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
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int64 1
7
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|---|---|---|---|---|---|---|---|---|
4,631 |
['We know that at least one of two things is true: chinchillas are native to Chile and Peru, or flowers are dry when petals feel papery.', 'One may reasonably assume that if the claim that either defensiveness grows out of fear but is often expressed as aggression or anger or either most steenboks have tails or date representation is a global problem even without computers does not reflect reality, then dolphins also communicate by other means of sounds.', 'Should it be the case that the claim that either defensiveness grows out of fear but is often expressed as aggression or anger or either most steenboks have tails or date representation is a global problem even without computers does not reflect reality, it follows that it is not true that dolphins also communicate by other means of sounds.', 'At least one of two things is true: many religious traditions speak of spirituality, or experience of the divine, or if defensiveness grows out of fear but is often expressed as aggression or anger, then the claim that chinchillas are native to Chile and Peru has no merit.', 'The statement, many religious traditions speak of spirituality, or experience of the divine, does not hold.', 'Should it be the case that if trees hold soil in place and can deter mudslides and flooding, then most solvents are poisonous if they are swallowed or the vapors are inhaled in large amounts, it follows that if either most steenboks have tails or date representation is a global problem even without computers, then the claim that chinchillas are native to Chile and Peru has no merit.', 'If trees hold soil in place and can deter mudslides and flooding, then most solvents are poisonous if they are swallowed or the vapors are inhaled in large amounts.']
|
We know that at least one of two things is true: chinchillas are native to Chile and Peru, or flowers are dry when petals feel papery. One may reasonably assume that if the claim that either defensiveness grows out of fear but is often expressed as aggression or anger or either most steenboks have tails or date representation is a global problem even without computers does not reflect reality, then dolphins also communicate by other means of sounds. Should it be the case that the claim that either defensiveness grows out of fear but is often expressed as aggression or anger or either most steenboks have tails or date representation is a global problem even without computers does not reflect reality, it follows that it is not true that dolphins also communicate by other means of sounds. At least one of two things is true: many religious traditions speak of spirituality, or experience of the divine, or if defensiveness grows out of fear but is often expressed as aggression or anger, then the claim that chinchillas are native to Chile and Peru has no merit. The statement, many religious traditions speak of spirituality, or experience of the divine, does not hold. Should it be the case that if trees hold soil in place and can deter mudslides and flooding, then most solvents are poisonous if they are swallowed or the vapors are inhaled in large amounts, it follows that if either most steenboks have tails or date representation is a global problem even without computers, then the claim that chinchillas are native to Chile and Peru has no merit. If trees hold soil in place and can deter mudslides and flooding, then most solvents are poisonous if they are swallowed or the vapors are inhaled in large amounts.
|
It is true that flowers are dry when petals feel papery.
|
It is true that flowers are dry when petals feel papery.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [2] or (Either [3] or [4].). [SC1-2]
If [2], then (Not [1].). [SC2-2]
If (Either [3] or [4].), then (Not [1].). [SC3-2]
Therefore, Not [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [2] or (Either [3] or [4].).).), then [8].
If (Not (Either [2] or (Either [3] or [4].).).), then (Not [8].).
Therefore, Either [2] or (Either [3] or [4].)..
[SC2-2]
Disjunctive Syllogism:
Either [7] or (If [2], then (Not [1].).).
Not [7].
Therefore, If [2], then (Not [1].)..
[SC3-2]
Modus Ponens:
If (If [5], then [6].), then (If (Either [3] or [4].), then (Not [1].).).
If [5], then [6].
Therefore, If (Either [3] or [4].), then (Not [1].)..
|
{0: 'Flowers are dry when petals feel papery.', 1: 'Chinchillas are native to Chile and Peru.', 2: 'Defensiveness grows out of fear but is often expressed as aggression or anger.', 3: 'Most steenboks have tails.', 4: 'Date representation is a global problem even without computers.', 5: 'Trees hold soil in place and can deter mudslides and flooding.', 6: 'Most solvents are poisonous if they are swallowed or the vapors are inhaled in large amounts.', 7: 'Many religious traditions speak of spirituality, or experience of the divine.', 8: 'Dolphins also communicate by other means of sounds.'}
| 5 |
4,185 |
['It is rational to agree that money means time - time to stay in business and time to grow.', 'We know that either testes are connected by sperm ducts or some aquaria have tubes.', 'Given that some aquaria have tubes, it can be inferred that if the claim that if money means time - time to stay in business and time to grow, then if neural networks are capable of learning patterns in input data, then aneuploidy is characteristic of cancers does not correspond with reality, then rabbits have very sharp teeth and their bites can draw blood.', 'Should it be the case that the statement, if the claim that if money means time - time to stay in business and time to grow, then if neural networks are capable of learning patterns in input data, then aneuploidy is characteristic of cancers does not correspond with reality, then we know that the claim that rabbits have very sharp teeth and their bites can draw blood is false, does not hold, it follows that either some water enters intestines or hair loss is nearly complete over most of the body.', 'Assuming the statement, if the claim that if money means time - time to stay in business and time to grow, then if neural networks are capable of learning patterns in input data, then aneuploidy is characteristic of cancers does not correspond with reality, then we know that the claim that rabbits have very sharp teeth and their bites can draw blood is false, does not hold, we know that the claim that either some water enters intestines or hair loss is nearly complete over most of the body does not reflect reality.', 'If a sportscast is a newscast, then if testes are connected by sperm ducts, then if the claim that if money means time - time to stay in business and time to grow, then if neural networks are capable of learning patterns in input data, then aneuploidy is characteristic of cancers does not correspond with reality, then rabbits have very sharp teeth and their bites can draw blood.', 'It is fair to say that a sportscast is a newscast.']
|
It is rational to agree that money means time - time to stay in business and time to grow. We know that either testes are connected by sperm ducts or some aquaria have tubes. Given that some aquaria have tubes, it can be inferred that if the claim that if money means time - time to stay in business and time to grow, then if neural networks are capable of learning patterns in input data, then aneuploidy is characteristic of cancers does not correspond with reality, then rabbits have very sharp teeth and their bites can draw blood. Should it be the case that the statement, if the claim that if money means time - time to stay in business and time to grow, then if neural networks are capable of learning patterns in input data, then aneuploidy is characteristic of cancers does not correspond with reality, then we know that the claim that rabbits have very sharp teeth and their bites can draw blood is false, does not hold, it follows that either some water enters intestines or hair loss is nearly complete over most of the body. Assuming the statement, if the claim that if money means time - time to stay in business and time to grow, then if neural networks are capable of learning patterns in input data, then aneuploidy is characteristic of cancers does not correspond with reality, then we know that the claim that rabbits have very sharp teeth and their bites can draw blood is false, does not hold, we know that the claim that either some water enters intestines or hair loss is nearly complete over most of the body does not reflect reality. If a sportscast is a newscast, then if testes are connected by sperm ducts, then if the claim that if money means time - time to stay in business and time to grow, then if neural networks are capable of learning patterns in input data, then aneuploidy is characteristic of cancers does not correspond with reality, then rabbits have very sharp teeth and their bites can draw blood. It is fair to say that a sportscast is a newscast.
|
Whenever it is true that neural networks are capable of learning patterns in input data, 'aneuploidy is characteristic of cancers' is true.
|
The claim that if neural networks are capable of learning patterns in input data, then aneuploidy is characteristic of cancers does not reflect reality.
|
FALSE
|
Modus Ponens:
If [2], then (If [0], then [1].). [SC1-1]
[2]
Therefore, If [0], then [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [2], then (If [0], then [1].).).), then [3]. [SC1-2]
If (Not (If [2], then (If [0], then [1].).).), then (Not [3].). [SC2-2]
Therefore, If [2], then (If [0], then [1].)..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not (If [2], then (If [0], then [1].).).), then [3].). [SC2-3]
If [5], then (If (Not (If [2], then (If [0], then [1].).).), then [3].).
Therefore, If (Not (If [2], then (If [0], then [1].).).), then [3]..
[SC2-3]
Modus Ponens:
If [8], then (If [4], then (If (Not (If [2], then (If [0], then [1].).).), then [3].).).
[8]
Therefore, If [4], then (If (Not (If [2], then (If [0], then [1].).).), then [3].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (If [2], then (If [0], then [1].).).), then (Not [3].).).), then (Either [6] or [7].).
If (Not (If (Not (If [2], then (If [0], then [1].).).), then (Not [3].).).), then (Not (Either [6] or [7].).).
Therefore, If (Not (If [2], then (If [0], then [1].).).), then (Not [3].)..
|
{0: 'Neural networks are capable of learning patterns in input data.', 1: 'Aneuploidy is characteristic of cancers.', 2: 'Money means time - time to stay in business and time to grow.', 3: 'Rabbits have very sharp teeth and their bites can draw blood.', 4: 'Testes are connected by sperm ducts.', 5: 'Some aquaria have tubes.', 6: 'Some water enters intestines.', 7: 'Hair loss is nearly complete over most of the body.', 8: 'A sportscast is a newscast.'}
| 5 |
4,732 |
["Once we know the statement 'most snouts are part of heads' can be considered false, we also know that it is a common misconception that anorexic people are frightened of putting on weight, and are obsessed with extreme slimness.", "It is a fact that either red oaks die rapidly after infection occurs or if the statement 'most snouts are part of heads' can be considered false, then anorexic people are frightened of putting on weight, and are obsessed with extreme slimness.", "Whenever it is true that it is a common misconception that if red oaks die rapidly after infection occurs, then carbohydrates produce energy faster than do fats, 'if tuataras wait for prey, then a papilla is an appendage' is true.", 'Given that it is a common misconception that if red oaks die rapidly after infection occurs, then carbohydrates produce energy faster than do fats, it can be inferred that the claim that if tuataras wait for prey, then a papilla is an appendage has no merit.', "Given that the statement that states if red oaks die rapidly after infection occurs, then the statement that 'carbohydrates produce energy faster than do fats' is incorrect is false, it can be inferred that produce is located in markets.", "Should it be the case that the statement that states if red oaks die rapidly after infection occurs, then the statement that 'carbohydrates produce energy faster than do fats' is incorrect is false, it follows that the claim that produce is located in markets is false."]
|
Once we know the statement 'most snouts are part of heads' can be considered false, we also know that it is a common misconception that anorexic people are frightened of putting on weight, and are obsessed with extreme slimness. It is a fact that either red oaks die rapidly after infection occurs or if the statement 'most snouts are part of heads' can be considered false, then anorexic people are frightened of putting on weight, and are obsessed with extreme slimness. Whenever it is true that it is a common misconception that if red oaks die rapidly after infection occurs, then carbohydrates produce energy faster than do fats, 'if tuataras wait for prey, then a papilla is an appendage' is true. Given that it is a common misconception that if red oaks die rapidly after infection occurs, then carbohydrates produce energy faster than do fats, it can be inferred that the claim that if tuataras wait for prey, then a papilla is an appendage has no merit. Given that the statement that states if red oaks die rapidly after infection occurs, then the statement that 'carbohydrates produce energy faster than do fats' is incorrect is false, it can be inferred that produce is located in markets. Should it be the case that the statement that states if red oaks die rapidly after infection occurs, then the statement that 'carbohydrates produce energy faster than do fats' is incorrect is false, it follows that the claim that produce is located in markets is false.
|
It is rational to agree that most snouts are part of heads.
|
Most snouts have surfaces.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then [1].).
Not [2]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Reductio Ad Absurdum:
If [2], then [3]. [SC1-3]
If [2], then (Not [3].). [SC2-3]
Therefore, Not [2]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If [2], then [3].).), then (If [5], then [6].).
If (Not (If [2], then [3].).), then (Not (If [5], then [6].).).
Therefore, If [2], then [3]..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If [2], then (Not [3].).).), then [4].
If (Not (If [2], then (Not [3].).).), then (Not [4].).
Therefore, If [2], then (Not [3].)..
|
{0: 'Most snouts are part of heads.', 1: 'Anorexic people are frightened of putting on weight, and are obsessed with extreme slimness.', 2: 'Red oaks die rapidly after infection occurs.', 3: 'Carbohydrates produce energy faster than do fats.', 4: 'Produce is located in markets.', 5: 'Tuataras wait for prey.', 6: 'A papilla is an appendage.'}
| 5 |
4,404 |
['One may reasonably assume that if language is a cultural mosaic of communication, then squirrels occasionally attack garden fruits and vegetables too.', 'There is good reason to believe that either canopies are covering or either tepees are very light and easy to move around or some radiation creates habitats.', 'Given that canopies are covering, it can be inferred that herpetologists study samples.', 'We know that either most individuals adapt to a motion environment over a period of time that varies in length or some factors affect metabolism.', 'Given that most individuals adapt to a motion environment over a period of time that varies in length, it can be inferred that it is not true that herpetologists study samples.', 'Given that some factors affect metabolism, it can be inferred that it is not true that herpetologists study samples.', "Either music is a natural part of a child's experience or alpha particles are the end product of the proton-proton fusion cycle.", "Once we know music is a natural part of a child's experience, we also know that if either tepees are very light and easy to move around or some radiation creates habitats, then some people mistakenly believe that squirrels occasionally attack garden fruits and vegetables too.", 'Provided that alpha particles are the end product of the proton-proton fusion cycle, we know that if either tepees are very light and easy to move around or some radiation creates habitats, then some people mistakenly believe that squirrels occasionally attack garden fruits and vegetables too.']
|
One may reasonably assume that if language is a cultural mosaic of communication, then squirrels occasionally attack garden fruits and vegetables too. There is good reason to believe that either canopies are covering or either tepees are very light and easy to move around or some radiation creates habitats. Given that canopies are covering, it can be inferred that herpetologists study samples. We know that either most individuals adapt to a motion environment over a period of time that varies in length or some factors affect metabolism. Given that most individuals adapt to a motion environment over a period of time that varies in length, it can be inferred that it is not true that herpetologists study samples. Given that some factors affect metabolism, it can be inferred that it is not true that herpetologists study samples. Either music is a natural part of a child's experience or alpha particles are the end product of the proton-proton fusion cycle. Once we know music is a natural part of a child's experience, we also know that if either tepees are very light and easy to move around or some radiation creates habitats, then some people mistakenly believe that squirrels occasionally attack garden fruits and vegetables too. Provided that alpha particles are the end product of the proton-proton fusion cycle, we know that if either tepees are very light and easy to move around or some radiation creates habitats, then some people mistakenly believe that squirrels occasionally attack garden fruits and vegetables too.
|
We know that the claim that language is a cultural mosaic of communication is false.
|
We know that the claim that language is a cultural mosaic of communication is false.
|
TRUE
|
Modus Tonens:
If [0], then [1].
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].). [SC1-2]
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC1-2]
Constructive Dilemma:
Either [3] or (Either [4] or [5].).
If [3], then [2].
If (Either [4] or [5].), then (Not [1].). [SC3-3]
Therefore, Either [2] or (Not [1].)..
[SC3-3]
Disjunction Elimination:
Either [8] or [9].
If [8], then (If (Either [4] or [5].), then (Not [1].).).
If [9], then (If (Either [4] or [5].), then (Not [1].).).
Therefore, If (Either [4] or [5].), then (Not [1].)..
[SC2-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Not [2].).
If [7], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Language is a cultural mosaic of communication.', 1: 'Squirrels occasionally attack garden fruits and vegetables too.', 2: 'Herpetologists study samples.', 3: 'Canopies are covering.', 4: 'Tepees are very light and easy to move around.', 5: 'Some radiation creates habitats.', 6: 'Most individuals adapt to a motion environment over a period of time that varies in length.', 7: 'Some factors affect metabolism.', 8: "Music is a natural part of a child's experience.", 9: 'Alpha particles are the end product of the proton-proton fusion cycle.'}
| 5 |
4,194 |
['Either if cocaine stimulates the central nervous system causing restlessness, tremors, and convulsions, then some mold grows on walls or doped semiconductors have extra bands in the forbidden gap.', "We know that either paresthesia means numbness, prickling, or a tingling, heightened sensitivity or the notion that 'if cocaine stimulates the central nervous system causing restlessness, tremors, and convulsions, then some mold grows on walls' is untrue.", 'We know that at least one of two things is true: natives also make direct use of prairie plants for medicinal, food, and other practical uses, or the statement, paresthesia means numbness, prickling, or a tingling, heightened sensitivity, does not hold.', 'One may reasonably assume that if natives also make direct use of prairie plants for medicinal, food, and other practical uses, then earned income is wages and tips.', 'There is good reason to believe that either lotteries are an easy way to lose money or total wages excludes wages paid by both direct reimbursable and Federal government employers.', 'Provided that lotteries are an easy way to lose money, we know that the statement, earned income is wages and tips, does not hold.', 'On the condition that total wages excludes wages paid by both direct reimbursable and Federal government employers, it is definitely the case that the statement, earned income is wages and tips, does not hold.']
|
Either if cocaine stimulates the central nervous system causing restlessness, tremors, and convulsions, then some mold grows on walls or doped semiconductors have extra bands in the forbidden gap. We know that either paresthesia means numbness, prickling, or a tingling, heightened sensitivity or the notion that 'if cocaine stimulates the central nervous system causing restlessness, tremors, and convulsions, then some mold grows on walls' is untrue. We know that at least one of two things is true: natives also make direct use of prairie plants for medicinal, food, and other practical uses, or the statement, paresthesia means numbness, prickling, or a tingling, heightened sensitivity, does not hold. One may reasonably assume that if natives also make direct use of prairie plants for medicinal, food, and other practical uses, then earned income is wages and tips. There is good reason to believe that either lotteries are an easy way to lose money or total wages excludes wages paid by both direct reimbursable and Federal government employers. Provided that lotteries are an easy way to lose money, we know that the statement, earned income is wages and tips, does not hold. On the condition that total wages excludes wages paid by both direct reimbursable and Federal government employers, it is definitely the case that the statement, earned income is wages and tips, does not hold.
|
It is rational to agree that doped semiconductors have extra bands in the forbidden gap.
|
It is rational to agree that doped semiconductors have extra bands in the forbidden gap.
|
TRUE
|
Disjunctive Syllogism:
Either (If [1], then [2].) or [0].
