2-1]
Hypothetical Syllogism:
If [1], then [6].
If [6], then (Not [0].).
Therefore, If [1], then (Not [0].)..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then (Not [0].).).), then [3].
If (Not (If [2], then (Not [0].).).), then (Not [3].).
Therefore, If [2], then (Not [0].)..
|
{0: 'Critical nutrients play important roles.', 1: 'Police is capable of arrests.', 2: 'Toads have more bulbous bodies, dry warty-looking skin and tend to crawl.', 3: 'Most hurricanes provide weather.', 4: 'Fungi produce and excrete a huge and complex array of enzymes.', 5: 'Wolves primarily eat meat.', 6: 'Taxation is imposition.'}
| 4 |
3,978 |
['It is rational to believe that either dogs mainly cool themselves by panting- breathing in through the nose and out through the mouth or if sulfur is needed by plants in about the same quantities as phosphorus, then water lilies are heavy feeders for the best foliage and flower production.', 'On the condition that dogs mainly cool themselves by panting- breathing in through the nose and out through the mouth, it is definitely the case that either specific heat is the calories per weight of substance or those that suggest bodywork is manual labor are wrong.', "Whenever it is true that if sulfur is needed by plants in about the same quantities as phosphorus, then water lilies are heavy feeders for the best foliage and flower production, 'either specific heat is the calories per weight of substance or those that suggest bodywork is manual labor are wrong' is true.", 'If specific heat is the calories per weight of substance, then oceans remain one of the key parts of the climate system that are poorly observed and understood.', "Whenever it is true that oceans remain one of the key parts of the climate system that are poorly observed and understood, 'bears can easily peel a window or door off the car for something as small as a gum wrapper' is true.", "Given that oceans remain one of the key parts of the climate system that are poorly observed and understood, it can be inferred that the statement that 'bears can easily peel a window or door off the car for something as small as a gum wrapper' is incorrect."]
|
It is rational to believe that either dogs mainly cool themselves by panting- breathing in through the nose and out through the mouth or if sulfur is needed by plants in about the same quantities as phosphorus, then water lilies are heavy feeders for the best foliage and flower production. On the condition that dogs mainly cool themselves by panting- breathing in through the nose and out through the mouth, it is definitely the case that either specific heat is the calories per weight of substance or those that suggest bodywork is manual labor are wrong. Whenever it is true that if sulfur is needed by plants in about the same quantities as phosphorus, then water lilies are heavy feeders for the best foliage and flower production, 'either specific heat is the calories per weight of substance or those that suggest bodywork is manual labor are wrong' is true. If specific heat is the calories per weight of substance, then oceans remain one of the key parts of the climate system that are poorly observed and understood. Whenever it is true that oceans remain one of the key parts of the climate system that are poorly observed and understood, 'bears can easily peel a window or door off the car for something as small as a gum wrapper' is true. Given that oceans remain one of the key parts of the climate system that are poorly observed and understood, it can be inferred that the statement that 'bears can easily peel a window or door off the car for something as small as a gum wrapper' is incorrect.
|
Those that suggest bodywork is manual labor are wrong.
|
It is true that bodywork is manual labor.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then (Either [1] or (Not [0].).).
If (If [4], then [5].), then (Either [1] or (Not [0].).).
Therefore, Either [1] or (Not [0].)..
[SC2-1]
Modus Tonens:
If [1], then [2].
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Reductio Ad Absurdum:
If [2], then [6].
If [2], then (Not [6].).
Therefore, Not [2]..
|
{0: 'Bodywork is manual labor.', 1: 'Specific heat is the calories per weight of substance.', 2: 'Oceans remain one of the key parts of the climate system that are poorly observed and understood.', 3: 'Dogs mainly cool themselves by panting- breathing in through the nose and out through the mouth.', 4: 'Sulfur is needed by plants in about the same quantities as phosphorus.', 5: 'Water lilies are heavy feeders for the best foliage and flower production.', 6: 'Bears can easily peel a window or door off the car for something as small as a gum wrapper.'}
| 4 |
3,771 |
['Assuming we know that the claim that if we know that the claim that sea urchins possess both a water vascular system and a hemal system, the latter containing blood is false, then pahoehoe is Hawaiian term for lava with a smooth, ropy, wrinkled, and billowy surface is false, we know that forests influence the local and probably global climates.', 'On the condition that we know that the claim that if we know that the claim that sea urchins possess both a water vascular system and a hemal system, the latter containing blood is false, then pahoehoe is Hawaiian term for lava with a smooth, ropy, wrinkled, and billowy surface is false, it is definitely the case that it is not the case that forests influence the local and probably global climates.', 'Either one or both of these statements are true: zoysia is a warm season grass that turns brown early in the fall and stays brown until late spring, or noses have chambers.', "One may reasonably assume that if zoysia is a warm season grass that turns brown early in the fall and stays brown until late spring, then the statement 'pahoehoe is Hawaiian term for lava with a smooth, ropy, wrinkled, and billowy surface' can be considered false.", "Once we know some western tanagers get feathers, we also know that if noses have chambers, then the statement 'pahoehoe is Hawaiian term for lava with a smooth, ropy, wrinkled, and billowy surface' can be considered false.", "The statement 'some western tanagers get feathers' is true."]