Not (If [1], then [2].). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [3] or (Not (If [1], then [2].).).
Not [3]. [SC2-2]
Therefore, Not (If [1], then [2].)..
[SC2-2]
Disjunctive Syllogism:
Either [4] or (Not [3].).
Not [4]. [SC2-3]
Therefore, Not [3]..
[SC2-3]
Modus Tonens:
If [4], then [5].
Not [5]. [SC2-4]
Therefore, Not [4]..
[SC2-4]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Not [5].).
If [7], then (Not [5].).
Therefore, Not [5]..
|
{0: 'Doped semiconductors have extra bands in the forbidden gap.', 1: 'Cocaine stimulates the central nervous system causing restlessness, tremors, and convulsions.', 2: 'Some mold grows on walls.', 3: 'Paresthesia means numbness, prickling, or a tingling, heightened sensitivity.', 4: 'Natives also make direct use of prairie plants for medicinal, food, and other practical uses.', 5: 'Earned income is wages and tips.', 6: 'Lotteries are an easy way to lose money.', 7: 'Total wages excludes wages paid by both direct reimbursable and Federal government employers.'}
| 5 |
4,564 |
['On the condition that if depression represents the major cause of suicides, then slugs react the same way to beer or honey, it is definitely the case that nylon is synthetic fiber.', 'It is reasonable to believe that most people are engaged in sexual behavior.', "It is a fact that either stress is the body's reaction to an event that is experienced as disturbing or threatening or soil tests help farmers optimize their use of fertilizer and reduce the potential for runoff.", "Provided that stress is the body's reaction to an event that is experienced as disturbing or threatening, we know that either corals seem to absorb water more than other mushrooms or white mangrove tends to grow at slightly higher elevations than red and black mangrove.", 'Assuming soil tests help farmers optimize their use of fertilizer and reduce the potential for runoff, we know that either corals seem to absorb water more than other mushrooms or white mangrove tends to grow at slightly higher elevations than red and black mangrove.', 'We know that at least one of two things is true: if sugar can cause loss of tissue elasticity and function, then carmakers are automakers, or nuts are also higher in fiber and a good source of plant proteins.', 'On the condition that if sugar can cause loss of tissue elasticity and function, then carmakers are automakers, it is definitely the case that if most people are engaged in sexual behavior, then if either corals seem to absorb water more than other mushrooms or white mangrove tends to grow at slightly higher elevations than red and black mangrove, then if if depression represents the major cause of suicides, then slugs react the same way to beer or honey, then the claim that nylon is synthetic fiber does not reflect reality.', 'Once we know nuts are also higher in fiber and a good source of plant proteins, we also know that if most people are engaged in sexual behavior, then if either corals seem to absorb water more than other mushrooms or white mangrove tends to grow at slightly higher elevations than red and black mangrove, then if if depression represents the major cause of suicides, then slugs react the same way to beer or honey, then the claim that nylon is synthetic fiber does not reflect reality.']
|
On the condition that if depression represents the major cause of suicides, then slugs react the same way to beer or honey, it is definitely the case that nylon is synthetic fiber. It is reasonable to believe that most people are engaged in sexual behavior. It is a fact that either stress is the body's reaction to an event that is experienced as disturbing or threatening or soil tests help farmers optimize their use of fertilizer and reduce the potential for runoff. Provided that stress is the body's reaction to an event that is experienced as disturbing or threatening, we know that either corals seem to absorb water more than other mushrooms or white mangrove tends to grow at slightly higher elevations than red and black mangrove. Assuming soil tests help farmers optimize their use of fertilizer and reduce the potential for runoff, we know that either corals seem to absorb water more than other mushrooms or white mangrove tends to grow at slightly higher elevations than red and black mangrove. We know that at least one of two things is true: if sugar can cause loss of tissue elasticity and function, then carmakers are automakers, or nuts are also higher in fiber and a good source of plant proteins. On the condition that if sugar can cause loss of tissue elasticity and function, then carmakers are automakers, it is definitely the case that if most people are engaged in sexual behavior, then if either corals seem to absorb water more than other mushrooms or white mangrove tends to grow at slightly higher elevations than red and black mangrove, then if if depression represents the major cause of suicides, then slugs react the same way to beer or honey, then the claim that nylon is synthetic fiber does not reflect reality. Once we know nuts are also higher in fiber and a good source of plant proteins, we also know that if most people are engaged in sexual behavior, then if either corals seem to absorb water more than other mushrooms or white mangrove tends to grow at slightly higher elevations than red and black mangrove, then if if depression represents the major cause of suicides, then slugs react the same way to beer or honey, then the claim that nylon is synthetic fiber does not reflect reality.
|
Some people mistakenly believe that if depression represents the major cause of suicides, then slugs react the same way to beer or honey.
|
Some people mistakenly believe that if depression represents the major cause of suicides, then slugs react the same way to beer or honey.
|
TRUE
|
Reductio Ad Absurdum:
If (If [0], then [1].), then [2].
If (If [0], then [1].), then (Not [2].). [SC2-1]
Therefore, Not (If [0], then [1].)..
[SC2-1]
Modus Ponens:
If (Either [3] or [4].), then (If (If [0], then [1].), then (Not [2].).). [SC1-2]
Either [3] or [4]. [SC2-2]
Therefore, If (If [0], then [1].), then (Not [2].)..
[SC1-2]
Modus Ponens:
If [5], then (If (Either [3] or [4].), then (If (If [0], then [1].), then (Not [2].).).). [SC1-3]
[5]
Therefore, If (Either [3] or [4].), then (If (If [0], then [1].), then (Not [2].).)..
[SC1-3]
Disjunction Elimination:
Either (If [8], then [9].) or [10].
If (If [8], then [9].), then (If [5], then (If (Either [3] or [4].), then (If (If [0], then [1].), then (Not [2].).).).).
If [10], then (If [5], then (If (Either [3] or [4].), then (If (If [0], then [1].), then (Not [2].).).).).
Therefore, If [5], then (If (Either [3] or [4].), then (If (If [0], then [1].), then (Not [2].).).)..
[SC2-2]
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]..
|
{0: 'Depression represents the major cause of suicides.', 1: 'Slugs react the same way to beer or honey.', 2: 'Nylon is synthetic fiber.', 3: 'Corals seem to absorb water more than other mushrooms.', 4: 'White mangrove tends to grow at slightly higher elevations than red and black mangrove.', 5: 'Most people are engaged in sexual behavior.', 6: "Stress is the body's reaction to an event that is experienced as disturbing or threatening.", 7: 'Soil tests help farmers optimize their use of fertilizer and reduce the potential for runoff.', 8: 'Sugar can cause loss of tissue elasticity and function.', 9: 'Carmakers are automakers.', 10: 'Nuts are also higher in fiber and a good source of plant proteins.'}
| 5 |
4,401 |
['One may reasonably assume that if deer are native wildlife and are regulated by the Wildlife Code of Missouri, then if planes can crash, then either a hassock is a seat or cases attract attention.', 'One may reasonably assume that if consumerism is a cause, then if planes can crash, then either a hassock is a seat or cases attract attention.', 'One may reasonably assume that if a pussy is a fanny, then if planes can crash, then it is not true that either a hassock is a seat or cases attract attention.', 'It is rational to agree that a pussy is a fanny.', 'Given that if credit unions offer employee benefits such as payroll deduction and direct deposit, then rust dissolves into the water giving it a brownish color, it can be inferred that either deer are native wildlife and are regulated by the Wildlife Code of Missouri or consumerism is a cause.', 'When credit unions offer employee benefits such as payroll deduction and direct deposit is true, it follows that most oils work well when diffused.', 'One may reasonably assume that if most oils work well when diffused, then rust dissolves into the water giving it a brownish color.']
|
One may reasonably assume that if deer are native wildlife and are regulated by the Wildlife Code of Missouri, then if planes can crash, then either a hassock is a seat or cases attract attention. One may reasonably assume that if consumerism is a cause, then if planes can crash, then either a hassock is a seat or cases attract attention. One may reasonably assume that if a pussy is a fanny, then if planes can crash, then it is not true that either a hassock is a seat or cases attract attention. It is rational to agree that a pussy is a fanny. Given that if credit unions offer employee benefits such as payroll deduction and direct deposit, then rust dissolves into the water giving it a brownish color, it can be inferred that either deer are native wildlife and are regulated by the Wildlife Code of Missouri or consumerism is a cause. When credit unions offer employee benefits such as payroll deduction and direct deposit is true, it follows that most oils work well when diffused. One may reasonably assume that if most oils work well when diffused, then rust dissolves into the water giving it a brownish color.
|
It is a common misconception that planes can crash.
|
It is a common misconception that planes can crash.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then (Either [1] or [2].). [SC1-1]
If [0], then (Not (Either [1] or [2].).). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (If [0], then (Either [1] or [2].).).
If [4], then (If [0], then (Either [1] or [2].).).
Therefore, If [0], then (Either [1] or [2].)..
[SC1-2]
Modus Ponens:
If (If [6], then [7].), then (Either [3] or [4].).
If [6], then [7]. [SC2-3]
Therefore, Either [3] or [4]..
[SC2-3]
Hypothetical Syllogism:
If [6], then [8].
If [8], then [7].
Therefore, If [6], then [7]..
[SC2-1]
Modus Ponens:
If [5], then (If [0], then (Not (Either [1] or [2].).).).
[5]
Therefore, If [0], then (Not (Either [1] or [2].).)..
|
{0: 'Planes can crash.', 1: 'A hassock is a seat.', 2: 'Cases attract attention.', 3: 'Deer are native wildlife and are regulated by the Wildlife Code of Missouri.', 4: 'Consumerism is a cause.', 5: 'A pussy is a fanny.', 6: 'Credit unions offer employee benefits such as payroll deduction and direct deposit.', 7: 'Rust dissolves into the water giving it a brownish color.', 8: 'Most oils work well when diffused.'}
| 5 |
4,530 |
['It is rational to believe that either many species reproduce asexually, and for many others sex is optional or tin is very soft and malleable and is very sensitive to superficial dirt cutting.', 'When tin is very soft and malleable and is very sensitive to superficial dirt cutting is true, it follows that if psoriasis runs in families, then arterioles have thick smooth muscular walls.', "Whenever it is true that we know that the claim that psoriasis runs in families is false, 'muntjacs have (part) cytoplasm' is true.", 'Either one or both of these statements are true: cells function like miniature factories, constructing new molecules from raw materials, or integrity is active mainly in North America and Australia.', 'Provided that cells function like miniature factories, constructing new molecules from raw materials, we know that if many species reproduce asexually, and for many others sex is optional, then if psoriasis runs in families, then arterioles have thick smooth muscular walls.', 'When integrity is active mainly in North America and Australia is true, it follows that if many species reproduce asexually, and for many others sex is optional, then if psoriasis runs in families, then arterioles have thick smooth muscular walls.', 'When muntjacs have (part) cytoplasm is true, it follows that quills have properties.', "Should it be the case that muntjacs have (part) cytoplasm, it follows that the notion that 'quills have properties' is untrue."]
|
It is rational to believe that either many species reproduce asexually, and for many others sex is optional or tin is very soft and malleable and is very sensitive to superficial dirt cutting. When tin is very soft and malleable and is very sensitive to superficial dirt cutting is true, it follows that if psoriasis runs in families, then arterioles have thick smooth muscular walls. Whenever it is true that we know that the claim that psoriasis runs in families is false, 'muntjacs have (part) cytoplasm' is true. Either one or both of these statements are true: cells function like miniature factories, constructing new molecules from raw materials, or integrity is active mainly in North America and Australia. Provided that cells function like miniature factories, constructing new molecules from raw materials, we know that if many species reproduce asexually, and for many others sex is optional, then if psoriasis runs in families, then arterioles have thick smooth muscular walls. When integrity is active mainly in North America and Australia is true, it follows that if many species reproduce asexually, and for many others sex is optional, then if psoriasis runs in families, then arterioles have thick smooth muscular walls. When muntjacs have (part) cytoplasm is true, it follows that quills have properties. Should it be the case that muntjacs have (part) cytoplasm, it follows that the notion that 'quills have properties' is untrue.
|
We can assume that arterioles have thick smooth muscular walls.
|
Some people mistakenly believe that arterioles have thick smooth muscular walls.
|
FALSE
|
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].). [SC2-2]
If [4], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC2-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [3], then (If [1], then [0].).).
If [6], then (If [3], then (If [1], then [0].).).
Therefore, If [3], then (If [1], then [0].)..
[SC2-1]
Modus Tonens:
If (Not [1].), then [2].
Not [2]. [SC2-2]
Therefore, [1].
[SC2-2]
Reductio Ad Absurdum:
If [2], then [7].
If [2], then (Not [7].).
Therefore, Not [2]..
|
{0: 'Arterioles have thick smooth muscular walls.', 1: 'Psoriasis runs in families.', 2: 'Muntjacs have (part) cytoplasm.', 3: 'Many species reproduce asexually, and for many others sex is optional.', 4: 'Tin is very soft and malleable and is very sensitive to superficial dirt cutting.', 5: 'Cells function like miniature factories, constructing new molecules from raw materials.', 6: 'Integrity is active mainly in North America and Australia.', 7: 'Quills have properties.'}
| 5 |
4,656 |
['Either human resource specialists help employees or either absolute delay is the delay that occurs at some reference frequency or mitosis ensures that chromosomal DNA and protein are equally distributed to the offspring cells.', 'Either one or both of these statements are true: most malls also have roofs so people can shop inside, or a savings bond is a government bond.', "So long as a savings bond is a government bond, 'if human resource specialists help employees, then massage involves applying pressure to the soft tissues of the body, such as the muscles' is true.", 'Once we know we know that the claim that if either absolute delay is the delay that occurs at some reference frequency or mitosis ensures that chromosomal DNA and protein are equally distributed to the offspring cells, then massage involves applying pressure to the soft tissues of the body, such as the muscles is false, we also know that heat affects matter.', 'Either one or both of these statements are true: fluoroacetic acid is highly toxic to animal life, or valvular lesions heal completely or become progressively worse.', 'When fluoroacetic acid is highly toxic to animal life is true, it follows that if most malls also have roofs so people can shop inside, then if human resource specialists help employees, then massage involves applying pressure to the soft tissues of the body, such as the muscles.', 'Given that valvular lesions heal completely or become progressively worse, it can be inferred that if most malls also have roofs so people can shop inside, then if human resource specialists help employees, then massage involves applying pressure to the soft tissues of the body, such as the muscles.', 'Either weeds can grow in very dry conditions or media literacy is an essential part of exposing the consumerist goals underlying media content.', 'Provided that weeds can grow in very dry conditions, we know that if we know that the claim that if either absolute delay is the delay that occurs at some reference frequency or mitosis ensures that chromosomal DNA and protein are equally distributed to the offspring cells, then massage involves applying pressure to the soft tissues of the body, such as the muscles is false, then the statement that states heat affects matter is false.', 'Given that media literacy is an essential part of exposing the consumerist goals underlying media content, it can be inferred that if we know that the claim that if either absolute delay is the delay that occurs at some reference frequency or mitosis ensures that chromosomal DNA and protein are equally distributed to the offspring cells, then massage involves applying pressure to the soft tissues of the body, such as the muscles is false, then the statement that states heat affects matter is false.']
|
Either human resource specialists help employees or either absolute delay is the delay that occurs at some reference frequency or mitosis ensures that chromosomal DNA and protein are equally distributed to the offspring cells. Either one or both of these statements are true: most malls also have roofs so people can shop inside, or a savings bond is a government bond. So long as a savings bond is a government bond, 'if human resource specialists help employees, then massage involves applying pressure to the soft tissues of the body, such as the muscles' is true. Once we know we know that the claim that if either absolute delay is the delay that occurs at some reference frequency or mitosis ensures that chromosomal DNA and protein are equally distributed to the offspring cells, then massage involves applying pressure to the soft tissues of the body, such as the muscles is false, we also know that heat affects matter. Either one or both of these statements are true: fluoroacetic acid is highly toxic to animal life, or valvular lesions heal completely or become progressively worse. When fluoroacetic acid is highly toxic to animal life is true, it follows that if most malls also have roofs so people can shop inside, then if human resource specialists help employees, then massage involves applying pressure to the soft tissues of the body, such as the muscles. Given that valvular lesions heal completely or become progressively worse, it can be inferred that if most malls also have roofs so people can shop inside, then if human resource specialists help employees, then massage involves applying pressure to the soft tissues of the body, such as the muscles. Either weeds can grow in very dry conditions or media literacy is an essential part of exposing the consumerist goals underlying media content. Provided that weeds can grow in very dry conditions, we know that if we know that the claim that if either absolute delay is the delay that occurs at some reference frequency or mitosis ensures that chromosomal DNA and protein are equally distributed to the offspring cells, then massage involves applying pressure to the soft tissues of the body, such as the muscles is false, then the statement that states heat affects matter is false. Given that media literacy is an essential part of exposing the consumerist goals underlying media content, it can be inferred that if we know that the claim that if either absolute delay is the delay that occurs at some reference frequency or mitosis ensures that chromosomal DNA and protein are equally distributed to the offspring cells, then massage involves applying pressure to the soft tissues of the body, such as the muscles is false, then the statement that states heat affects matter is false.
|
It is rational to agree that massage involves applying pressure to the soft tissues of the body, such as the muscles.
|
The statement, massage involves applying pressure to the soft tissues of the body, such as the muscles, does not hold.
|
FALSE
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].).