|
Assuming we know that the claim that if we know that the claim that sea urchins possess both a water vascular system and a hemal system, the latter containing blood is false, then pahoehoe is Hawaiian term for lava with a smooth, ropy, wrinkled, and billowy surface is false, we know that forests influence the local and probably global climates. On the condition that we know that the claim that if we know that the claim that sea urchins possess both a water vascular system and a hemal system, the latter containing blood is false, then pahoehoe is Hawaiian term for lava with a smooth, ropy, wrinkled, and billowy surface is false, it is definitely the case that it is not the case that forests influence the local and probably global climates. Either one or both of these statements are true: zoysia is a warm season grass that turns brown early in the fall and stays brown until late spring, or noses have chambers. One may reasonably assume that if zoysia is a warm season grass that turns brown early in the fall and stays brown until late spring, then the statement 'pahoehoe is Hawaiian term for lava with a smooth, ropy, wrinkled, and billowy surface' can be considered false. Once we know some western tanagers get feathers, we also know that if noses have chambers, then the statement 'pahoehoe is Hawaiian term for lava with a smooth, ropy, wrinkled, and billowy surface' can be considered false. The statement 'some western tanagers get feathers' is true.
|
We can assume that sea urchins possess both a water vascular system and a hemal system, the latter containing blood.
|
Sea urchins are the major grazer on kelp, climbing up the holdfasts and chewing through the stipes.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then [1].).), then [4].
If (Not (If (Not [0].), then [1].).), then (Not [4].).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (Not [1].).
If [3], then (Not [1].). [SC3-2]
Therefore, Not [1]..
[SC3-2]
Modus Ponens:
If [5], then (If [3], then (Not [1].).).
[5]
Therefore, If [3], then (Not [1].)..
|
{0: 'Sea urchins possess both a water vascular system and a hemal system, the latter containing blood.', 1: 'Pahoehoe is Hawaiian term for lava with a smooth, ropy, wrinkled, and billowy surface.', 2: 'Zoysia is a warm season grass that turns brown early in the fall and stays brown until late spring.', 3: 'Noses have chambers.', 4: 'Forests influence the local and probably global climates.', 5: 'Some western tanagers get feathers.'}
| 4 |
3,728 |
['One may reasonably assume that if the claim that if all religions try to teach Love, then murder is an earth-bound evil is false, then redtails come in a variety of color phases, ranging from nearly white to nearly black.', 'It is rational to believe that either some observers even look for high-energy particles called cosmic rays which come from deep space or if all religions try to teach Love, then some people mistakenly believe that murder is an earth-bound evil.', 'It is not the case that some observers even look for high-energy particles called cosmic rays which come from deep space.', 'At least one of two things is true: a mortal is a cause, or macular degeneration is degeneration.', 'Once we know a mortal is a cause, we also know that if the claim that if all religions try to teach Love, then murder is an earth-bound evil is false, then it is a common misconception that redtails come in a variety of color phases, ranging from nearly white to nearly black.', 'One may reasonably assume that if macular degeneration is degeneration, then if the claim that if all religions try to teach Love, then murder is an earth-bound evil is false, then it is a common misconception that redtails come in a variety of color phases, ranging from nearly white to nearly black.']
|
One may reasonably assume that if the claim that if all religions try to teach Love, then murder is an earth-bound evil is false, then redtails come in a variety of color phases, ranging from nearly white to nearly black. It is rational to believe that either some observers even look for high-energy particles called cosmic rays which come from deep space or if all religions try to teach Love, then some people mistakenly believe that murder is an earth-bound evil. It is not the case that some observers even look for high-energy particles called cosmic rays which come from deep space. At least one of two things is true: a mortal is a cause, or macular degeneration is degeneration. Once we know a mortal is a cause, we also know that if the claim that if all religions try to teach Love, then murder is an earth-bound evil is false, then it is a common misconception that redtails come in a variety of color phases, ranging from nearly white to nearly black. One may reasonably assume that if macular degeneration is degeneration, then if the claim that if all religions try to teach Love, then murder is an earth-bound evil is false, then it is a common misconception that redtails come in a variety of color phases, ranging from nearly white to nearly black.
|
We know that the claim that all religions try to teach Love is false.
|
It is a simple truth that all religions try to teach Love.
|
FALSE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then [2].
If (Not (If [0], then [1].).), then (Not [2].). [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not (If [0], then [1].).), then (Not [2].).).
If [5], then (If (Not (If [0], then [1].).), then (Not [2].).).
Therefore, If (Not (If [0], then [1].).), then (Not [2].)..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (If [0], then (Not [1].).).
Not [3].
Therefore, If [0], then (Not [1].)..
|
{0: 'All religions try to teach Love.', 1: 'Murder is an earth-bound evil.', 2: 'Redtails come in a variety of color phases, ranging from nearly white to nearly black.', 3: 'Some observers even look for high-energy particles called cosmic rays which come from deep space.', 4: 'A mortal is a cause.', 5: 'Macular degeneration is degeneration.'}
| 4 |
3,911 |
["So long as the statement that states facts contribute to exploration is false, 'most phones have security features that block outgoing calls to certain numbers without a password' is true.", 'On the condition that most phones have security features that block outgoing calls to certain numbers without a password, it is definitely the case that neurons have a nucleus that contains genes.', 'Given that most phones have security features that block outgoing calls to certain numbers without a password, it can be inferred that agricultural biotechnology is one of the most promising developments in modern science.', 'Either one or both of these statements are true: cactuses have many adaptations for living in places that are sometimes dry for a long time , or anger is sin from the sin nature.', 'Provided that cactuses have many adaptations for living in places that are sometimes dry for a long time , we know that if agricultural biotechnology is one of the most promising developments in modern science, then the statement, neurons have a nucleus that contains genes, does not hold.', 'Assuming anger is sin from the sin nature, we know that if agricultural biotechnology is one of the most promising developments in modern science, then the statement, neurons have a nucleus that contains genes, does not hold.']
|
So long as the statement that states facts contribute to exploration is false, 'most phones have security features that block outgoing calls to certain numbers without a password' is true. On the condition that most phones have security features that block outgoing calls to certain numbers without a password, it is definitely the case that neurons have a nucleus that contains genes. Given that most phones have security features that block outgoing calls to certain numbers without a password, it can be inferred that agricultural biotechnology is one of the most promising developments in modern science. Either one or both of these statements are true: cactuses have many adaptations for living in places that are sometimes dry for a long time , or anger is sin from the sin nature. Provided that cactuses have many adaptations for living in places that are sometimes dry for a long time , we know that if agricultural biotechnology is one of the most promising developments in modern science, then the statement, neurons have a nucleus that contains genes, does not hold. Assuming anger is sin from the sin nature, we know that if agricultural biotechnology is one of the most promising developments in modern science, then the statement, neurons have a nucleus that contains genes, does not hold.
|
The idea that facts contribute to exploration is true.
|
Facts are statements that can be verified or proved.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2].
If [1], then (Not [2].). [SC2-2]
Therefore, Not [1]..
[SC2-2]
Hypothetical Syllogism:
If [1], then [3].
If [3], then (Not [2].). [SC2-3]
Therefore, If [1], then (Not [2].)..
[SC2-3]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [3], then (Not [2].).).
If [5], then (If [3], then (Not [2].).).
Therefore, If [3], then (Not [2].)..
|
{0: 'Facts contribute to exploration.', 1: 'Most phones have security features that block outgoing calls to certain numbers without a password.', 2: 'Neurons have a nucleus that contains genes.', 3: 'Agricultural biotechnology is one of the most promising developments in modern science.', 4: 'Cactuses have many adaptations for living in places that are sometimes dry for a long time .', 5: 'Anger is sin from the sin nature.'}
| 4 |
3,807 |
["On the condition that the statement 'if most earth has enough water, then many organisms reproduce asexually' can be considered false, it is definitely the case that market share is important for long term stability of any business.", 'When market share is important for long term stability of any business is true, it follows that either some rodents are located in ecosystems or vaccines contain a killed form of the virus, and appear to be safe and effective.', "The statement 'sediment can move around quickly, but it takes a long time to break down bedrock' can be considered true.", "When the statement that 'if sediment can move around quickly, but it takes a long time to break down bedrock, then it is a common misconception that either some rodents are located in ecosystems or vaccines contain a killed form of the virus, and appear to be safe and effective' is incorrect is true, it follows that neodymium magnets contain iron, boron and the rare-earth element neodymium.", "Assuming the statement that 'if sediment can move around quickly, but it takes a long time to break down bedrock, then it is a common misconception that either some rodents are located in ecosystems or vaccines contain a killed form of the virus, and appear to be safe and effective' is incorrect, we know that the statement, neodymium magnets contain iron, boron and the rare-earth element neodymium, does not hold."]
|
On the condition that the statement 'if most earth has enough water, then many organisms reproduce asexually' can be considered false, it is definitely the case that market share is important for long term stability of any business. When market share is important for long term stability of any business is true, it follows that either some rodents are located in ecosystems or vaccines contain a killed form of the virus, and appear to be safe and effective. The statement 'sediment can move around quickly, but it takes a long time to break down bedrock' can be considered true. When the statement that 'if sediment can move around quickly, but it takes a long time to break down bedrock, then it is a common misconception that either some rodents are located in ecosystems or vaccines contain a killed form of the virus, and appear to be safe and effective' is incorrect is true, it follows that neodymium magnets contain iron, boron and the rare-earth element neodymium. Assuming the statement that 'if sediment can move around quickly, but it takes a long time to break down bedrock, then it is a common misconception that either some rodents are located in ecosystems or vaccines contain a killed form of the virus, and appear to be safe and effective' is incorrect, we know that the statement, neodymium magnets contain iron, boron and the rare-earth element neodymium, does not hold.
|
If most earth has enough water, then many organisms reproduce asexually.
|
The notion that 'if most earth has enough water, then many organisms reproduce asexually' is untrue.
|
FALSE
|
Modus Tonens:
If (Not (If [0], then [1].).), then (Either [2] or [3].). [SC1-1]
Not (Either [2] or [3].). [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Hypothetical Syllogism:
If (Not (If [0], then [1].).), then [5].
If [5], then (Either [2] or [3].).
Therefore, If (Not (If [0], then [1].).), then (Either [2] or [3].)..
[SC2-1]
Modus Ponens:
If [4], then (Not (Either [2] or [3].).). [SC1-2]
[4]
Therefore, Not (Either [2] or [3].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [4], then (Not (Either [2] or [3].).).).), then [6].
If (Not (If [4], then (Not (Either [2] or [3].).).).), then (Not [6].).
Therefore, If [4], then (Not (Either [2] or [3].).)..
|
{0: 'Most earth has enough water.', 1: 'Many organisms reproduce asexually.', 2: 'Some rodents are located in ecosystems.', 3: 'Vaccines contain a killed form of the virus, and appear to be safe and effective.', 4: 'Sediment can move around quickly, but it takes a long time to break down bedrock.', 5: 'Market share is important for long term stability of any business.', 6: 'Neodymium magnets contain iron, boron and the rare-earth element neodymium.'}
| 4 |
3,322 |
['We know that at least one of two things is true: mystics aspire after spiritualization in the man opposite the crisis in the outer world, or cells use vesicles to signal each other in a variety of ways.', 'If mystics aspire after spiritualization in the man opposite the crisis in the outer world, then normal grief can produce many of the same symptoms as depression.', 'At least one of two things is true: ground plane is an implement for smoothing the soil, or moisture is essential to all life and the tiny seeds are no exception.', 'One may reasonably assume that if ground plane is an implement for smoothing the soil, then if most food provides nutrition, then if cells use vesicles to signal each other in a variety of ways, then most devastate diseases have severe consequences.', "Whenever it is true that moisture is essential to all life and the tiny seeds are no exception, 'if most food provides nutrition, then if cells use vesicles to signal each other in a variety of ways, then most devastate diseases have severe consequences' is true.", "So long as social sciences are interdisciplinary in nature, 'most food provides nutrition' is true.", 'We can assume that social sciences are interdisciplinary in nature.']