If [1], then [0]. [SC2-1]
If (Either [2] or [3].), then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [1], then [0].). [SC2-2]
If [6], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC2-2]
Disjunction Elimination:
Either [9] or [10].
If [9], then (If [5], then (If [1], then [0].).).
If [10], then (If [5], then (If [1], then [0].).).
Therefore, If [5], then (If [1], then [0].)..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If (Either [2] or [3].), then [0].).), then [4].
If (Not (If (Either [2] or [3].), then [0].).), then (Not [4].). [SC2-2]
Therefore, If (Either [2] or [3].), then [0]..
[SC2-2]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If (Not (If (Either [2] or [3].), then [0].).), then (Not [4].).).
If [8], then (If (Not (If (Either [2] or [3].), then [0].).), then (Not [4].).).
Therefore, If (Not (If (Either [2] or [3].), then [0].).), then (Not [4].)..
|
{0: 'Massage involves applying pressure to the soft tissues of the body, such as the muscles.', 1: 'Human resource specialists help employees.', 2: 'Absolute delay is the delay that occurs at some reference frequency.', 3: 'Mitosis ensures that chromosomal DNA and protein are equally distributed to the offspring cells.', 4: 'Heat affects matter.', 5: 'Most malls also have roofs so people can shop inside.', 6: 'A savings bond is a government bond.', 7: 'Weeds can grow in very dry conditions.', 8: 'Media literacy is an essential part of exposing the consumerist goals underlying media content.', 9: 'Fluoroacetic acid is highly toxic to animal life.', 10: 'Valvular lesions heal completely or become progressively worse.'}
| 5 |
4,441 |
['It is a common misconception that chronic glaucoma is the most common form of the condition.', "Given that we know that the claim that if the statement 'human activities lead to effects' can be considered false, then chronic glaucoma is the most common form of the condition is false, it can be inferred that resistance becomes a problem when bacteria causing a disease withstand antibiotic therapy.", 'Either revolutions are usually political in their nature or if resistance becomes a problem when bacteria causing a disease withstand antibiotic therapy, then reward systems affect customer satisfaction.', 'The claim that revolutions are usually political in their nature does not reflect reality.', "So long as reward systems affect customer satisfaction, 'genesis teaches a point at which time began' is true.", "Whenever it is true that reward systems affect customer satisfaction, 'the claim that genesis teaches a point at which time began does not correspond with reality' is true."]
|
It is a common misconception that chronic glaucoma is the most common form of the condition. Given that we know that the claim that if the statement 'human activities lead to effects' can be considered false, then chronic glaucoma is the most common form of the condition is false, it can be inferred that resistance becomes a problem when bacteria causing a disease withstand antibiotic therapy. Either revolutions are usually political in their nature or if resistance becomes a problem when bacteria causing a disease withstand antibiotic therapy, then reward systems affect customer satisfaction. The claim that revolutions are usually political in their nature does not reflect reality. So long as reward systems affect customer satisfaction, 'genesis teaches a point at which time began' is true. Whenever it is true that reward systems affect customer satisfaction, 'the claim that genesis teaches a point at which time began does not correspond with reality' is true.
|
It is a simple truth that human activities lead to effects.
|
The statement that 'human activities lead to effects' is incorrect.
|
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]
Modus Tonens:
If [2], then [3]. [SC1-3]
Not [3]. [SC2-3]
Therefore, Not [2]..
[SC1-3]
Disjunctive Syllogism:
Either [5] or (If [2], then [3].).
Not [5].
Therefore, If [2], then [3]..
[SC2-3]
Reductio Ad Absurdum:
If [3], then [4].
If [3], then (Not [4].).
Therefore, Not [3]..
|
{0: 'Human activities lead to effects.', 1: 'Chronic glaucoma is the most common form of the condition.', 2: 'Resistance becomes a problem when bacteria causing a disease withstand antibiotic therapy.', 3: 'Reward systems affect customer satisfaction.', 4: 'Genesis teaches a point at which time began.', 5: 'Revolutions are usually political in their nature.'}
| 5 |
4,132 |
["So long as bags contain possessions, 'if the claim that bulbs consist of filament does not correspond with reality, then most air has air pressure' is true.", "The statement 'bags contain possessions' is true.", "Assuming cyclists are the ones who have the most to lose when running a stop sign or light, we know that the statement that 'most air has air pressure' is incorrect.", "Whenever it is true that frogs respond to stimuli, 'the statement that 'most air has air pressure' is incorrect' is true.", 'When decreased enrollment is a national trend due to the aging of the population is true, it follows that either cyclists are the ones who have the most to lose when running a stop sign or light or frogs respond to stimuli.', 'Given that if some tortoises live on islands, then abortion is a crime against an existing being, it can be inferred that either cyclists are the ones who have the most to lose when running a stop sign or light or frogs respond to stimuli.', "When the notion that 'either decreased enrollment is a national trend due to the aging of the population or if some tortoises live on islands, then abortion is a crime against an existing being' is untrue is true, it follows that either otters are mammals or soul food is food.", 'The claim that either otters are mammals or soul food is food does not reflect reality.']
|
So long as bags contain possessions, 'if the claim that bulbs consist of filament does not correspond with reality, then most air has air pressure' is true. The statement 'bags contain possessions' is true. Assuming cyclists are the ones who have the most to lose when running a stop sign or light, we know that the statement that 'most air has air pressure' is incorrect. Whenever it is true that frogs respond to stimuli, 'the statement that 'most air has air pressure' is incorrect' is true. When decreased enrollment is a national trend due to the aging of the population is true, it follows that either cyclists are the ones who have the most to lose when running a stop sign or light or frogs respond to stimuli. Given that if some tortoises live on islands, then abortion is a crime against an existing being, it can be inferred that either cyclists are the ones who have the most to lose when running a stop sign or light or frogs respond to stimuli. When the notion that 'either decreased enrollment is a national trend due to the aging of the population or if some tortoises live on islands, then abortion is a crime against an existing being' is untrue is true, it follows that either otters are mammals or soul food is food. The claim that either otters are mammals or soul food is food does not reflect reality.
|
bulbs consist of filament.
|
The notion that 'bulbs consist of filament' is untrue.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [4], then (If (Not [0].), then [1].).
[4]
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3]. [SC1-2]
If [2], then (Not [1].).
If [3], then (Not [1].).
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either [5] or (If [6], then [7].). [SC1-3]
If [5], then (Either [2] or [3].).
If (If [6], then [7].), then (Either [2] or [3].).
Therefore, Either [2] or [3]..
[SC1-3]
Modus Tonens:
If (Not (Either [5] or (If [6], then [7].).).), then (Either [8] or [9].).
Not (Either [8] or [9].).
Therefore, Either [5] or (If [6], then [7].)..
|
{0: 'Bulbs consist of filament.', 1: 'Most air has air pressure.', 2: 'Cyclists are the ones who have the most to lose when running a stop sign or light.', 3: 'Frogs respond to stimuli.', 4: 'Bags contain possessions.', 5: 'Decreased enrollment is a national trend due to the aging of the population.', 6: 'Some tortoises live on islands.', 7: 'Abortion is a crime against an existing being.', 8: 'Otters are mammals.', 9: 'Soul food is food.'}
| 5 |
4,233 |
["So long as it is not true that common cockleburs have hooks, 'biochemical analyses show excretion' is true.", 'When biochemical analyses show excretion is true, it follows that either eclipses can give a relationship a sense of purpose if one was lacking, or a reason for leaving or interest rates are, by definition, rates of return.', 'Once we know the claim that if biochemical analyses show excretion, then those that suggest either eclipses can give a relationship a sense of purpose if one was lacking, or a reason for leaving or interest rates are, by definition, rates of return are wrong is false, we also know that deciduous trees drop their leaves in the fall and grow new ones in the spring.', 'Those that suggest contain refine sugar includes white sugar are right.', 'Assuming the claim that if contain refine sugar includes white sugar, then if the claim that if biochemical analyses show excretion, then those that suggest either eclipses can give a relationship a sense of purpose if one was lacking, or a reason for leaving or interest rates are, by definition, rates of return are wrong is false, then the statement that states deciduous trees drop their leaves in the fall and grow new ones in the spring is false has no merit, we know that bubble wraps are located in post offices.', "So long as the claim that if contain refine sugar includes white sugar, then if the claim that if biochemical analyses show excretion, then those that suggest either eclipses can give a relationship a sense of purpose if one was lacking, or a reason for leaving or interest rates are, by definition, rates of return are wrong is false, then the statement that states deciduous trees drop their leaves in the fall and grow new ones in the spring is false has no merit, 'it is not the case that bubble wraps are located in post offices' is true."]
|
So long as it is not true that common cockleburs have hooks, 'biochemical analyses show excretion' is true. When biochemical analyses show excretion is true, it follows that either eclipses can give a relationship a sense of purpose if one was lacking, or a reason for leaving or interest rates are, by definition, rates of return. Once we know the claim that if biochemical analyses show excretion, then those that suggest either eclipses can give a relationship a sense of purpose if one was lacking, or a reason for leaving or interest rates are, by definition, rates of return are wrong is false, we also know that deciduous trees drop their leaves in the fall and grow new ones in the spring. Those that suggest contain refine sugar includes white sugar are right. Assuming the claim that if contain refine sugar includes white sugar, then if the claim that if biochemical analyses show excretion, then those that suggest either eclipses can give a relationship a sense of purpose if one was lacking, or a reason for leaving or interest rates are, by definition, rates of return are wrong is false, then the statement that states deciduous trees drop their leaves in the fall and grow new ones in the spring is false has no merit, we know that bubble wraps are located in post offices. So long as the claim that if contain refine sugar includes white sugar, then if the claim that if biochemical analyses show excretion, then those that suggest either eclipses can give a relationship a sense of purpose if one was lacking, or a reason for leaving or interest rates are, by definition, rates of return are wrong is false, then the statement that states deciduous trees drop their leaves in the fall and grow new ones in the spring is false has no merit, 'it is not the case that bubble wraps are located in post offices' is true.
|
Those that suggest common cockleburs have hooks are right.
|
Most common cockleburs have hooks.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If [1], then (Either [2] or [3].).
If [1], then (Not (Either [2] or [3].).). [SC2-2]
Therefore, Not [1]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [1], then (Not (Either [2] or [3].).).).), then [4].
If (Not (If [1], then (Not (Either [2] or [3].).).).), then (Not [4].). [SC2-3]
Therefore, If [1], then (Not (Either [2] or [3].).)..
[SC2-3]
Modus Ponens:
If [5], then (If (Not (If [1], then (Not (Either [2] or [3].).).).), then (Not [4].).). [SC1-4]
[5]
Therefore, If (Not (If [1], then (Not (Either [2] or [3].).).).), then (Not [4].)..
[SC1-4]
Reductio Ad Absurdum:
If (Not (If [5], then (If (Not (If [1], then (Not (Either [2] or [3].).).).), then (Not [4].).).).), then [6].
If (Not (If [5], then (If (Not (If [1], then (Not (Either [2] or [3].).).).), then (Not [4].).).).), then (Not [6].).
Therefore, If [5], then (If (Not (If [1], then (Not (Either [2] or [3].).).).), then (Not [4].).)..
|
{0: 'Common cockleburs have hooks.', 1: 'Biochemical analyses show excretion.', 2: 'Eclipses can give a relationship a sense of purpose if one was lacking, or a reason for leaving.', 3: 'Interest rates are, by definition, rates of return.', 4: 'Deciduous trees drop their leaves in the fall and grow new ones in the spring.', 5: 'Contain refine sugar includes white sugar.', 6: 'Bubble wraps are located in post offices.'}
| 5 |
4,173 |
['Once we know cockroaches can live for about a week after they lose their head, we also know that train tickets are located in trains.', 'When cockroaches can live for about a week after they lose their head is true, it follows that the claim that train tickets are located in trains does not reflect reality.', "So long as most calendars contain indexes to persons, places and ships, 'if it is not the case that several states impose restrictions on the use of living wills, then british doctors prescribe bibliotherapy for the stressed-out and depressed' is true.", 'It is the case that most calendars contain indexes to persons, places and ships.', 'Assuming tenrecs have (part) sections, we know that if british doctors prescribe bibliotherapy for the stressed-out and depressed, then cockroaches can live for about a week after they lose their head.', "The statement 'tenrecs have (part) sections' is true."]
|
Once we know cockroaches can live for about a week after they lose their head, we also know that train tickets are located in trains. When cockroaches can live for about a week after they lose their head is true, it follows that the claim that train tickets are located in trains does not reflect reality. So long as most calendars contain indexes to persons, places and ships, 'if it is not the case that several states impose restrictions on the use of living wills, then british doctors prescribe bibliotherapy for the stressed-out and depressed' is true. It is the case that most calendars contain indexes to persons, places and ships. Assuming tenrecs have (part) sections, we know that if british doctors prescribe bibliotherapy for the stressed-out and depressed, then cockroaches can live for about a week after they lose their head. The statement 'tenrecs have (part) sections' is true.
|
The claim that several states impose restrictions on the use of living wills is true.
|
The claim that several states impose restrictions on the use of living wills is true.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [2]. [SC1-2]
If [2], then [1]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Ponens:
If [4], then (If (Not [0].), then [2].).
[4]
Therefore, If (Not [0].), then [2]..
[SC2-2]
Modus Ponens:
If [5], then (If [2], then [1].).
[5]
Therefore, If [2], then [1]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [3].
If [1], then (Not [3].).
Therefore, Not [1]..
|
{0: 'Several states impose restrictions on the use of living wills.', 1: 'Cockroaches can live for about a week after they lose their head.', 2: 'British doctors prescribe bibliotherapy for the stressed-out and depressed.', 3: 'Train tickets are located in trains.', 4: 'Most calendars contain indexes to persons, places and ships.', 5: 'Tenrecs have (part) sections.'}
| 5 |
4,428 |
['One may reasonably assume that if tapering provides a decrease in drag and increase in lift which is most effective at high speeds, then stomach acid is also important in producing ulcers.', 'The claim that women also have orgasms through vaginal stimulation does not correspond with reality.', 'At least one of two things is true: satellite imagery shows buoyant plumes respond, on the scale of hours, to changes in winds, or rods are specialized for vision in dim light and cones mediate vision in bright light.', 'Assuming satellite imagery shows buoyant plumes respond, on the scale of hours, to changes in winds, we know that it is a common misconception that skulls have features.', 'One may reasonably assume that if rods are specialized for vision in dim light and cones mediate vision in bright light, then it is a common misconception that skulls have features.', "So long as the claim that if the claim that if the notion that 'tapering provides a decrease in drag and increase in lift which is most effective at high speeds' is untrue, then skulls have features is false, then women also have orgasms through vaginal stimulation is false, 'renal carcinoma tend to develop in older animals' is true.", 'The claim that renal carcinoma tend to develop in older animals has no merit.']
|
One may reasonably assume that if tapering provides a decrease in drag and increase in lift which is most effective at high speeds, then stomach acid is also important in producing ulcers. The claim that women also have orgasms through vaginal stimulation does not correspond with reality. At least one of two things is true: satellite imagery shows buoyant plumes respond, on the scale of hours, to changes in winds, or rods are specialized for vision in dim light and cones mediate vision in bright light. Assuming satellite imagery shows buoyant plumes respond, on the scale of hours, to changes in winds, we know that it is a common misconception that skulls have features. One may reasonably assume that if rods are specialized for vision in dim light and cones mediate vision in bright light, then it is a common misconception that skulls have features. So long as the claim that if the claim that if the notion that 'tapering provides a decrease in drag and increase in lift which is most effective at high speeds' is untrue, then skulls have features is false, then women also have orgasms through vaginal stimulation is false, 'renal carcinoma tend to develop in older animals' is true. The claim that renal carcinoma tend to develop in older animals has no merit.
|
The statement 'stomach acid is also important in producing ulcers' is true.
|
Stomach acid contains acid.
|
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 [3]. [SC1-3]
Not [3].
Therefore, If (Not [1].), then [2]..
[SC1-3]
Modus Tonens:
If (Not (If (Not (If (Not [1].), then [2].).), then [3].).), then [6].
Not [6].
Therefore, If (Not (If (Not [1].), then [2].).), then [3]..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Not [2].).
If [5], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Stomach acid is also important in producing ulcers.', 1: 'Tapering provides a decrease in drag and increase in lift which is most effective at high speeds.', 2: 'Skulls have features.', 3: 'Women also have orgasms through vaginal stimulation.', 4: 'Satellite imagery shows buoyant plumes respond, on the scale of hours, to changes in winds.', 5: 'Rods are specialized for vision in dim light and cones mediate vision in bright light.', 6: 'Renal carcinoma tend to develop in older animals.'}
| 5 |
4,567 |
['Either one or both of these statements are true: either coots feed on small fish or aluminum bats are quite different than wooden ones, or the claim that streets are urban areas is false.', 'At least one of two things is true: bacteria reproduce asexually by fission in which the cell divides into two parts, or fibrocystic changes are a normal condition caused by growth of fibrous tissue and small cysts.', 'When bacteria reproduce asexually by fission in which the cell divides into two parts is true, it follows that moose have (part) sterna.', 'Provided that fibrocystic changes are a normal condition caused by growth of fibrous tissue and small cysts, we know that the statement, either coots feed on small fish or aluminum bats are quite different than wooden ones, does not hold.', 'It is not the case that suppers have (part) sandwiches.', 'We know that either some cave dwellers use fire or muscle mass is reduced as muscles atrophy with disuse.', 'Given that some cave dwellers use fire, it can be inferred that if moose have (part) sterna, then suppers have (part) sandwiches.', 'If muscle mass is reduced as muscles atrophy with disuse, then if moose have (part) sterna, then suppers have (part) sandwiches.']
|
Either one or both of these statements are true: either coots feed on small fish or aluminum bats are quite different than wooden ones, or the claim that streets are urban areas is false. At least one of two things is true: bacteria reproduce asexually by fission in which the cell divides into two parts, or fibrocystic changes are a normal condition caused by growth of fibrous tissue and small cysts. When bacteria reproduce asexually by fission in which the cell divides into two parts is true, it follows that moose have (part) sterna. Provided that fibrocystic changes are a normal condition caused by growth of fibrous tissue and small cysts, we know that the statement, either coots feed on small fish or aluminum bats are quite different than wooden ones, does not hold. It is not the case that suppers have (part) sandwiches. We know that either some cave dwellers use fire or muscle mass is reduced as muscles atrophy with disuse. Given that some cave dwellers use fire, it can be inferred that if moose have (part) sterna, then suppers have (part) sandwiches. If muscle mass is reduced as muscles atrophy with disuse, then if moose have (part) sterna, then suppers have (part) sandwiches.
|
The claim that streets are urban areas is false.
|
The claim that streets are urban areas is false.
|
TRUE
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or (Not [0].).
Not (Either [1] or [2].). [SC2-1]
Therefore, Not [0]..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (Not (Either [1] or [2].).). [SC1-2]
Not [3]. [SC2-2]
Therefore, Not (Either [1] or [2].)..
[SC1-2]
Constructive Dilemma:
Either [4] or [5].
If [4], then [3].
If [5], then (Not (Either [1] or [2].).).
Therefore, Either [3] or (Not (Either [1] or [2].).)..
[SC2-2]
Modus Tonens:
If [3], then [6]. [SC1-3]
Not [6].
Therefore, Not [3]..
[SC1-3]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If [3], then [6].).
If [8], then (If [3], then [6].).
Therefore, If [3], then [6]..
|
{0: 'Streets are urban areas.', 1: 'Coots feed on small fish.', 2: 'Aluminum bats are quite different than wooden ones.', 3: 'Moose have (part) sterna.', 4: 'Bacteria reproduce asexually by fission in which the cell divides into two parts.', 5: 'Fibrocystic changes are a normal condition caused by growth of fibrous tissue and small cysts.', 6: 'Suppers have (part) sandwiches.', 7: 'Some cave dwellers use fire.', 8: 'Muscle mass is reduced as muscles atrophy with disuse.'}
| 5 |
4,967 |
['Should it be the case that the claim that american robins defend territory does not correspond with reality, it follows that hens have brown eyes, cocks have white eyes.', "On the condition that the claim that if smoking is a way to lose weight for some kids, then if the claim that american robins defend territory does not correspond with reality, then the notion that 'hens have brown eyes, cocks have white eyes' is untrue does not correspond with reality, it is definitely the case that if spring brings new life as animals are born and eggs hatch, then goose barnacles are usually white shells with a wormlike neck.", 'If the claim that smoking is a way to lose weight for some kids does not correspond with reality, then brush fire is fire.', 'It is a common misconception that brush fire is fire.', "It is rational to believe that either hormone therapy is considered when the cancer has spread outside the prostate or if the claim that if smoking is a way to lose weight for some kids, then if the claim that american robins defend territory does not correspond with reality, then the notion that 'hens have brown eyes, cocks have white eyes' is untrue does not correspond with reality, then some people mistakenly believe that if spring brings new life as animals are born and eggs hatch, then goose barnacles are usually white shells with a wormlike neck.", 'Some people mistakenly believe that hormone therapy is considered when the cancer has spread outside the prostate.']
|
Should it be the case that the claim that american robins defend territory does not correspond with reality, it follows that hens have brown eyes, cocks have white eyes. On the condition that the claim that if smoking is a way to lose weight for some kids, then if the claim that american robins defend territory does not correspond with reality, then the notion that 'hens have brown eyes, cocks have white eyes' is untrue does not correspond with reality, it is definitely the case that if spring brings new life as animals are born and eggs hatch, then goose barnacles are usually white shells with a wormlike neck. If the claim that smoking is a way to lose weight for some kids does not correspond with reality, then brush fire is fire. It is a common misconception that brush fire is fire. It is rational to believe that either hormone therapy is considered when the cancer has spread outside the prostate or if the claim that if smoking is a way to lose weight for some kids, then if the claim that american robins defend territory does not correspond with reality, then the notion that 'hens have brown eyes, cocks have white eyes' is untrue does not correspond with reality, then some people mistakenly believe that if spring brings new life as animals are born and eggs hatch, then goose barnacles are usually white shells with a wormlike neck. Some people mistakenly believe that hormone therapy is considered when the cancer has spread outside the prostate.
|
The claim that american robins defend territory is true.
|
The claim that american robins defend territory is true.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [2], then (If (Not [0].), then (Not [1].).). [SC1-2]
[2] [SC2-2]
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then (If [3], then [4].).
If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then (Not (If [3], then [4].).). [SC2-3]
Therefore, If [2], then (If (Not [0].), then (Not [1].).)..
[SC2-3]
Disjunctive Syllogism:
Either [6] or (If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then (Not (If [3], then [4].).).).
Not [6].
Therefore, If (Not (If [2], then (If (Not [0].), then (Not [1].).).).), then (Not (If [3], then [4].).)..
[SC2-2]
Modus Tonens:
If (Not [2].), then [5].
Not [5].
Therefore, [2].
|
{0: 'American robins defend territory.', 1: 'Hens have brown eyes, cocks have white eyes.', 2: 'Smoking is a way to lose weight for some kids.', 3: 'Spring brings new life as animals are born and eggs hatch.', 4: 'Goose barnacles are usually white shells with a wormlike neck.', 5: 'Brush fire is fire.', 6: 'Hormone therapy is considered when the cancer has spread outside the prostate.'}
| 5 |
4,758 |
["Assuming vernal pools have vegetation which changes along with the shifting water levels, we know that reptiles have complex, shelled eggs similar to a bird's, which are laid on land.", 'It is rational to believe that either contraction is decrease or some surfaces produce light.', "Once we know contraction is decrease, we also know that if some parathyroid glands are behind thyroid glands, then if vernal pools have vegetation which changes along with the shifting water levels, then the claim that reptiles have complex, shelled eggs similar to a bird's, which are laid on land does not correspond with reality.", "Whenever it is true that some surfaces produce light, 'if some parathyroid glands are behind thyroid glands, then if vernal pools have vegetation which changes along with the shifting water levels, then the claim that reptiles have complex, shelled eggs similar to a bird's, which are laid on land does not correspond with reality' is true.", 'We know that the claim that male mandrills have teeth is false.', 'Provided that the statement that states if the claim that some parathyroid glands are behind thyroid glands is false, then male mandrills have teeth is false, we know that yeasts are fungi and related to mushrooms.', 'Should it be the case that the statement that states if the claim that some parathyroid glands are behind thyroid glands is false, then male mandrills have teeth is false, it follows that the claim that yeasts are fungi and related to mushrooms does not correspond with reality.']
|
Assuming vernal pools have vegetation which changes along with the shifting water levels, we know that reptiles have complex, shelled eggs similar to a bird's, which are laid on land. It is rational to believe that either contraction is decrease or some surfaces produce light. Once we know contraction is decrease, we also know that if some parathyroid glands are behind thyroid glands, then if vernal pools have vegetation which changes along with the shifting water levels, then the claim that reptiles have complex, shelled eggs similar to a bird's, which are laid on land does not correspond with reality. Whenever it is true that some surfaces produce light, 'if some parathyroid glands are behind thyroid glands, then if vernal pools have vegetation which changes along with the shifting water levels, then the claim that reptiles have complex, shelled eggs similar to a bird's, which are laid on land does not correspond with reality' is true. We know that the claim that male mandrills have teeth is false. Provided that the statement that states if the claim that some parathyroid glands are behind thyroid glands is false, then male mandrills have teeth is false, we know that yeasts are fungi and related to mushrooms. Should it be the case that the statement that states if the claim that some parathyroid glands are behind thyroid glands is false, then male mandrills have teeth is false, it follows that the claim that yeasts are fungi and related to mushrooms does not correspond with reality.
|
The notion that 'vernal pools have vegetation which changes along with the shifting water levels' is untrue.
|
The notion that 'vernal pools have vegetation which changes along with the shifting water levels' is untrue.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then [1].
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC2-1]
Modus Ponens:
If [2], then (If [0], then (Not [1].).). [SC1-2]
[2] [SC2-2]
Therefore, If [0], then (Not [1].)..
[SC1-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If [2], then (If [0], then (Not [1].).).).
If [4], then (If [2], then (If [0], then (Not [1].).).).
Therefore, If [2], then (If [0], then (Not [1].).)..
[SC2-2]
Modus Tonens:
If (Not [2].), then [5]. [SC1-3]
Not [5].
Therefore, [2].
[SC1-3]
Reductio Ad Absurdum:
If (Not (If (Not [2].), then [5].).), then [6].
If (Not (If (Not [2].), then [5].).), then (Not [6].).
Therefore, If (Not [2].), then [5]..
|
{0: 'Vernal pools have vegetation which changes along with the shifting water levels.', 1: "Reptiles have complex, shelled eggs similar to a bird's, which are laid on land.", 2: 'Some parathyroid glands are behind thyroid glands.', 3: 'Contraction is decrease.', 4: 'Some surfaces produce light.', 5: 'Male mandrills have teeth.', 6: 'Yeasts are fungi and related to mushrooms.'}
| 5 |
4,626 |
['The claim that planaria can only move again a solid surface like a stone, stick or leaf does not reflect reality.', "On the condition that those that suggest if the notion that 'cambrian rocks underlie Ohio but are nowhere exposed at the surface' is untrue, then planaria can only move again a solid surface like a stone, stick or leaf are wrong, it is definitely the case that blue skies are purple in dying hue.", 'Either some brands contain vitamins, herbs, and other compounds or either either dead organisms decay quickly in the hot, moist rain forest environment or lizards abound in ancient cultures and history or we know that the claim that blue skies are purple in dying hue is false.', "The statement that 'some brands contain vitamins, herbs, and other compounds' is incorrect.", 'Should it be the case that either dead organisms decay quickly in the hot, moist rain forest environment or lizards abound in ancient cultures and history, it follows that plastic has good elasticity and high plastic deformation ratio.', 'It is not true that plastic has good elasticity and high plastic deformation ratio.']
|
The claim that planaria can only move again a solid surface like a stone, stick or leaf does not reflect reality. On the condition that those that suggest if the notion that 'cambrian rocks underlie Ohio but are nowhere exposed at the surface' is untrue, then planaria can only move again a solid surface like a stone, stick or leaf are wrong, it is definitely the case that blue skies are purple in dying hue. Either some brands contain vitamins, herbs, and other compounds or either either dead organisms decay quickly in the hot, moist rain forest environment or lizards abound in ancient cultures and history or we know that the claim that blue skies are purple in dying hue is false. The statement that 'some brands contain vitamins, herbs, and other compounds' is incorrect. Should it be the case that either dead organisms decay quickly in the hot, moist rain forest environment or lizards abound in ancient cultures and history, it follows that plastic has good elasticity and high plastic deformation ratio. It is not true that plastic has good elasticity and high plastic deformation ratio.
|
The statement 'cambrian rocks underlie Ohio but are nowhere exposed at the surface' can be considered true.
|
Cambrian rocks contain the first abundant record of shelly fossils.
|
Uncertain
|
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 (Either [3] or [4].) or (Not [2].). [SC1-3]
Not (Either [3] or [4].). [SC2-3]
Therefore, Not [2]..
[SC1-3]
Disjunctive Syllogism:
Either [6] or (Either (Either [3] or [4].) or (Not [2].).).
Not [6].
Therefore, Either (Either [3] or [4].) or (Not [2].)..
[SC2-3]
Modus Tonens:
If (Either [3] or [4].), then [5].
Not [5].
Therefore, Not (Either [3] or [4].)..
|
{0: 'Cambrian rocks underlie Ohio but are nowhere exposed at the surface.', 1: 'Planaria can only move again a solid surface like a stone, stick or leaf.', 2: 'Blue skies are purple in dying hue.', 3: 'Dead organisms decay quickly in the hot, moist rain forest environment.', 4: 'Lizards abound in ancient cultures and history.', 5: 'Plastic has good elasticity and high plastic deformation ratio.', 6: 'Some brands contain vitamins, herbs, and other compounds.'}
| 5 |
4,096 |
['At least one of two things is true: applications require resistant materials, or either primary bronchi enter lungs or some seeds attract ants.', 'On the condition that applications require resistant materials, it is definitely the case that either odors also leave a lasting scent-sation or monkeys feed on fruit.', 'If either primary bronchi enter lungs or some seeds attract ants, then either odors also leave a lasting scent-sation or monkeys feed on fruit.', 'When sprites are barely visible to the naked eye is true, it follows that the claim that odors also leave a lasting scent-sation does not reflect reality.', 'It is a fact that either either brazil nut trees reach height or human faces are asymmetrical, and usually the facial muscles on one side convey more tension or sprites are barely visible to the naked eye.', 'We know that at least one of two things is true: most nerves regulate activities, or a collective farm is a collective.', 'Assuming most nerves regulate activities, we know that the claim that either brazil nut trees reach height or human faces are asymmetrical, and usually the facial muscles on one side convey more tension has no merit.', 'If a collective farm is a collective, then the claim that either brazil nut trees reach height or human faces are asymmetrical, and usually the facial muscles on one side convey more tension has no merit.']
|
At least one of two things is true: applications require resistant materials, or either primary bronchi enter lungs or some seeds attract ants. On the condition that applications require resistant materials, it is definitely the case that either odors also leave a lasting scent-sation or monkeys feed on fruit. If either primary bronchi enter lungs or some seeds attract ants, then either odors also leave a lasting scent-sation or monkeys feed on fruit. When sprites are barely visible to the naked eye is true, it follows that the claim that odors also leave a lasting scent-sation does not reflect reality. It is a fact that either either brazil nut trees reach height or human faces are asymmetrical, and usually the facial muscles on one side convey more tension or sprites are barely visible to the naked eye. We know that at least one of two things is true: most nerves regulate activities, or a collective farm is a collective. Assuming most nerves regulate activities, we know that the claim that either brazil nut trees reach height or human faces are asymmetrical, and usually the facial muscles on one side convey more tension has no merit. If a collective farm is a collective, then the claim that either brazil nut trees reach height or human faces are asymmetrical, and usually the facial muscles on one side convey more tension has no merit.
|
Many people rightly believe that monkeys feed on fruit.
|
It is not the case that monkeys feed on fruit.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or (Either [4] or [5].).
If [3], then (Either [1] or [0].).
If (Either [4] or [5].), then (Either [1] or [0].).
Therefore, Either [1] or [0]..
[SC2-1]
Modus Ponens:
If [2], then (Not [1].).
[2] [SC2-2]
Therefore, Not [1]..
[SC2-2]
Disjunctive Syllogism:
Either (Either [6] or [7].) or [2].
Not (Either [6] or [7].). [SC2-3]
Therefore, [2].
[SC2-3]
Disjunction Elimination:
Either [8] or [9].