|
We know that at least one of two things is true: mystics aspire after spiritualization in the man opposite the crisis in the outer world, or cells use vesicles to signal each other in a variety of ways. If mystics aspire after spiritualization in the man opposite the crisis in the outer world, then normal grief can produce many of the same symptoms as depression. At least one of two things is true: ground plane is an implement for smoothing the soil, or moisture is essential to all life and the tiny seeds are no exception. One may reasonably assume that if ground plane is an implement for smoothing the soil, then if most food provides nutrition, then if cells use vesicles to signal each other in a variety of ways, then most devastate diseases have severe consequences. Whenever it is true that moisture is essential to all life and the tiny seeds are no exception, 'if most food provides nutrition, then if cells use vesicles to signal each other in a variety of ways, then most devastate diseases have severe consequences' is true. So long as social sciences are interdisciplinary in nature, 'most food provides nutrition' is true. We can assume that social sciences are interdisciplinary in nature.
|
We know that at least one of two things is true: normal grief can produce many of the same symptoms as depression, or most devastate diseases have severe consequences.
|
We know that at least one of two things is true: normal grief can produce many of the same symptoms as depression, or most devastate diseases have severe consequences.
|
TRUE
|
Constructive Dilemma:
Either [2] or [3].
If [2], then [0].
If [3], then [1]. [SC3-1]
Therefore, Either [0] or [1]..
[SC3-1]
Modus Ponens:
If [4], then (If [3], then [1].). [SC1-2]
[4] [SC2-2]
Therefore, If [3], then [1]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [4], then (If [3], then [1].).).
If [6], then (If [4], then (If [3], then [1].).).
Therefore, If [4], then (If [3], then [1].)..
[SC2-2]
Modus Ponens:
If [7], then [4].
[7]
Therefore, [4].
|
{0: 'Normal grief can produce many of the same symptoms as depression.', 1: 'Most devastate diseases have severe consequences.', 2: 'Mystics aspire after spiritualization in the man opposite the crisis in the outer world.', 3: 'Cells use vesicles to signal each other in a variety of ways.', 4: 'Most food provides nutrition.', 5: 'Ground plane is an implement for smoothing the soil.', 6: 'Moisture is essential to all life and the tiny seeds are no exception.', 7: 'Social sciences are interdisciplinary in nature.'}
| 4 |
3,556 |
['Should it be the case that if paw isa body part, then people learn who they are by studying where they are and where they come from, it follows that either most hamburgers contain grind beef or if cockatoos are known for their loud vocalizations which are also used in communication, then yogis have (part) necks.', 'When paw isa body part is true, it follows that people learn who they are by studying where they are and where they come from.', "Either if dams can be arch, gravity, or embankment dams, then european nurses use to denote diagnostic and intervention phenomena or if most hamburgers contain grind beef, then the notion that 'sporting events are located in television' is untrue.", 'Those that suggest if dams can be arch, gravity, or embankment dams, then european nurses use to denote diagnostic and intervention phenomena are wrong.', "Either one or both of these statements are true: blackbucks eat grass, or if if cockatoos are known for their loud vocalizations which are also used in communication, then yogis have (part) necks, then the notion that 'sporting events are located in television' is untrue.", 'The claim that blackbucks eat grass is false.']
|
Should it be the case that if paw isa body part, then people learn who they are by studying where they are and where they come from, it follows that either most hamburgers contain grind beef or if cockatoos are known for their loud vocalizations which are also used in communication, then yogis have (part) necks. When paw isa body part is true, it follows that people learn who they are by studying where they are and where they come from. Either if dams can be arch, gravity, or embankment dams, then european nurses use to denote diagnostic and intervention phenomena or if most hamburgers contain grind beef, then the notion that 'sporting events are located in television' is untrue. Those that suggest if dams can be arch, gravity, or embankment dams, then european nurses use to denote diagnostic and intervention phenomena are wrong. Either one or both of these statements are true: blackbucks eat grass, or if if cockatoos are known for their loud vocalizations which are also used in communication, then yogis have (part) necks, then the notion that 'sporting events are located in television' is untrue. The claim that blackbucks eat grass is false.
|
The notion that 'sporting events are located in television' is untrue.
|
It is a simple truth that sporting events are located in television.
|
FALSE
|
Disjunction Elimination:
Either [1] or (If [2], then [3].). [SC1-1]
If [1], then (Not [0].). [SC2-1]
If (If [2], then [3].), then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If (If [4], then [5].), then (Either [1] or (If [2], then [3].).).
If [4], then [5].
Therefore, Either [1] or (If [2], then [3].)..
[SC2-1]
Disjunctive Syllogism:
Either (If [6], then [7].) or (If [1], then (Not [0].).).
Not (If [6], then [7].).
Therefore, If [1], then (Not [0].)..
[SC3-1]
Disjunctive Syllogism:
Either [8] or (If (If [2], then [3].), then (Not [0].).).
Not [8].
Therefore, If (If [2], then [3].), then (Not [0].)..
|
{0: 'Sporting events are located in television.', 1: 'Most hamburgers contain grind beef.', 2: 'Cockatoos are known for their loud vocalizations which are also used in communication.', 3: 'Yogis have (part) necks.', 4: 'Paw isa body part.', 5: 'People learn who they are by studying where they are and where they come from.', 6: 'Dams can be arch, gravity, or embankment dams.', 7: 'European nurses use to denote diagnostic and intervention phenomena.', 8: 'Blackbucks eat grass.'}
| 4 |
3,357 |
['We know that either low level relates to greater incidence of infections and slow recovery or portals are cavities.', 'Provided that low level relates to greater incidence of infections and slow recovery, we know that earth is one of the planets orbiting a star called the Sun.', "So long as pianos have keyboards, 'if portals are cavities, then earth is one of the planets orbiting a star called the Sun' is true.", 'At least one of two things is true: indian pipes are wildflowers, or relays are passage.', 'Given that indian pipes are wildflowers, it can be inferred that either pianos have keyboards or cascades are a sequence of steps.', 'On the condition that relays are passage, it is definitely the case that either pianos have keyboards or cascades are a sequence of steps.', 'On the condition that cascades are a sequence of steps, it is definitely the case that some atoms are part of lead.', 'Should it be the case that some atoms are part of lead, it follows that if portals are cavities, then earth is one of the planets orbiting a star called the Sun.']
|
We know that either low level relates to greater incidence of infections and slow recovery or portals are cavities. Provided that low level relates to greater incidence of infections and slow recovery, we know that earth is one of the planets orbiting a star called the Sun. So long as pianos have keyboards, 'if portals are cavities, then earth is one of the planets orbiting a star called the Sun' is true. At least one of two things is true: indian pipes are wildflowers, or relays are passage. Given that indian pipes are wildflowers, it can be inferred that either pianos have keyboards or cascades are a sequence of steps. On the condition that relays are passage, it is definitely the case that either pianos have keyboards or cascades are a sequence of steps. On the condition that cascades are a sequence of steps, it is definitely the case that some atoms are part of lead. Should it be the case that some atoms are part of lead, it follows that if portals are cavities, then earth is one of the planets orbiting a star called the Sun.
|
Those that suggest earth is one of the planets orbiting a star called the Sun are right.
|
Earth is a planet where there is oxygen and other elements.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC3-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (If [2], then [0].).
If [4], then (If [2], then [0].). [SC3-2]
Therefore, If [2], then [0]..
[SC1-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Either [3] or [4].).
If [7], then (Either [3] or [4].).
Therefore, Either [3] or [4]..
[SC3-2]
Hypothetical Syllogism:
If [4], then [5].
If [5], then (If [2], then [0].).
Therefore, If [4], then (If [2], then [0].)..
|
{0: 'Earth is one of the planets orbiting a star called the Sun.', 1: 'Low level relates to greater incidence of infections and slow recovery.', 2: 'Portals are cavities.', 3: 'Pianos have keyboards.', 4: 'Cascades are a sequence of steps.', 5: 'Some atoms are part of lead.', 6: 'Indian pipes are wildflowers.', 7: 'Relays are passage.'}
| 4 |
3,069 |
['Assuming most wallpaper is paper or fabric coated with vinyl, we know that ice storms are known to cause accidents , take power lines down and cause serious damage .', 'Given that ice storms are known to cause accidents , take power lines down and cause serious damage , it can be inferred that it is a common misconception that if african american grandmothers assume responsibility, then hate is fear.', 'Either music is an expression of emotion and the words an expression of thought or tourism plays an important role in the economy.', 'Given that tourism plays an important role in the economy, it can be inferred that most wallpaper is paper or fabric coated with vinyl.', 'When mechanized agriculture requires more fossil energy is true, it follows that if music is an expression of emotion and the words an expression of thought, then most wallpaper is paper or fabric coated with vinyl.', 'It is rational to agree that mechanized agriculture requires more fossil energy.']
|
Assuming most wallpaper is paper or fabric coated with vinyl, we know that ice storms are known to cause accidents , take power lines down and cause serious damage . Given that ice storms are known to cause accidents , take power lines down and cause serious damage , it can be inferred that it is a common misconception that if african american grandmothers assume responsibility, then hate is fear. Either music is an expression of emotion and the words an expression of thought or tourism plays an important role in the economy. Given that tourism plays an important role in the economy, it can be inferred that most wallpaper is paper or fabric coated with vinyl. When mechanized agriculture requires more fossil energy is true, it follows that if music is an expression of emotion and the words an expression of thought, then most wallpaper is paper or fabric coated with vinyl. It is rational to agree that mechanized agriculture requires more fossil energy.
|
It is a common misconception that if african american grandmothers assume responsibility, then hate is fear.
|
The claim that haiyen city is between Shanghai and Hangchow, and by the sea is false.
|
Uncertain
|
Modus Ponens:
If [2], then (Not (If [0], then [1].).). [SC1-1]
[2] [SC2-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Hypothetical Syllogism:
If [2], then [5].
If [5], then (Not (If [0], then [1].).).
Therefore, If [2], then (Not (If [0], then [1].).)..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then [2]. [SC2-2]
If [4], then [2].
Therefore, [2].
[SC2-2]
Modus Ponens:
If [6], then (If [3], then [2].).