If [8], then (Not (Either [6] or [7].).).
If [9], then (Not (Either [6] or [7].).).
Therefore, Not (Either [6] or [7].)..
|
{0: 'Monkeys feed on fruit.', 1: 'Odors also leave a lasting scent-sation.', 2: 'Sprites are barely visible to the naked eye.', 3: 'Applications require resistant materials.', 4: 'Primary bronchi enter lungs.', 5: 'Some seeds attract ants.', 6: 'Brazil nut trees reach height.', 7: 'Human faces are asymmetrical, and usually the facial muscles on one side convey more tension.', 8: 'Most nerves regulate activities.', 9: 'A collective farm is a collective.'}
| 5 |
4,781 |
['Given that excess water vapor forms clouds, it can be inferred that it is not true that ceilings are capable of sags.', 'It is not true that irradiated meat is also highly susceptible to cross-contamination with food poisoning bacteria.', 'Provided that measurements are the raw data gathered from comparing an entity to a standard, we know that if horizons is a place for kids who have grown up, who want to be treated as adults, then either irradiated meat is also highly susceptible to cross-contamination with food poisoning bacteria or if excess water vapor forms clouds, then ceilings are capable of sags.', 'It is true that measurements are the raw data gathered from comparing an entity to a standard.', 'Once we know most hydras have legends, we also know that horizons is a place for kids who have grown up, who want to be treated as adults.', 'We can assume that most hydras have legends.']
|
Given that excess water vapor forms clouds, it can be inferred that it is not true that ceilings are capable of sags. It is not true that irradiated meat is also highly susceptible to cross-contamination with food poisoning bacteria. Provided that measurements are the raw data gathered from comparing an entity to a standard, we know that if horizons is a place for kids who have grown up, who want to be treated as adults, then either irradiated meat is also highly susceptible to cross-contamination with food poisoning bacteria or if excess water vapor forms clouds, then ceilings are capable of sags. It is true that measurements are the raw data gathered from comparing an entity to a standard. Once we know most hydras have legends, we also know that horizons is a place for kids who have grown up, who want to be treated as adults. We can assume that most hydras have legends.
|
The claim that excess water vapor forms clouds does not correspond with reality.
|
The claim that excess water vapor forms clouds does not correspond with reality.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].).
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [0], then [1].). [SC1-2]
Not [2].
Therefore, If [0], then [1]..
[SC1-2]
Modus Ponens:
If [3], then (Either [2] or (If [0], then [1].).). [SC1-3]
[3] [SC2-3]
Therefore, Either [2] or (If [0], then [1].)..
[SC1-3]
Modus Ponens:
If [4], then (If [3], then (Either [2] or (If [0], then [1].).).).
[4]
Therefore, If [3], then (Either [2] or (If [0], then [1].).)..
[SC2-3]
Modus Ponens:
If [5], then [3].
[5]
Therefore, [3].
|
{0: 'Excess water vapor forms clouds.', 1: 'Ceilings are capable of sags.', 2: 'Irradiated meat is also highly susceptible to cross-contamination with food poisoning bacteria.', 3: 'Horizons is a place for kids who have grown up, who want to be treated as adults.', 4: 'Measurements are the raw data gathered from comparing an entity to a standard.', 5: 'Most hydras have legends.'}
| 5 |
4,499 |
['Assuming some particles accumulate in nuclei, we know that if detectors detect effects, then cyclic twins are caused by repeated twinning around a rotation axis.', 'Those that suggest some particles accumulate in nuclei are right.', 'Once we know detectors detect effects, we also know that some animals leave homes.', 'On the condition that search engines are supposedly neutral ways of finding information on the Web, it is definitely the case that if some animals leave homes, then we know that the claim that cyclic twins are caused by repeated twinning around a rotation axis is false.', "So long as either fluid mechanics is the study of the forces and motions of liquids and gases or education is the basic right of all children, 'search engines are supposedly neutral ways of finding information on the Web' is true.", 'We know that at least one of two things is true: fluid mechanics is the study of the forces and motions of liquids and gases, or education is the basic right of all children.']
|
Assuming some particles accumulate in nuclei, we know that if detectors detect effects, then cyclic twins are caused by repeated twinning around a rotation axis. Those that suggest some particles accumulate in nuclei are right. Once we know detectors detect effects, we also know that some animals leave homes. On the condition that search engines are supposedly neutral ways of finding information on the Web, it is definitely the case that if some animals leave homes, then we know that the claim that cyclic twins are caused by repeated twinning around a rotation axis is false. So long as either fluid mechanics is the study of the forces and motions of liquids and gases or education is the basic right of all children, 'search engines are supposedly neutral ways of finding information on the Web' is true. We know that at least one of two things is true: fluid mechanics is the study of the forces and motions of liquids and gases, or education is the basic right of all children.
|
It is not the case that detectors detect effects.
|
It is not the case that detectors measure carbon-monoxide concentrations and exposure time.
|
Uncertain
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [2], then (If [0], then [1].).
[2]
Therefore, If [0], then [1]..
[SC2-1]
Hypothetical Syllogism:
If [0], then [3].
If [3], then (Not [1].). [SC2-2]
Therefore, If [0], then (Not [1].)..
[SC2-2]
Modus Ponens:
If [4], then (If [3], then (Not [1].).).
[4] [SC2-3]
Therefore, If [3], then (Not [1].)..
[SC2-3]
Modus Ponens:
If (Either [5] or [6].), then [4].
Either [5] or [6].
Therefore, [4].
|
{0: 'Detectors detect effects.', 1: 'Cyclic twins are caused by repeated twinning around a rotation axis.', 2: 'Some particles accumulate in nuclei.', 3: 'Some animals leave homes.', 4: 'Search engines are supposedly neutral ways of finding information on the Web.', 5: 'Fluid mechanics is the study of the forces and motions of liquids and gases.', 6: 'Education is the basic right of all children.'}
| 5 |
4,074 |
['The statement, features relate to body compositions, does not hold.', 'When detergents can pose a problem, however, especially if they contain bleach is true, it follows that schisms are ruptures.', 'The claim that detergents can pose a problem, however, especially if they contain bleach is true.', 'Either thieves often take advantage of darkness to steal everything from water skis to boats and motors or if tinctures are a useful form of herbal medicines, then many monarchs use the red sweet clover during their stay.', "So long as if tinctures are a useful form of herbal medicines, then many monarchs use the red sweet clover during their stay, 'either features relate to body compositions or if schisms are ruptures, then emotional abuse can also coincide with a child's developmental stages and challenges' is true.", "Assuming it is a common misconception that if thieves often take advantage of darkness to steal everything from water skis to boats and motors, then either features relate to body compositions or if schisms are ruptures, then emotional abuse can also coincide with a child's developmental stages and challenges, we know that sarcoidosis is a multisystem granulomatous disorder.", "The statement that 'sarcoidosis is a multisystem granulomatous disorder' is incorrect."]
|
The statement, features relate to body compositions, does not hold. When detergents can pose a problem, however, especially if they contain bleach is true, it follows that schisms are ruptures. The claim that detergents can pose a problem, however, especially if they contain bleach is true. Either thieves often take advantage of darkness to steal everything from water skis to boats and motors or if tinctures are a useful form of herbal medicines, then many monarchs use the red sweet clover during their stay. So long as if tinctures are a useful form of herbal medicines, then many monarchs use the red sweet clover during their stay, 'either features relate to body compositions or if schisms are ruptures, then emotional abuse can also coincide with a child's developmental stages and challenges' is true. Assuming it is a common misconception that if thieves often take advantage of darkness to steal everything from water skis to boats and motors, then either features relate to body compositions or if schisms are ruptures, then emotional abuse can also coincide with a child's developmental stages and challenges, we know that sarcoidosis is a multisystem granulomatous disorder. The statement that 'sarcoidosis is a multisystem granulomatous disorder' is incorrect.
|
The statement 'emotional abuse can also coincide with a child's developmental stages and challenges' is true.
|
Emotional abuse IS abuse.
|
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].). [SC1-2]
Not [3].
Therefore, If [1], then [0]..
[SC1-2]
Disjunction Elimination:
Either [4] or (If [5], then [6].).
If [4], then (Either [3] or (If [1], then [0].).). [SC2-3]
If (If [5], then [6].), then (Either [3] or (If [1], then [0].).).
Therefore, Either [3] or (If [1], then [0].)..
[SC2-3]
Modus Tonens:
If (Not (If [4], then (Either [3] or (If [1], then [0].).).).), then [7].
Not [7].
Therefore, If [4], then (Either [3] or (If [1], then [0].).)..
[SC2-1]
Modus Ponens:
If [2], then [1].
[2]
Therefore, [1].
|
{0: "Emotional abuse can also coincide with a child's developmental stages and challenges.", 1: 'Schisms are ruptures.', 2: 'Detergents can pose a problem, however, especially if they contain bleach.', 3: 'Features relate to body compositions.', 4: 'Thieves often take advantage of darkness to steal everything from water skis to boats and motors.', 5: 'Tinctures are a useful form of herbal medicines.', 6: 'Many monarchs use the red sweet clover during their stay.', 7: 'Sarcoidosis is a multisystem granulomatous disorder.'}
| 5 |
4,089 |
['Either one or both of these statements are true: blacks spend five times as much as whites, or technology can prevent or reduce the adverse effects of terrorist acts.', 'We know that at least one of two things is true: prostitution is the oldest profession, or either if malleability is physical properties, then most soils have concentrations of calcium or tigers are endangered species.', 'We know that the claim that prostitution is the oldest profession is false.', 'Provided that if malleability is physical properties, then most soils have concentrations of calcium, we know that some nutrients lead to deficiencies.', 'Should it be the case that some nutrients lead to deficiencies, it follows that some people mistakenly believe that blacks spend five times as much as whites.', 'If some people experience hypoglycaemic symptoms just before a main meal, then if tigers are endangered species, then some people mistakenly believe that blacks spend five times as much as whites.', 'some people experience hypoglycaemic symptoms just before a main meal.']
|
Either one or both of these statements are true: blacks spend five times as much as whites, or technology can prevent or reduce the adverse effects of terrorist acts. We know that at least one of two things is true: prostitution is the oldest profession, or either if malleability is physical properties, then most soils have concentrations of calcium or tigers are endangered species. We know that the claim that prostitution is the oldest profession is false. Provided that if malleability is physical properties, then most soils have concentrations of calcium, we know that some nutrients lead to deficiencies. Should it be the case that some nutrients lead to deficiencies, it follows that some people mistakenly believe that blacks spend five times as much as whites. If some people experience hypoglycaemic symptoms just before a main meal, then if tigers are endangered species, then some people mistakenly believe that blacks spend five times as much as whites. some people experience hypoglycaemic symptoms just before a main meal.
|
It is true that technology can prevent or reduce the adverse effects of terrorist acts.
|
We know that the claim that technology can prevent or reduce the adverse effects of terrorist acts is false.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either (If [2], then [3].) or [4]. [SC1-2]
If (If [2], then [3].), then (Not [1].). [SC2-2]
If [4], then (Not [1].). [SC3-2]
Therefore, Not [1]..
[SC1-2]
Disjunctive Syllogism:
Either [5] or (Either (If [2], then [3].) or [4].).
Not [5].
Therefore, Either (If [2], then [3].) or [4]..
[SC2-2]
Hypothetical Syllogism:
If (If [2], then [3].), then [7].
If [7], then (Not [1].).
Therefore, If (If [2], then [3].), then (Not [1].)..
[SC3-2]
Modus Ponens:
If [6], then (If [4], then (Not [1].).).
[6]
Therefore, If [4], then (Not [1].)..
|
{0: 'Technology can prevent or reduce the adverse effects of terrorist acts.', 1: 'Blacks spend five times as much as whites.', 2: 'Malleability is physical properties.', 3: 'Most soils have concentrations of calcium.', 4: 'Tigers are endangered species.', 5: 'Prostitution is the oldest profession.', 6: 'Some people experience hypoglycaemic symptoms just before a main meal.', 7: 'Some nutrients lead to deficiencies.'}
| 5 |
4,609 |
['Either one or both of these statements are true: natality refers to number of young individuals born or hatched per unit of time, or depression is a common problem in chronic pain patients.', 'The claim that ftp servers are servers does not reflect reality.', 'Provided that either parthenogenesis also occurs in some lizards or food irradiation exposes food to high levels of radiant energy to kill dangerous microorganisms, we know that ftp servers are servers.', 'It is a fact that either some marmosets occupy forest patches or either either parthenogenesis also occurs in some lizards or food irradiation exposes food to high levels of radiant energy to kill dangerous microorganisms or aflatoxins are highly toxic to livestock, poultry and people.', 'It is not true that some marmosets occupy forest patches.', "If the notion that 'if aflatoxins are highly toxic to livestock, poultry and people, then the statement 'natality refers to number of young individuals born or hatched per unit of time' can be considered false' is untrue, then either safe storage requires levels or cannabis is more popularly known as marijuana.", "The statement that 'either safe storage requires levels or cannabis is more popularly known as marijuana' is incorrect."]
|
Either one or both of these statements are true: natality refers to number of young individuals born or hatched per unit of time, or depression is a common problem in chronic pain patients. The claim that ftp servers are servers does not reflect reality. Provided that either parthenogenesis also occurs in some lizards or food irradiation exposes food to high levels of radiant energy to kill dangerous microorganisms, we know that ftp servers are servers. It is a fact that either some marmosets occupy forest patches or either either parthenogenesis also occurs in some lizards or food irradiation exposes food to high levels of radiant energy to kill dangerous microorganisms or aflatoxins are highly toxic to livestock, poultry and people. It is not true that some marmosets occupy forest patches. If the notion that 'if aflatoxins are highly toxic to livestock, poultry and people, then the statement 'natality refers to number of young individuals born or hatched per unit of time' can be considered false' is untrue, then either safe storage requires levels or cannabis is more popularly known as marijuana. The statement that 'either safe storage requires levels or cannabis is more popularly known as marijuana' is incorrect.
|
It is fair to say that depression is a common problem in chronic pain patients.
|
The claim that depression is a common problem in chronic pain patients does not reflect reality.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].). [SC1-2]
Not [2].
Therefore, Not [1]..
[SC1-2]
Constructive Dilemma:
Either (Either [3] or [4].) or [5]. [SC1-3]
If (Either [3] or [4].), then [2].
If [5], then (Not [1].). [SC3-3]
Therefore, Either [2] or (Not [1].)..
[SC1-3]
Disjunctive Syllogism:
Either [8] or (Either (Either [3] or [4].) or [5].).
Not [8].
Therefore, Either (Either [3] or [4].) or [5]..
[SC3-3]
Modus Tonens:
If (Not (If [5], then (Not [1].).).), then (Either [6] or [7].).
Not (Either [6] or [7].).
Therefore, If [5], then (Not [1].)..
|
{0: 'Depression is a common problem in chronic pain patients.', 1: 'Natality refers to number of young individuals born or hatched per unit of time.', 2: 'Ftp servers are servers.', 3: 'Parthenogenesis also occurs in some lizards.', 4: 'Food irradiation exposes food to high levels of radiant energy to kill dangerous microorganisms.', 5: 'Aflatoxins are highly toxic to livestock, poultry and people.', 6: 'Safe storage requires levels.', 7: 'Cannabis is more popularly known as marijuana.', 8: 'Some marmosets occupy forest patches.'}
| 5 |
4,000 |
['The claim that skates are fish does not reflect reality.', 'Should it be the case that cankerworms eat tree and shrub foliage, it follows that if either hmong girls wear traditional costumes on holidays or physicians can reduce the incidence of domestic violence, then radio controlled planes can, and have, killed people.', "The statement 'cankerworms eat tree and shrub foliage' can be considered true.", 'Should it be the case that herbs continue to make inroads in health care, it follows that if radio controlled planes can, and have, killed people, then skates are fish.', "Whenever it is true that strict hygiene is especially important for children, 'if radio controlled planes can, and have, killed people, then skates are fish' is true.", 'On the condition that the statement that states either herbs continue to make inroads in health care or strict hygiene is especially important for children is false, it is definitely the case that urinals are toilets.', 'Once we know the statement that states either herbs continue to make inroads in health care or strict hygiene is especially important for children is false, we also know that some people mistakenly believe that urinals are toilets.']
|
The claim that skates are fish does not reflect reality. Should it be the case that cankerworms eat tree and shrub foliage, it follows that if either hmong girls wear traditional costumes on holidays or physicians can reduce the incidence of domestic violence, then radio controlled planes can, and have, killed people. The statement 'cankerworms eat tree and shrub foliage' can be considered true. Should it be the case that herbs continue to make inroads in health care, it follows that if radio controlled planes can, and have, killed people, then skates are fish. Whenever it is true that strict hygiene is especially important for children, 'if radio controlled planes can, and have, killed people, then skates are fish' is true. On the condition that the statement that states either herbs continue to make inroads in health care or strict hygiene is especially important for children is false, it is definitely the case that urinals are toilets. Once we know the statement that states either herbs continue to make inroads in health care or strict hygiene is especially important for children is false, we also know that some people mistakenly believe that urinals are toilets.
|
It is not the case that either hmong girls wear traditional costumes on holidays or physicians can reduce the incidence of domestic violence.
|
It is not the case that either hmong girls wear traditional costumes on holidays or physicians can reduce the incidence of domestic violence.
|
TRUE
|
Modus Tonens:
If (Either [0] or [1].), then [2]. [SC1-1]
Not [2].
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Hypothetical Syllogism:
If (Either [0] or [1].), then [3]. [SC1-2]
If [3], then [2]. [SC2-2]
Therefore, If (Either [0] or [1].), then [2]..
[SC1-2]
Modus Ponens:
If [4], then (If (Either [0] or [1].), then [3].).
[4]
Therefore, If (Either [0] or [1].), then [3]..
[SC2-2]
Disjunction Elimination:
Either [5] or [6]. [SC1-3]
If [5], then (If [3], then [2].).
If [6], then (If [3], then [2].).
Therefore, If [3], then [2]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (Either [5] or [6].).), then [7].
If (Not (Either [5] or [6].).), then (Not [7].).
Therefore, Either [5] or [6]..
|
{0: 'Hmong girls wear traditional costumes on holidays.', 1: 'Physicians can reduce the incidence of domestic violence.', 2: 'Skates are fish.', 3: 'Radio controlled planes can, and have, killed people.', 4: 'Cankerworms eat tree and shrub foliage.', 5: 'Herbs continue to make inroads in health care.', 6: 'Strict hygiene is especially important for children.', 7: 'Urinals are toilets.'}
| 5 |
4,392 |
['There is good reason to believe that either basting is important to the effectiveness of slow cooking lean meats or many religions have the objective to recruit and dilute other belief systems other than their own.', 'Either colonic irrigation is irrigation or a coho is salmon.', "When a coho is salmon is true, it follows that the statement 'basting is important to the effectiveness of slow cooking lean meats' can be considered false.", 'Assuming ownership is the beginning of the steps to freedom, we know that historians describe history.', 'Should it be the case that ownership is the beginning of the steps to freedom, it follows that it is a common misconception that historians describe history.', 'If the claim that if colonic irrigation is irrigation, then ownership is the beginning of the steps to freedom is false, then balance is basic to walking properly with crutches.', 'Given that the claim that if colonic irrigation is irrigation, then ownership is the beginning of the steps to freedom is false, it can be inferred that the claim that balance is basic to walking properly with crutches does not reflect reality.']
|
There is good reason to believe that either basting is important to the effectiveness of slow cooking lean meats or many religions have the objective to recruit and dilute other belief systems other than their own. Either colonic irrigation is irrigation or a coho is salmon. When a coho is salmon is true, it follows that the statement 'basting is important to the effectiveness of slow cooking lean meats' can be considered false. Assuming ownership is the beginning of the steps to freedom, we know that historians describe history. Should it be the case that ownership is the beginning of the steps to freedom, it follows that it is a common misconception that historians describe history. If the claim that if colonic irrigation is irrigation, then ownership is the beginning of the steps to freedom is false, then balance is basic to walking properly with crutches. Given that the claim that if colonic irrigation is irrigation, then ownership is the beginning of the steps to freedom is false, it can be inferred that the claim that balance is basic to walking properly with crutches does not reflect reality.
|
The idea that many religions have the objective to recruit and dilute other belief systems other than their own is true.
|
Most religions have a cosmogeny either explicitly or implicitly.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].). [SC1-2]
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC1-2]
Constructive Dilemma:
Either [3] or [4].
If [3], then [2]. [SC2-3]
If [4], then (Not [1].).
Therefore, Either [2] or (Not [1].)..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If [3], then [2].).), then [6].
If (Not (If [3], then [2].).), then (Not [6].).
Therefore, If [3], then [2]..
[SC2-2]
Reductio Ad Absurdum:
If [2], then [5].
If [2], then (Not [5].).
Therefore, Not [2]..
|
{0: 'Many religions have the objective to recruit and dilute other belief systems other than their own.', 1: 'Basting is important to the effectiveness of slow cooking lean meats.', 2: 'Ownership is the beginning of the steps to freedom.', 3: 'Colonic irrigation is irrigation.', 4: 'A coho is salmon.', 5: 'Historians describe history.', 6: 'Balance is basic to walking properly with crutches.'}
| 5 |
4,476 |
['We know that at least one of two things is true: puffins have (part) chests, or either phytoplankton are microscopic plants that live in the water like diatoms small, single-celled algae or keepers have (part) human bodies.', 'On the condition that some floods occur seasonally when winter snows melt and combine with spring rains, it is definitely the case that if puffins have (part) chests, then spatter cones are formed if gases and lava sputter out of a crack in the side of a cone.', 'On the condition that the claim that if either phytoplankton are microscopic plants that live in the water like diatoms small, single-celled algae or keepers have (part) human bodies, then spatter cones are formed if gases and lava sputter out of a crack in the side of a cone does not correspond with reality, it is definitely the case that some veins carry carbon dioxide.', 'We know that either most infants consume food or some floods occur seasonally when winter snows melt and combine with spring rains.', 'It is not the case that most infants consume food.', 'On the condition that it is not the case that if the claim that if either phytoplankton are microscopic plants that live in the water like diatoms small, single-celled algae or keepers have (part) human bodies, then spatter cones are formed if gases and lava sputter out of a crack in the side of a cone does not correspond with reality, then the claim that some veins carry carbon dioxide is false, it is definitely the case that surface temperatures are important in making sure there are no condensation problems.', 'Some people mistakenly believe that surface temperatures are important in making sure there are no condensation problems.']
|
We know that at least one of two things is true: puffins have (part) chests, or either phytoplankton are microscopic plants that live in the water like diatoms small, single-celled algae or keepers have (part) human bodies. On the condition that some floods occur seasonally when winter snows melt and combine with spring rains, it is definitely the case that if puffins have (part) chests, then spatter cones are formed if gases and lava sputter out of a crack in the side of a cone. On the condition that the claim that if either phytoplankton are microscopic plants that live in the water like diatoms small, single-celled algae or keepers have (part) human bodies, then spatter cones are formed if gases and lava sputter out of a crack in the side of a cone does not correspond with reality, it is definitely the case that some veins carry carbon dioxide. We know that either most infants consume food or some floods occur seasonally when winter snows melt and combine with spring rains. It is not the case that most infants consume food. On the condition that it is not the case that if the claim that if either phytoplankton are microscopic plants that live in the water like diatoms small, single-celled algae or keepers have (part) human bodies, then spatter cones are formed if gases and lava sputter out of a crack in the side of a cone does not correspond with reality, then the claim that some veins carry carbon dioxide is false, it is definitely the case that surface temperatures are important in making sure there are no condensation problems. Some people mistakenly believe that surface temperatures are important in making sure there are no condensation problems.
|
The statement 'spatter cones are formed if gases and lava sputter out of a crack in the side of a cone' is true.
|
Spatter cones are steep sided, conical hills built from the spatter of lava fountains.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].).
If [1], then [0]. [SC2-1]
If (Either [2] or [3].), then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [4], then (If [1], then [0].).
[4] [SC2-2]
Therefore, If [1], then [0]..
[SC2-2]
Disjunctive Syllogism:
Either [7] or [4].
Not [7].
Therefore, [4].
[SC3-1]
Reductio Ad Absurdum:
If (Not (If (Either [2] or [3].), then [0].).), then [5].
If (Not (If (Either [2] or [3].), then [0].).), then (Not [5].). [SC2-2]
Therefore, If (Either [2] or [3].), then [0]..
[SC2-2]
Modus Tonens:
If (Not (If (Not (If (Either [2] or [3].), then [0].).), then (Not [5].).).), then [6].
Not [6].
Therefore, If (Not (If (Either [2] or [3].), then [0].).), then (Not [5].)..
|
{0: 'Spatter cones are formed if gases and lava sputter out of a crack in the side of a cone.', 1: 'Puffins have (part) chests.', 2: 'Phytoplankton are microscopic plants that live in the water like diatoms small, single-celled algae.', 3: 'Keepers have (part) human bodies.', 4: 'Some floods occur seasonally when winter snows melt and combine with spring rains.', 5: 'Some veins carry carbon dioxide.', 6: 'Surface temperatures are important in making sure there are no condensation problems.', 7: 'Most infants consume food.'}
| 5 |
4,799 |
['One may reasonably assume that if accent color is same as body color, except on black or white cars, when accent color is red, then fruits develop from the ovary wall of the flower after the plant eggs have been fertilized.', "The notion that 'any existence deprived of freedom is a form of death' is untrue.", 'It is not true that either guinea is a least developed country or genealogy is another branch of history.', 'It is not true that most cacti are self-sterile, requiring pollen from a different individual plant.', 'It is rational to believe that either some spot hyenas stay with mothers or limiting resources are things that are vital for survival and reproduction.', 'One may reasonably assume that if some spot hyenas stay with mothers, then if those that suggest either either guinea is a least developed country or genealogy is another branch of history or either any existence deprived of freedom is a form of death or accent color is same as body color, except on black or white cars, when accent color is red are wrong, then most cacti are self-sterile, requiring pollen from a different individual plant.', 'Given that limiting resources are things that are vital for survival and reproduction, it can be inferred that if those that suggest either either guinea is a least developed country or genealogy is another branch of history or either any existence deprived of freedom is a form of death or accent color is same as body color, except on black or white cars, when accent color is red are wrong, then most cacti are self-sterile, requiring pollen from a different individual plant.']
|
One may reasonably assume that if accent color is same as body color, except on black or white cars, when accent color is red, then fruits develop from the ovary wall of the flower after the plant eggs have been fertilized. The notion that 'any existence deprived of freedom is a form of death' is untrue. It is not true that either guinea is a least developed country or genealogy is another branch of history. It is not true that most cacti are self-sterile, requiring pollen from a different individual plant. It is rational to believe that either some spot hyenas stay with mothers or limiting resources are things that are vital for survival and reproduction. One may reasonably assume that if some spot hyenas stay with mothers, then if those that suggest either either guinea is a least developed country or genealogy is another branch of history or either any existence deprived of freedom is a form of death or accent color is same as body color, except on black or white cars, when accent color is red are wrong, then most cacti are self-sterile, requiring pollen from a different individual plant. Given that limiting resources are things that are vital for survival and reproduction, it can be inferred that if those that suggest either either guinea is a least developed country or genealogy is another branch of history or either any existence deprived of freedom is a form of death or accent color is same as body color, except on black or white cars, when accent color is red are wrong, then most cacti are self-sterile, requiring pollen from a different individual plant.
|
The claim that fruits develop from the ovary wall of the flower after the plant eggs have been fertilized is true.
|
The claim that fruits develop from the ovary wall of the flower after the plant eggs have been fertilized does not correspond with reality.
|
FALSE
|
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]
Disjunctive Syllogism:
Either (Either [3] or [4].) or (Either [2] or [1].). [SC1-3]
Not (Either [3] or [4].).
Therefore, Either [2] or [1]..
[SC1-3]
Modus Tonens:
If (Not (Either (Either [3] or [4].) or (Either [2] or [1].).).), then [5]. [SC1-4]
Not [5].
Therefore, Either (Either [3] or [4].) or (Either [2] or [1].)..
[SC1-4]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If (Not (Either (Either [3] or [4].) or (Either [2] or [1].).).), then [5].).
If [7], then (If (Not (Either (Either [3] or [4].) or (Either [2] or [1].).).), then [5].).
Therefore, If (Not (Either (Either [3] or [4].) or (Either [2] or [1].).).), then [5]..
|
{0: 'Fruits develop from the ovary wall of the flower after the plant eggs have been fertilized.', 1: 'Accent color is same as body color, except on black or white cars, when accent color is red.', 2: 'Any existence deprived of freedom is a form of death.', 3: 'Guinea is a least developed country.', 4: 'Genealogy is another branch of history.', 5: 'Most cacti are self-sterile, requiring pollen from a different individual plant.', 6: 'Some spot hyenas stay with mothers.', 7: 'Limiting resources are things that are vital for survival and reproduction.'}
| 5 |
4,519 |
['Assuming the claim that if participants eat vegetables, then multinational corporations can purchase or start enterprises easily does not reflect reality, we know that if individuals meet daily protein requirements, then web designers spend a great deal of time on the Internet and have seen thousands of web sites.', 'At least one of two things is true: carnivores feed on live prey, or grapefruit has a rich history of medicinal purposes as well.', 'Provided that carnivores feed on live prey, we know that it is not the case that multinational corporations can purchase or start enterprises easily.', 'When grapefruit has a rich history of medicinal purposes as well is true, it follows that it is not the case that multinational corporations can purchase or start enterprises easily.', 'The statement that states tobacco smoking plays an aggravating role is right.', 'It is a fact that either ketones make blood more acidic or soil organisms prey on crop pests and are food for above-ground animals.', "On the condition that ketones make blood more acidic, it is definitely the case that if tobacco smoking plays an aggravating role, then if the claim that if participants eat vegetables, then multinational corporations can purchase or start enterprises easily does not reflect reality, then the notion that 'if individuals meet daily protein requirements, then web designers spend a great deal of time on the Internet and have seen thousands of web sites' is untrue.", "Provided that soil organisms prey on crop pests and are food for above-ground animals, we know that if tobacco smoking plays an aggravating role, then if the claim that if participants eat vegetables, then multinational corporations can purchase or start enterprises easily does not reflect reality, then the notion that 'if individuals meet daily protein requirements, then web designers spend a great deal of time on the Internet and have seen thousands of web sites' is untrue."]
|
Assuming the claim that if participants eat vegetables, then multinational corporations can purchase or start enterprises easily does not reflect reality, we know that if individuals meet daily protein requirements, then web designers spend a great deal of time on the Internet and have seen thousands of web sites. At least one of two things is true: carnivores feed on live prey, or grapefruit has a rich history of medicinal purposes as well. Provided that carnivores feed on live prey, we know that it is not the case that multinational corporations can purchase or start enterprises easily. When grapefruit has a rich history of medicinal purposes as well is true, it follows that it is not the case that multinational corporations can purchase or start enterprises easily. The statement that states tobacco smoking plays an aggravating role is right. It is a fact that either ketones make blood more acidic or soil organisms prey on crop pests and are food for above-ground animals. On the condition that ketones make blood more acidic, it is definitely the case that if tobacco smoking plays an aggravating role, then if the claim that if participants eat vegetables, then multinational corporations can purchase or start enterprises easily does not reflect reality, then the notion that 'if individuals meet daily protein requirements, then web designers spend a great deal of time on the Internet and have seen thousands of web sites' is untrue. Provided that soil organisms prey on crop pests and are food for above-ground animals, we know that if tobacco smoking plays an aggravating role, then if the claim that if participants eat vegetables, then multinational corporations can purchase or start enterprises easily does not reflect reality, then the notion that 'if individuals meet daily protein requirements, then web designers spend a great deal of time on the Internet and have seen thousands of web sites' is untrue.
|
The statement that 'participants eat vegetables' is incorrect.
|
Those that suggest participants receive food are wrong.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then (If [4], then [5].).
If (Not (If [0], then [1].).), then (Not (If [4], then [5].).). [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Modus Ponens:
If [6], then (If (Not (If [0], then [1].).), then (Not (If [4], then [5].).).). [SC1-3]
[6]
Therefore, If (Not (If [0], then [1].).), then (Not (If [4], then [5].).)..
[SC1-3]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If [6], then (If (Not (If [0], then [1].).), then (Not (If [4], then [5].).).).).
If [8], then (If [6], then (If (Not (If [0], then [1].).), then (Not (If [4], then [5].).).).).
Therefore, If [6], then (If (Not (If [0], then [1].).), then (Not (If [4], then [5].).).)..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (Not [1].).
If [3], then (Not [1].).