[6]
Therefore, If [3], then [2]..
|
{0: 'African american grandmothers assume responsibility.', 1: 'Hate is fear.', 2: 'Most wallpaper is paper or fabric coated with vinyl.', 3: 'Music is an expression of emotion and the words an expression of thought.', 4: 'Tourism plays an important role in the economy.', 5: 'Ice storms are known to cause accidents , take power lines down and cause serious damage .', 6: 'Mechanized agriculture requires more fossil energy.'}
| 4 |
3,514 |
["So long as some people work with math, 'if involuntary smoking is a cause of disease, including lung cancer, in healthy non-smokers, then hot water is used to smooth the surface and form a tighter bond between new ice and existing ice' is true.", 'some people work with math.', "On the condition that the notion that 'involuntary smoking is a cause of disease, including lung cancer, in healthy non-smokers' is untrue, it is definitely the case that many common brands contribute to skin being dry and itchy.", "Given that the notion that 'involuntary smoking is a cause of disease, including lung cancer, in healthy non-smokers' is untrue, it can be inferred that impact printing is a dying technology.", 'Should it be the case that impact printing is a dying technology, it follows that the claim that many common brands contribute to skin being dry and itchy is false.']
|
So long as some people work with math, 'if involuntary smoking is a cause of disease, including lung cancer, in healthy non-smokers, then hot water is used to smooth the surface and form a tighter bond between new ice and existing ice' is true. some people work with math. On the condition that the notion that 'involuntary smoking is a cause of disease, including lung cancer, in healthy non-smokers' is untrue, it is definitely the case that many common brands contribute to skin being dry and itchy. Given that the notion that 'involuntary smoking is a cause of disease, including lung cancer, in healthy non-smokers' is untrue, it can be inferred that impact printing is a dying technology. Should it be the case that impact printing is a dying technology, it follows that the claim that many common brands contribute to skin being dry and itchy is false.
|
It is rational to agree that hot water is used to smooth the surface and form a tighter bond between new ice and existing ice.
|
It is rational to agree that hot water is used to smooth the surface and form a tighter bond between new ice and existing ice.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (If [1], then [0].).
[3]
Therefore, If [1], then [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then [2].
If (Not [1].), then (Not [2].). [SC2-2]
Therefore, [1].
[SC2-2]
Hypothetical Syllogism:
If (Not [1].), then [4].
If [4], then (Not [2].).
Therefore, If (Not [1].), then (Not [2].)..
|
{0: 'Hot water is used to smooth the surface and form a tighter bond between new ice and existing ice.', 1: 'Involuntary smoking is a cause of disease, including lung cancer, in healthy non-smokers.', 2: 'Many common brands contribute to skin being dry and itchy.', 3: 'Some people work with math.', 4: 'Impact printing is a dying technology.'}
| 4 |
3,509 |
['Provided that forces stimulate growth, we know that an eaglet is a young bird.', "So long as the claim that if either truth is the only way to teach children or evolution is demoted from science to theory and creationism is elevated from theory to science, then forces stimulate growth is false, 'energy flow is the amount of energy that is transferred through a food chain up the trophic level' is true.", 'The claim that energy flow is the amount of energy that is transferred through a food chain up the trophic level has no merit.', 'Either one or both of these statements are true: hypothyroidism is a common disease of middle age and older dogs, or some red monkeys have ranges.', "Whenever it is true that hypothyroidism is a common disease of middle age and older dogs, 'either truth is the only way to teach children or evolution is demoted from science to theory and creationism is elevated from theory to science' is true.", 'Given that some red monkeys have ranges, it can be inferred that either truth is the only way to teach children or evolution is demoted from science to theory and creationism is elevated from theory to science.']
|
Provided that forces stimulate growth, we know that an eaglet is a young bird. So long as the claim that if either truth is the only way to teach children or evolution is demoted from science to theory and creationism is elevated from theory to science, then forces stimulate growth is false, 'energy flow is the amount of energy that is transferred through a food chain up the trophic level' is true. The claim that energy flow is the amount of energy that is transferred through a food chain up the trophic level has no merit. Either one or both of these statements are true: hypothyroidism is a common disease of middle age and older dogs, or some red monkeys have ranges. Whenever it is true that hypothyroidism is a common disease of middle age and older dogs, 'either truth is the only way to teach children or evolution is demoted from science to theory and creationism is elevated from theory to science' is true. Given that some red monkeys have ranges, it can be inferred that either truth is the only way to teach children or evolution is demoted from science to theory and creationism is elevated from theory to science.
|
The claim that an eaglet is a young bird is true.
|
The claim that an eaglet is a young bird is true.
|
TRUE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If (Either [2] or [3].), then [1]. [SC1-2]
Either [2] or [3]. [SC2-2]
Therefore, [1].
[SC1-2]
Modus Tonens:
If (Not (If (Either [2] or [3].), then [1].).), then [6].
Not [6].
Therefore, If (Either [2] or [3].), then [1]..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Either [2] or [3].).
If [5], then (Either [2] or [3].).
Therefore, Either [2] or [3]..
|
{0: 'An eaglet is a young bird.', 1: 'Forces stimulate growth.', 2: 'Truth is the only way to teach children.', 3: 'Evolution is demoted from science to theory and creationism is elevated from theory to science.', 4: 'Hypothyroidism is a common disease of middle age and older dogs.', 5: 'Some red monkeys have ranges.', 6: 'Energy flow is the amount of energy that is transferred through a food chain up the trophic level.'}
| 4 |
3,340 |
['We know that at least one of two things is true: potassium is used by plants for flower color and size, or rhythmic jerks can occur during sleep, with associated dystonic posturing during wakefulness.', 'On the condition that potassium is used by plants for flower color and size, it is definitely the case that the claim that water pollution is due to wastewater emissions from both countries in a shared border waterway has no merit.', 'It is the case that covens tend to meet together for ritual purposes once a month, at new moon.', 'Either one or both of these statements are true: plain water can cause problems, such as lowering the amount of salt or sugar in the blood, or sound pulses are emitted, reflected off objects, and retrieved through the lower jaw.', 'Given that plain water can cause problems, such as lowering the amount of salt or sugar in the blood, it can be inferred that if covens tend to meet together for ritual purposes once a month, at new moon, then if potassium is used by plants for flower color and size, then water pollution is due to wastewater emissions from both countries in a shared border waterway.', 'Should it be the case that sound pulses are emitted, reflected off objects, and retrieved through the lower jaw, it follows that if covens tend to meet together for ritual purposes once a month, at new moon, then if potassium is used by plants for flower color and size, then water pollution is due to wastewater emissions from both countries in a shared border waterway.']