Therefore, Not [1]..
|
{0: 'Participants eat vegetables.', 1: 'Multinational corporations can purchase or start enterprises easily.', 2: 'Carnivores feed on live prey.', 3: 'Grapefruit has a rich history of medicinal purposes as well.', 4: 'Individuals meet daily protein requirements.', 5: 'Web designers spend a great deal of time on the Internet and have seen thousands of web sites.', 6: 'Tobacco smoking plays an aggravating role.', 7: 'Ketones make blood more acidic.', 8: 'Soil organisms prey on crop pests and are food for above-ground animals.'}
| 5 |
4,107 |
['If it is not true that if the claim that either most bacteria produce toxic substances or materialism thus begins with the thought of matter or material processes does not reflect reality, then chameleons have complex behavior, then mechanical devices can give a false sense of security.', "When it is not true that if the claim that either most bacteria produce toxic substances or materialism thus begins with the thought of matter or material processes does not reflect reality, then chameleons have complex behavior is true, it follows that the statement that 'mechanical devices can give a false sense of security' is incorrect.", 'We know that at least one of two things is true: mini workouts are important for keeping stress levels in check, or swing dance is a return to elegance, to touch dancing and the big band sound.', "Whenever it is true that swing dance is a return to elegance, to touch dancing and the big band sound, 'if the claim that either most bacteria produce toxic substances or materialism thus begins with the thought of matter or material processes does not reflect reality, then the claim that chameleons have complex behavior does not correspond with reality' is true.", 'The statement that states temperature is measured in both centigrade and Fahrenheit is false.', 'There is good reason to believe that either either children grow and develop when they are encouraged in a warm and secure environment or cilia are tiny hairlike projections from cells that move with a wavelike motion or if it is not the case that if mini workouts are important for keeping stress levels in check, then if the claim that either most bacteria produce toxic substances or materialism thus begins with the thought of matter or material processes does not reflect reality, then the claim that chameleons have complex behavior does not correspond with reality, then temperature is measured in both centigrade and Fahrenheit.', "The notion that 'either children grow and develop when they are encouraged in a warm and secure environment or cilia are tiny hairlike projections from cells that move with a wavelike motion' is untrue."]
|
If it is not true that if the claim that either most bacteria produce toxic substances or materialism thus begins with the thought of matter or material processes does not reflect reality, then chameleons have complex behavior, then mechanical devices can give a false sense of security. When it is not true that if the claim that either most bacteria produce toxic substances or materialism thus begins with the thought of matter or material processes does not reflect reality, then chameleons have complex behavior is true, it follows that the statement that 'mechanical devices can give a false sense of security' is incorrect. We know that at least one of two things is true: mini workouts are important for keeping stress levels in check, or swing dance is a return to elegance, to touch dancing and the big band sound. Whenever it is true that swing dance is a return to elegance, to touch dancing and the big band sound, 'if the claim that either most bacteria produce toxic substances or materialism thus begins with the thought of matter or material processes does not reflect reality, then the claim that chameleons have complex behavior does not correspond with reality' is true. The statement that states temperature is measured in both centigrade and Fahrenheit is false. There is good reason to believe that either either children grow and develop when they are encouraged in a warm and secure environment or cilia are tiny hairlike projections from cells that move with a wavelike motion or if it is not the case that if mini workouts are important for keeping stress levels in check, then if the claim that either most bacteria produce toxic substances or materialism thus begins with the thought of matter or material processes does not reflect reality, then the claim that chameleons have complex behavior does not correspond with reality, then temperature is measured in both centigrade and Fahrenheit. The notion that 'either children grow and develop when they are encouraged in a warm and secure environment or cilia are tiny hairlike projections from cells that move with a wavelike motion' is untrue.
|
Either one or both of these statements are true: most bacteria produce toxic substances, or materialism thus begins with the thought of matter or material processes.
|
It is a fact that either some bacteria produce dangerous toxins or materialism is a system of metaphysics.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
If (Not (Either [0] or [1].).), then (Not [2].). [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not (Either [0] or [1].).), then [2].).), then [5].
If (Not (If (Not (Either [0] or [1].).), then [2].).), then (Not [5].).
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If (Not (Either [0] or [1].).), then (Not [2].).). [SC2-2]
If [4], then (If (Not (Either [0] or [1].).), then (Not [2].).).
Therefore, If (Not (Either [0] or [1].).), then (Not [2].)..
[SC2-2]
Modus Tonens:
If (Not (If [3], then (If (Not (Either [0] or [1].).), then (Not [2].).).).), then [6]. [SC1-3]
Not [6].
Therefore, If [3], then (If (Not (Either [0] or [1].).), then (Not [2].).)..
[SC1-3]
Disjunctive Syllogism:
Either (Either [7] or [8].) or (If (Not (If [3], then (If (Not (Either [0] or [1].).), then (Not [2].).).).), then [6].).
Not (Either [7] or [8].).
Therefore, If (Not (If [3], then (If (Not (Either [0] or [1].).), then (Not [2].).).).), then [6]..
|
{0: 'Most bacteria produce toxic substances.', 1: 'Materialism thus begins with the thought of matter or material processes.', 2: 'Chameleons have complex behavior.', 3: 'Mini workouts are important for keeping stress levels in check.', 4: 'Swing dance is a return to elegance, to touch dancing and the big band sound.', 5: 'Mechanical devices can give a false sense of security.', 6: 'Temperature is measured in both centigrade and Fahrenheit.', 7: 'Children grow and develop when they are encouraged in a warm and secure environment.', 8: 'Cilia are tiny hairlike projections from cells that move with a wavelike motion.'}
| 5 |
4,708 |
["One may reasonably assume that if nutritionists debate soy's health benefits, then physical therapists assist with mobility.", "Provided that a history lesson is a lesson, we know that either nutritionists debate soy's health benefits or winds are a key factor in determining global weather patterns.", 'There is good reason to believe that either granite occurs in two separate masses or if winds are a key factor in determining global weather patterns, then physical therapists assist with mobility.', 'There is good reason to believe that either most flowers grow in many places or many marketers focus efforts on the health and welfare of customers and people in the community.', 'One may reasonably assume that if most flowers grow in many places, then a history lesson is a lesson.', 'Should it be the case that many marketers focus efforts on the health and welfare of customers and people in the community, it follows that a history lesson is a lesson.', 'On the condition that granite occurs in two separate masses, it is definitely the case that power chords are especially popular among rock and blues music.', 'Some people mistakenly believe that power chords are especially popular among rock and blues music.']
|
One may reasonably assume that if nutritionists debate soy's health benefits, then physical therapists assist with mobility. Provided that a history lesson is a lesson, we know that either nutritionists debate soy's health benefits or winds are a key factor in determining global weather patterns. There is good reason to believe that either granite occurs in two separate masses or if winds are a key factor in determining global weather patterns, then physical therapists assist with mobility. There is good reason to believe that either most flowers grow in many places or many marketers focus efforts on the health and welfare of customers and people in the community. One may reasonably assume that if most flowers grow in many places, then a history lesson is a lesson. Should it be the case that many marketers focus efforts on the health and welfare of customers and people in the community, it follows that a history lesson is a lesson. On the condition that granite occurs in two separate masses, it is definitely the case that power chords are especially popular among rock and blues music. Some people mistakenly believe that power chords are especially popular among rock and blues music.
|
It is a simple truth that physical therapists assist with mobility.
|
Physical therapists target mobility skills.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [4], then (Either [1] or [2].).
[4] [SC2-2]
Therefore, Either [1] or [2]..
[SC2-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then [4].
If [7], then [4].
Therefore, [4].
[SC3-1]
Disjunctive Syllogism:
Either [3] or (If [2], then [0].).
Not [3]. [SC2-2]
Therefore, If [2], then [0]..
[SC2-2]
Modus Tonens:
If [3], then [5].
Not [5].
Therefore, Not [3]..
|
{0: 'Physical therapists assist with mobility.', 1: "Nutritionists debate soy's health benefits.", 2: 'Winds are a key factor in determining global weather patterns.', 3: 'Granite occurs in two separate masses.', 4: 'A history lesson is a lesson.', 5: 'Power chords are especially popular among rock and blues music.', 6: 'Most flowers grow in many places.', 7: 'Many marketers focus efforts on the health and welfare of customers and people in the community.'}
| 5 |
4,634 |
['There is good reason to believe that either intellectual property is intangible property or doctors are also human, and they have their own problems.', 'If most starlings enter nests, then the claim that intellectual property is intangible property is false.', 'Either either movers have (part) sections or inversions are books or nutritional deprivation causes calcium loss from bones, which become brittle and prone to breakage.', 'Provided that either movers have (part) sections or inversions are books, we know that most starlings enter nests.', 'Once we know nutritional deprivation causes calcium loss from bones, which become brittle and prone to breakage, we also know that pink noise has an equal amount of energy per octave of bandwidth.', 'It is rational to believe that either corticosteroids are the drugs which are usually administered in an attempt to stop the inflammation or if most walkers do walk at least half an hour at a time, but fewer walk four or more times a week, then some cockroaches become public health problems.', "Whenever it is true that corticosteroids are the drugs which are usually administered in an attempt to stop the inflammation, 'if pink noise has an equal amount of energy per octave of bandwidth, then most starlings enter nests' is true.", "Whenever it is true that if most walkers do walk at least half an hour at a time, but fewer walk four or more times a week, then some cockroaches become public health problems, 'if pink noise has an equal amount of energy per octave of bandwidth, then most starlings enter nests' is true."]
|
There is good reason to believe that either intellectual property is intangible property or doctors are also human, and they have their own problems. If most starlings enter nests, then the claim that intellectual property is intangible property is false. Either either movers have (part) sections or inversions are books or nutritional deprivation causes calcium loss from bones, which become brittle and prone to breakage. Provided that either movers have (part) sections or inversions are books, we know that most starlings enter nests. Once we know nutritional deprivation causes calcium loss from bones, which become brittle and prone to breakage, we also know that pink noise has an equal amount of energy per octave of bandwidth. It is rational to believe that either corticosteroids are the drugs which are usually administered in an attempt to stop the inflammation or if most walkers do walk at least half an hour at a time, but fewer walk four or more times a week, then some cockroaches become public health problems. Whenever it is true that corticosteroids are the drugs which are usually administered in an attempt to stop the inflammation, 'if pink noise has an equal amount of energy per octave of bandwidth, then most starlings enter nests' is true. Whenever it is true that if most walkers do walk at least half an hour at a time, but fewer walk four or more times a week, then some cockroaches become public health problems, 'if pink noise has an equal amount of energy per octave of bandwidth, then most starlings enter nests' is true.
|
The statement 'doctors are also human, and they have their own problems' is true.
|
The statement 'doctors are also human, and they have their own problems' can be considered false.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [2], then (Not [1].).
[2] [SC2-2]
Therefore, Not [1]..
[SC2-2]
Disjunction Elimination:
Either (Either [3] or [4].) or [5].
If (Either [3] or [4].), then [2].
If [5], then [2]. [SC3-3]
Therefore, [2].
[SC3-3]
Hypothetical Syllogism:
If [5], then [6].
If [6], then [2]. [SC2-4]
Therefore, If [5], then [2]..
[SC2-4]
Disjunction Elimination:
Either [7] or (If [8], then [9].).
If [7], then (If [6], then [2].).
If (If [8], then [9].), then (If [6], then [2].).
Therefore, If [6], then [2]..
|
{0: 'Doctors are also human, and they have their own problems.', 1: 'Intellectual property is intangible property.', 2: 'Most starlings enter nests.', 3: 'Movers have (part) sections.', 4: 'Inversions are books.', 5: 'Nutritional deprivation causes calcium loss from bones, which become brittle and prone to breakage.', 6: 'Pink noise has an equal amount of energy per octave of bandwidth.', 7: 'Corticosteroids are the drugs which are usually administered in an attempt to stop the inflammation.', 8: 'Most walkers do walk at least half an hour at a time, but fewer walk four or more times a week.', 9: 'Some cockroaches become public health problems.'}
| 5 |
4,223 |
["One may reasonably assume that if the claim that either some hanuman langurs have gray fur or vitreous humor fills the cavity behind the lens and comprises most of the eye's volume does not reflect reality, then if tranquility is no longer a molecule in the air people breathe, then puffballs have (part) vacuoles.", 'Assuming if tranquility is no longer a molecule in the air people breathe, then puffballs have (part) vacuoles, we know that either cougars drag prey or waists are drawstrings.', 'It is a fact that either either fellows are men or songs help to maintain the bond between the male and female or conflict resolution is often an important feature of workplace mediation.', "If the statement that 'if either fellows are men or songs help to maintain the bond between the male and female, then it is not the case that either cougars drag prey or waists are drawstrings' is incorrect, then wind speeds are generally light in the continental arctic interior throughout the year.", "So long as the statement that 'if either fellows are men or songs help to maintain the bond between the male and female, then it is not the case that either cougars drag prey or waists are drawstrings' is incorrect, 'it is not the case that wind speeds are generally light in the continental arctic interior throughout the year' is true.", 'Either one or both of these statements are true: if tea is located in cups, then young trees are especially susceptible to freeze injury, or most edible bananas originate in regions.', "Whenever it is true that if tea is located in cups, then young trees are especially susceptible to freeze injury, 'if conflict resolution is often an important feature of workplace mediation, then it is not the case that either cougars drag prey or waists are drawstrings' is true.", 'Provided that most edible bananas originate in regions, we know that if conflict resolution is often an important feature of workplace mediation, then it is not the case that either cougars drag prey or waists are drawstrings.']
|
One may reasonably assume that if the claim that either some hanuman langurs have gray fur or vitreous humor fills the cavity behind the lens and comprises most of the eye's volume does not reflect reality, then if tranquility is no longer a molecule in the air people breathe, then puffballs have (part) vacuoles. Assuming if tranquility is no longer a molecule in the air people breathe, then puffballs have (part) vacuoles, we know that either cougars drag prey or waists are drawstrings. It is a fact that either either fellows are men or songs help to maintain the bond between the male and female or conflict resolution is often an important feature of workplace mediation. If the statement that 'if either fellows are men or songs help to maintain the bond between the male and female, then it is not the case that either cougars drag prey or waists are drawstrings' is incorrect, then wind speeds are generally light in the continental arctic interior throughout the year. So long as the statement that 'if either fellows are men or songs help to maintain the bond between the male and female, then it is not the case that either cougars drag prey or waists are drawstrings' is incorrect, 'it is not the case that wind speeds are generally light in the continental arctic interior throughout the year' is true. Either one or both of these statements are true: if tea is located in cups, then young trees are especially susceptible to freeze injury, or most edible bananas originate in regions. Whenever it is true that if tea is located in cups, then young trees are especially susceptible to freeze injury, 'if conflict resolution is often an important feature of workplace mediation, then it is not the case that either cougars drag prey or waists are drawstrings' is true. Provided that most edible bananas originate in regions, we know that if conflict resolution is often an important feature of workplace mediation, then it is not the case that either cougars drag prey or waists are drawstrings.
|
We know that either some hanuman langurs have gray fur or vitreous humor fills the cavity behind the lens and comprises most of the eye's volume.
|
We know that either some hanuman langurs have gray fur or vitreous humor fills the cavity behind the lens and comprises most of the eye's volume.
|
TRUE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then (Either [2] or [3].). [SC1-1]
Not (Either [2] or [3].). [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Hypothetical Syllogism:
If (Not (Either [0] or [1].).), then (If [4], then [5].).
If (If [4], then [5].), then (Either [2] or [3].).
Therefore, If (Not (Either [0] or [1].).), then (Either [2] or [3].)..
[SC2-1]
Disjunction Elimination:
Either (Either [6] or [7].) or [8].
If (Either [6] or [7].), then (Not (Either [2] or [3].).). [SC2-2]
If [8], then (Not (Either [2] or [3].).). [SC3-2]
Therefore, Not (Either [2] or [3].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Either [6] or [7].), then (Not (Either [2] or [3].).).).), then [12].
If (Not (If (Either [6] or [7].), then (Not (Either [2] or [3].).).).), then (Not [12].).
Therefore, If (Either [6] or [7].), then (Not (Either [2] or [3].).)..
[SC3-2]
Disjunction Elimination:
Either (If [9], then [10].) or [11].
If (If [9], then [10].), then (If [8], then (Not (Either [2] or [3].).).).
If [11], then (If [8], then (Not (Either [2] or [3].).).).
Therefore, If [8], then (Not (Either [2] or [3].).)..
|
{0: 'Some hanuman langurs have gray fur.', 1: "Vitreous humor fills the cavity behind the lens and comprises most of the eye's volume.", 2: 'Cougars drag prey.', 3: 'Waists are drawstrings.', 4: 'Tranquility is no longer a molecule in the air people breathe.', 5: 'Puffballs have (part) vacuoles.', 6: 'Fellows are men.', 7: 'Songs help to maintain the bond between the male and female.', 8: 'Conflict resolution is often an important feature of workplace mediation.', 9: 'Tea is located in cups.', 10: 'Young trees are especially susceptible to freeze injury.', 11: 'Most edible bananas originate in regions.', 12: 'Wind speeds are generally light in the continental arctic interior throughout the year.'}
| 5 |
4,327 |
['The statement that states bluebirds have (part) rib cages is false.', 'Once we know herbivores roam continents, we also know that either bluebirds have (part) rib cages or heathers grow on hillsides.', 'Given that the claim that if some martial arts have dance-like moves, then herbivores roam continents has no merit, it can be inferred that protocols improve cost.', 'The claim that protocols improve cost is false.', 'Assuming those that suggest some martial arts have dance-like moves are wrong, we know that drug use can also cause birth defects.', "The notion that 'drug use can also cause birth defects' is untrue."]
|
The statement that states bluebirds have (part) rib cages is false. Once we know herbivores roam continents, we also know that either bluebirds have (part) rib cages or heathers grow on hillsides. Given that the claim that if some martial arts have dance-like moves, then herbivores roam continents has no merit, it can be inferred that protocols improve cost. The claim that protocols improve cost is false. Assuming those that suggest some martial arts have dance-like moves are wrong, we know that drug use can also cause birth defects. The notion that 'drug use can also cause birth defects' is untrue.
|
The claim that heathers grow on hillsides holds true.
|
The claim that heathers grow on hillsides does not correspond with reality.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (Either [1] or [0].).
[2] [SC2-2]
Therefore, Either [1] or [0]..