|
We know that at least one of two things is true: potassium is used by plants for flower color and size, or rhythmic jerks can occur during sleep, with associated dystonic posturing during wakefulness. On the condition that potassium is used by plants for flower color and size, it is definitely the case that the claim that water pollution is due to wastewater emissions from both countries in a shared border waterway has no merit. It is the case that covens tend to meet together for ritual purposes once a month, at new moon. Either one or both of these statements are true: plain water can cause problems, such as lowering the amount of salt or sugar in the blood, or sound pulses are emitted, reflected off objects, and retrieved through the lower jaw. Given that plain water can cause problems, such as lowering the amount of salt or sugar in the blood, it can be inferred that if covens tend to meet together for ritual purposes once a month, at new moon, then if potassium is used by plants for flower color and size, then water pollution is due to wastewater emissions from both countries in a shared border waterway. Should it be the case that sound pulses are emitted, reflected off objects, and retrieved through the lower jaw, it follows that if covens tend to meet together for ritual purposes once a month, at new moon, then if potassium is used by plants for flower color and size, then water pollution is due to wastewater emissions from both countries in a shared border waterway.
|
It is a simple truth that rhythmic jerks can occur during sleep, with associated dystonic posturing during wakefulness.
|
Small businesses sustain the families of their owners and the neighborhoods in which they reside.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2]. [SC1-2]
If [1], then (Not [2].).
Therefore, Not [1]..
[SC1-2]
Modus Ponens:
If [3], then (If [1], then [2].). [SC1-3]
[3]
Therefore, If [1], then [2]..
[SC1-3]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [3], then (If [1], then [2].).).
If [5], then (If [3], then (If [1], then [2].).).
Therefore, If [3], then (If [1], then [2].)..
|
{0: 'Rhythmic jerks can occur during sleep, with associated dystonic posturing during wakefulness.', 1: 'Potassium is used by plants for flower color and size.', 2: 'Water pollution is due to wastewater emissions from both countries in a shared border waterway.', 3: 'Covens tend to meet together for ritual purposes once a month, at new moon.', 4: 'Plain water can cause problems, such as lowering the amount of salt or sugar in the blood.', 5: 'Sound pulses are emitted, reflected off objects, and retrieved through the lower jaw.'}
| 4 |
3,221 |
['We know that at least one of two things is true: enucleation remains the most frequent treatment for retinoblastoma, or if diuretics are inexpensive and have shown effective in the treatment of hypertension, then warm air flows at high speeds over the surface of skin.', 'If if diuretics are inexpensive and have shown effective in the treatment of hypertension, then warm air flows at high speeds over the surface of skin, then if if most gorillas live in countries, then sustainability is a word that is most meaningful as a comprehensive term, then wings have edges.', 'Should it be the case that most gorillas live in countries, it follows that latchs are fasteners.', 'Assuming latchs are fasteners, we know that sustainability is a word that is most meaningful as a comprehensive term.', 'Provided that enucleation remains the most frequent treatment for retinoblastoma, we know that gimmicks are gimmicks.', 'Given that gimmicks are gimmicks, it can be inferred that if if most gorillas live in countries, then sustainability is a word that is most meaningful as a comprehensive term, then wings have edges.']
|
We know that at least one of two things is true: enucleation remains the most frequent treatment for retinoblastoma, or if diuretics are inexpensive and have shown effective in the treatment of hypertension, then warm air flows at high speeds over the surface of skin. If if diuretics are inexpensive and have shown effective in the treatment of hypertension, then warm air flows at high speeds over the surface of skin, then if if most gorillas live in countries, then sustainability is a word that is most meaningful as a comprehensive term, then wings have edges. Should it be the case that most gorillas live in countries, it follows that latchs are fasteners. Assuming latchs are fasteners, we know that sustainability is a word that is most meaningful as a comprehensive term. Provided that enucleation remains the most frequent treatment for retinoblastoma, we know that gimmicks are gimmicks. Given that gimmicks are gimmicks, it can be inferred that if if most gorillas live in countries, then sustainability is a word that is most meaningful as a comprehensive term, then wings have edges.
|
Those that suggest wings have edges are right.
|
Wings are part of division.
|
Uncertain
|
Modus Ponens:
If (If [1], then [2].), then [0]. [SC1-1]
If [1], then [2]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [4] or (If [5], then [6].).
If [4], then (If (If [1], then [2].), then [0].). [SC2-2]
If (If [5], then [6].), then (If (If [1], then [2].), then [0].).
Therefore, If (If [1], then [2].), then [0]..
[SC2-2]
Hypothetical Syllogism:
If [4], then [7].
If [7], then (If (If [1], then [2].), then [0].).
Therefore, If [4], then (If (If [1], then [2].), then [0].)..
[SC2-1]
Hypothetical Syllogism:
If [1], then [3].
If [3], then [2].
Therefore, If [1], then [2]..
|
{0: 'Wings have edges.', 1: 'Most gorillas live in countries.', 2: 'Sustainability is a word that is most meaningful as a comprehensive term.', 3: 'Latchs are fasteners.', 4: 'Enucleation remains the most frequent treatment for retinoblastoma.', 5: 'Diuretics are inexpensive and have shown effective in the treatment of hypertension.', 6: 'Warm air flows at high speeds over the surface of skin.', 7: 'Gimmicks are gimmicks.'}
| 4 |
3,928 |
['Assuming we know that the claim that either female polar bears reach maturity or cabbage is an excellent source of vitamin C and a good source of folacin and fiber is false, we know that research is an area of activity that has a very low level of reported participation.', 'Either one or both of these statements are true: most gardens consist of large rocks placed on top of sand or gravel, or baleen plates are somewhat triangular and arranged like teeth in a comb.', "Assuming most gardens consist of large rocks placed on top of sand or gravel, we know that if the statement that 'if we know that the claim that either female polar bears reach maturity or cabbage is an excellent source of vitamin C and a good source of folacin and fiber is false, then the notion that 'research is an area of activity that has a very low level of reported participation' is untrue' is incorrect, then spiders eat small insects.", "If baleen plates are somewhat triangular and arranged like teeth in a comb, then if the statement that 'if we know that the claim that either female polar bears reach maturity or cabbage is an excellent source of vitamin C and a good source of folacin and fiber is false, then the notion that 'research is an area of activity that has a very low level of reported participation' is untrue' is incorrect, then spiders eat small insects.", 'If spiders eat small insects, then police officers move into positions.', 'The statement, police officers move into positions, does not hold.']
|
Assuming we know that the claim that either female polar bears reach maturity or cabbage is an excellent source of vitamin C and a good source of folacin and fiber is false, we know that research is an area of activity that has a very low level of reported participation. Either one or both of these statements are true: most gardens consist of large rocks placed on top of sand or gravel, or baleen plates are somewhat triangular and arranged like teeth in a comb. Assuming most gardens consist of large rocks placed on top of sand or gravel, we know that if the statement that 'if we know that the claim that either female polar bears reach maturity or cabbage is an excellent source of vitamin C and a good source of folacin and fiber is false, then the notion that 'research is an area of activity that has a very low level of reported participation' is untrue' is incorrect, then spiders eat small insects. If baleen plates are somewhat triangular and arranged like teeth in a comb, then if the statement that 'if we know that the claim that either female polar bears reach maturity or cabbage is an excellent source of vitamin C and a good source of folacin and fiber is false, then the notion that 'research is an area of activity that has a very low level of reported participation' is untrue' is incorrect, then spiders eat small insects. If spiders eat small insects, then police officers move into positions. The statement, police officers move into positions, does not hold.
|
Either one or both of these statements are true: female polar bears reach maturity, or cabbage is an excellent source of vitamin C and a good source of folacin and fiber.
|
Either one or both of these statements are true: female polar bears reach maturity, or cabbage is an excellent source of vitamin C and a good source of folacin and fiber.
|
TRUE
|
Reductio Ad Absurdum:
If (Not (Either [0] or [1].).), then [2].
If (Not (Either [0] or [1].).), then (Not [2].). [SC2-1]
Therefore, Either [0] or [1]..
[SC2-1]
Modus Tonens:
If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [3]. [SC1-2]
Not [3]. [SC2-2]
Therefore, If (Not (Either [0] or [1].).), then (Not [2].)..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [3].).
If [6], then (If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [3].).
Therefore, If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [3]..
[SC2-2]
Modus Tonens:
If [3], then [4].
Not [4].
Therefore, Not [3]..
|
{0: 'Female polar bears reach maturity.', 1: 'Cabbage is an excellent source of vitamin C and a good source of folacin and fiber.', 2: 'Research is an area of activity that has a very low level of reported participation.', 3: 'Spiders eat small insects.', 4: 'Police officers move into positions.', 5: 'Most gardens consist of large rocks placed on top of sand or gravel.', 6: 'Baleen plates are somewhat triangular and arranged like teeth in a comb.'}
| 4 |
3,146 |
['It is the case that communities have problems.', 'It is a fact that either ear false foxgloves grow in regions or anatomies include faces.', 'It is not true that ear false foxgloves grow in regions.', "Whenever it is true that communities have problems, 'some seabirds live in regions' is true.", 'Given that some seabirds live in regions, it can be inferred that if anatomies include faces, then boobies have (part) flight feathers.']
|
It is the case that communities have problems. It is a fact that either ear false foxgloves grow in regions or anatomies include faces. It is not true that ear false foxgloves grow in regions. Whenever it is true that communities have problems, 'some seabirds live in regions' is true. Given that some seabirds live in regions, it can be inferred that if anatomies include faces, then boobies have (part) flight feathers.
|
Many people rightly believe that boobies have (part) flight feathers.
|
Many people rightly believe that boobies have (part) flight feathers.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (If [1], then [0].). [SC1-2]
[2]
Therefore, If [1], then [0]..
[SC1-2]
Hypothetical Syllogism:
If [2], then [4].
If [4], then (If [1], then [0].).
Therefore, If [2], then (If [1], then [0].)..
[SC2-1]
Disjunctive Syllogism:
Either [3] or [1].
Not [3].
Therefore, [1].
|
{0: 'Boobies have (part) flight feathers.', 1: 'Anatomies include faces.', 2: 'Communities have problems.', 3: 'Ear false foxgloves grow in regions.', 4: 'Some seabirds live in regions.'}
| 4 |
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