[SC2-2]
Modus Ponens:
If [3], then [2]. [SC1-3]
[3] [SC2-3]
Therefore, [2].
[SC1-3]
Modus Tonens:
If (Not (If [3], then [2].).), then [4].
Not [4].
Therefore, If [3], then [2]..
[SC2-3]
Modus Tonens:
If (Not [3].), then [5].
Not [5].
Therefore, [3].
|
{0: 'Heathers grow on hillsides.', 1: 'Bluebirds have (part) rib cages.', 2: 'Herbivores roam continents.', 3: 'Some martial arts have dance-like moves.', 4: 'Protocols improve cost.', 5: 'Drug use can also cause birth defects.'}
| 5 |
4,102 |
['Given that we know that the claim that either binary format is used for compressed files and graphics or benzodiazepines are very safe drugs if used sensibly is false, it can be inferred that divinity is seen as immanent.', "Whenever it is true that most megabats roost in the open, 'rotational grazing is the best medicine for all pastures, young or old' is true.", 'We know that at least one of two things is true: mature bees chew themselves out of the sealed cells to emerge, or chemicals are expensive and have associated environmental risks.', 'Given that mature bees chew themselves out of the sealed cells to emerge, it can be inferred that if the claim that if we know that the claim that either binary format is used for compressed files and graphics or benzodiazepines are very safe drugs if used sensibly is false, then some people mistakenly believe that divinity is seen as immanent does not correspond with reality, then the claim that rotational grazing is the best medicine for all pastures, young or old has no merit.', 'Should it be the case that chemicals are expensive and have associated environmental risks, it follows that if the claim that if we know that the claim that either binary format is used for compressed files and graphics or benzodiazepines are very safe drugs if used sensibly is false, then some people mistakenly believe that divinity is seen as immanent does not correspond with reality, then the claim that rotational grazing is the best medicine for all pastures, young or old has no merit.', 'Either colleagues are associates or if the claim that if we know that the claim that either binary format is used for compressed files and graphics or benzodiazepines are very safe drugs if used sensibly is false, then some people mistakenly believe that divinity is seen as immanent does not correspond with reality, then most megabats roost in the open.', 'It is not true that colleagues are associates.']
|
Given that we know that the claim that either binary format is used for compressed files and graphics or benzodiazepines are very safe drugs if used sensibly is false, it can be inferred that divinity is seen as immanent. Whenever it is true that most megabats roost in the open, 'rotational grazing is the best medicine for all pastures, young or old' is true. We know that at least one of two things is true: mature bees chew themselves out of the sealed cells to emerge, or chemicals are expensive and have associated environmental risks. Given that mature bees chew themselves out of the sealed cells to emerge, it can be inferred that if the claim that if we know that the claim that either binary format is used for compressed files and graphics or benzodiazepines are very safe drugs if used sensibly is false, then some people mistakenly believe that divinity is seen as immanent does not correspond with reality, then the claim that rotational grazing is the best medicine for all pastures, young or old has no merit. Should it be the case that chemicals are expensive and have associated environmental risks, it follows that if the claim that if we know that the claim that either binary format is used for compressed files and graphics or benzodiazepines are very safe drugs if used sensibly is false, then some people mistakenly believe that divinity is seen as immanent does not correspond with reality, then the claim that rotational grazing is the best medicine for all pastures, young or old has no merit. Either colleagues are associates or if the claim that if we know that the claim that either binary format is used for compressed files and graphics or benzodiazepines are very safe drugs if used sensibly is false, then some people mistakenly believe that divinity is seen as immanent does not correspond with reality, then most megabats roost in the open. It is not true that colleagues are associates.
|
Either binary format is used for compressed files and graphics or benzodiazepines are very safe drugs if used sensibly.
|
Either binary format is used for compressed files and graphics or benzodiazepines are very safe drugs if used sensibly.
|
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]
Reductio Ad Absurdum:
If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [3]. [SC1-2]
If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (Not [3].). [SC2-2]
Therefore, If (Not (Either [0] or [1].).), then (Not [2].)..
[SC1-2]
Hypothetical Syllogism:
If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [6]. [SC1-3]
If [6], then [3].
Therefore, If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [3]..
[SC1-3]
Disjunctive Syllogism:
Either [7] or (If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [6].).
Not [7].
Therefore, If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then [6]..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (Not [3].).).
If [5], then (If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (Not [3].).).
Therefore, If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (Not [3].)..
|
{0: 'Binary format is used for compressed files and graphics.', 1: 'Benzodiazepines are very safe drugs if used sensibly.', 2: 'Divinity is seen as immanent.', 3: 'Rotational grazing is the best medicine for all pastures, young or old.', 4: 'Mature bees chew themselves out of the sealed cells to emerge.', 5: 'Chemicals are expensive and have associated environmental risks.', 6: 'Most megabats roost in the open.', 7: 'Colleagues are associates.'}
| 5 |
4,704 |
['It is a fact that either most macaws eat fruit or either either psychiatrists can diagnose and treat depression, phobias, neuroses or most early cancers produce no symptoms or the statement, babies born to young teen mothers have a higher risk of serious health problems, does not hold.', 'On the condition that alligators excrete waste, it is definitely the case that it is not true that either psychiatrists can diagnose and treat depression, phobias, neuroses or most early cancers produce no symptoms.', 'alligators excrete waste.', "So long as geometry is a problem of the past, 'those that suggest most macaws eat fruit are wrong' is true.", 'We know that either anthropology teaches people how to be citizens of the world or geometry is a problem of the past.', 'It is not true that anthropology teaches people how to be citizens of the world.']
|
It is a fact that either most macaws eat fruit or either either psychiatrists can diagnose and treat depression, phobias, neuroses or most early cancers produce no symptoms or the statement, babies born to young teen mothers have a higher risk of serious health problems, does not hold. On the condition that alligators excrete waste, it is definitely the case that it is not true that either psychiatrists can diagnose and treat depression, phobias, neuroses or most early cancers produce no symptoms. alligators excrete waste. So long as geometry is a problem of the past, 'those that suggest most macaws eat fruit are wrong' is true. We know that either anthropology teaches people how to be citizens of the world or geometry is a problem of the past. It is not true that anthropology teaches people how to be citizens of the world.
|
The statement, babies born to young teen mothers have a higher risk of serious health problems, does not hold.
|
Those that suggest babies born to young teen mothers have a higher risk of serious health problems are right.
|
FALSE
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or (Not [0].). [SC1-1]
Not (Either [1] or [2].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (Either (Either [1] or [2].) or (Not [0].).).
Not [3]. [SC2-2]
Therefore, Either (Either [1] or [2].) or (Not [0].)..
[SC2-2]
Modus Ponens:
If [5], then (Not [3].).
[5] [SC2-3]
Therefore, Not [3]..
[SC2-3]
Disjunctive Syllogism:
Either [6] or [5].
Not [6].
Therefore, [5].
[SC2-1]
Modus Ponens:
If [4], then (Not (Either [1] or [2].).).
[4]
Therefore, Not (Either [1] or [2].)..
|
{0: 'Babies born to young teen mothers have a higher risk of serious health problems.', 1: 'Psychiatrists can diagnose and treat depression, phobias, neuroses.', 2: 'Most early cancers produce no symptoms.', 3: 'Most macaws eat fruit.', 4: 'Alligators excrete waste.', 5: 'Geometry is a problem of the past.', 6: 'Anthropology teaches people how to be citizens of the world.'}
| 5 |
4,475 |
['At least one of two things is true: if rubber is a common component of stoppers, cap liners, and parts of dropper assemblies, then most pitcher plants range in height, or physical activity releases tension and normalizes stress hormones.', 'When if rubber is a common component of stoppers, cap liners, and parts of dropper assemblies, then most pitcher plants range in height is true, it follows that either stingrays reside in the sands around the vessel along with turtles and garden eels or some men have a slight natural curve in their penis, which is nothing to worry about.', "At least one of two things is true: charge is the product of current and time for direct current, or the statement 'stingrays reside in the sands around the vessel along with turtles and garden eels' can be considered false.", 'Some people mistakenly believe that charge is the product of current and time for direct current.', 'Given that the statement that states if physical activity releases tension and normalizes stress hormones, then either stingrays reside in the sands around the vessel along with turtles and garden eels or some men have a slight natural curve in their penis, which is nothing to worry about is false, it can be inferred that blood carries fuel to the brain and waste products away from the brain.', "Given that the statement 'if the statement that states if physical activity releases tension and normalizes stress hormones, then either stingrays reside in the sands around the vessel along with turtles and garden eels or some men have a slight natural curve in their penis, which is nothing to worry about is false, then some people mistakenly believe that blood carries fuel to the brain and waste products away from the brain' can be considered false, it can be inferred that either hard outer shells serve vital protective functions or unattended children increase risk of fire play.", "So long as the statement 'if the statement that states if physical activity releases tension and normalizes stress hormones, then either stingrays reside in the sands around the vessel along with turtles and garden eels or some men have a slight natural curve in their penis, which is nothing to worry about is false, then some people mistakenly believe that blood carries fuel to the brain and waste products away from the brain' can be considered false, 'the claim that either hard outer shells serve vital protective functions or unattended children increase risk of fire play does not reflect reality' is true."]
|
At least one of two things is true: if rubber is a common component of stoppers, cap liners, and parts of dropper assemblies, then most pitcher plants range in height, or physical activity releases tension and normalizes stress hormones. When if rubber is a common component of stoppers, cap liners, and parts of dropper assemblies, then most pitcher plants range in height is true, it follows that either stingrays reside in the sands around the vessel along with turtles and garden eels or some men have a slight natural curve in their penis, which is nothing to worry about. At least one of two things is true: charge is the product of current and time for direct current, or the statement 'stingrays reside in the sands around the vessel along with turtles and garden eels' can be considered false. Some people mistakenly believe that charge is the product of current and time for direct current. Given that the statement that states if physical activity releases tension and normalizes stress hormones, then either stingrays reside in the sands around the vessel along with turtles and garden eels or some men have a slight natural curve in their penis, which is nothing to worry about is false, it can be inferred that blood carries fuel to the brain and waste products away from the brain. Given that the statement 'if the statement that states if physical activity releases tension and normalizes stress hormones, then either stingrays reside in the sands around the vessel along with turtles and garden eels or some men have a slight natural curve in their penis, which is nothing to worry about is false, then some people mistakenly believe that blood carries fuel to the brain and waste products away from the brain' can be considered false, it can be inferred that either hard outer shells serve vital protective functions or unattended children increase risk of fire play. So long as the statement 'if the statement that states if physical activity releases tension and normalizes stress hormones, then either stingrays reside in the sands around the vessel along with turtles and garden eels or some men have a slight natural curve in their penis, which is nothing to worry about is false, then some people mistakenly believe that blood carries fuel to the brain and waste products away from the brain' can be considered false, 'the claim that either hard outer shells serve vital protective functions or unattended children increase risk of fire play does not reflect reality' is true.
|
Those that suggest some men have a slight natural curve in their penis, which is nothing to worry about are right.
|
Those that suggest some men have a slight natural curve in their penis, which is nothing to worry about are right.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (If [2], then [3].) or [4].
If (If [2], then [3].), then (Either [1] or [0].).
If [4], then (Either [1] or [0].). [SC3-2]
Therefore, Either [1] or [0]..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If [4], then (Either [1] or [0].).).), then [6].
If (Not (If [4], then (Either [1] or [0].).).), then (Not [6].). [SC2-3]
Therefore, If [4], then (Either [1] or [0].)..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If (Not (If [4], then (Either [1] or [0].).).), then (Not [6].).).), then (Either [7] or [8].).
If (Not (If (Not (If [4], then (Either [1] or [0].).).), then (Not [6].).).), then (Not (Either [7] or [8].).).
Therefore, If (Not (If [4], then (Either [1] or [0].).).), then (Not [6].)..
[SC2-1]
Disjunctive Syllogism:
Either [5] or (Not [1].).
Not [5].
Therefore, Not [1]..
|
{0: 'Some men have a slight natural curve in their penis, which is nothing to worry about.', 1: 'Stingrays reside in the sands around the vessel along with turtles and garden eels.', 2: 'Rubber is a common component of stoppers, cap liners, and parts of dropper assemblies.', 3: 'Most pitcher plants range in height.', 4: 'Physical activity releases tension and normalizes stress hormones.', 5: 'Charge is the product of current and time for direct current.', 6: 'Blood carries fuel to the brain and waste products away from the brain.', 7: 'Hard outer shells serve vital protective functions.', 8: 'Unattended children increase risk of fire play.'}
| 5 |
4,213 |
['The claim that reduced populations are also less resilient to extreme, destructive events does not correspond with reality.', 'If either most soft drinks contain the element sodium which is a shiny silvery metal or pits are deep holes, then if the statement that states either reduced populations are also less resilient to extreme, destructive events or sewage is discharged into the sea by many communities around the world is false, then normative conflict involves disagreement over the standards and rules of the relationship.', 'Once we know flounder has (part) vertebrate feet, we also know that if the statement that states either reduced populations are also less resilient to extreme, destructive events or sewage is discharged into the sea by many communities around the world is false, then normative conflict involves disagreement over the standards and rules of the relationship.', 'Provided that some animals are located in Africa, we know that if the statement that states either reduced populations are also less resilient to extreme, destructive events or sewage is discharged into the sea by many communities around the world is false, then the statement that states normative conflict involves disagreement over the standards and rules of the relationship is false.', 'The statement that states some animals are located in Africa is right.', 'At least one of two things is true: betels are plants, or either either most soft drinks contain the element sodium which is a shiny silvery metal or pits are deep holes or flounder has (part) vertebrate feet.', 'It is a common misconception that betels are plants.']
|
The claim that reduced populations are also less resilient to extreme, destructive events does not correspond with reality. If either most soft drinks contain the element sodium which is a shiny silvery metal or pits are deep holes, then if the statement that states either reduced populations are also less resilient to extreme, destructive events or sewage is discharged into the sea by many communities around the world is false, then normative conflict involves disagreement over the standards and rules of the relationship. Once we know flounder has (part) vertebrate feet, we also know that if the statement that states either reduced populations are also less resilient to extreme, destructive events or sewage is discharged into the sea by many communities around the world is false, then normative conflict involves disagreement over the standards and rules of the relationship. Provided that some animals are located in Africa, we know that if the statement that states either reduced populations are also less resilient to extreme, destructive events or sewage is discharged into the sea by many communities around the world is false, then the statement that states normative conflict involves disagreement over the standards and rules of the relationship is false. The statement that states some animals are located in Africa is right. At least one of two things is true: betels are plants, or either either most soft drinks contain the element sodium which is a shiny silvery metal or pits are deep holes or flounder has (part) vertebrate feet. It is a common misconception that betels are plants.
|
The statement 'sewage is discharged into the sea by many communities around the world' can be considered true.
|
Most sewage includes liquid waste.
|
Uncertain
|
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 (Either [3] or [4].) or [5]. [SC1-3]
If (Either [3] or [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]..
[SC1-3]
Disjunctive Syllogism:
Either [7] or (Either (Either [3] or [4].) or [5].).
Not [7].
Therefore, Either (Either [3] or [4].) or [5]..
[SC2-2]
Modus Ponens:
If [6], then (If (Not (Either [1] or [0].).), then (Not [2].).).
[6]
Therefore, If (Not (Either [1] or [0].).), then (Not [2].)..
|
{0: 'Sewage is discharged into the sea by many communities around the world.', 1: 'Reduced populations are also less resilient to extreme, destructive events.', 2: 'Normative conflict involves disagreement over the standards and rules of the relationship.', 3: 'Most soft drinks contain the element sodium which is a shiny silvery metal.', 4: 'Pits are deep holes.', 5: 'Flounder has (part) vertebrate feet.', 6: 'Some animals are located in Africa.', 7: 'Betels are plants.'}
| 5 |
4,135 |
['Provided that the claim that front yards are used for leisure does not correspond with reality, we know that potassium behaves much like nitrogen, in that it dissolves quickly.', 'Provided that if religious practice enhances spiritual growth, then most plants start roots, we know that the claim that potassium behaves much like nitrogen, in that it dissolves quickly does not correspond with reality.', 'One may reasonably assume that if the claim that if religious practice enhances spiritual growth, then most plants start roots has no merit, then some plants have distribution.', 'Either one or both of these statements are true: medical symbols is the Guinea worm, or if waterfowls have (part) mouths, then phonograph isa machine.', 'Once we know medical symbols is the Guinea worm, we also know that the claim that some plants have distribution has no merit.', 'Once we know fast foods have a very high fat content with little nutritional value, we also know that if if waterfowls have (part) mouths, then phonograph isa machine, then the claim that some plants have distribution has no merit.', 'It is fair to say that fast foods have a very high fat content with little nutritional value.']
|
Provided that the claim that front yards are used for leisure does not correspond with reality, we know that potassium behaves much like nitrogen, in that it dissolves quickly. Provided that if religious practice enhances spiritual growth, then most plants start roots, we know that the claim that potassium behaves much like nitrogen, in that it dissolves quickly does not correspond with reality. One may reasonably assume that if the claim that if religious practice enhances spiritual growth, then most plants start roots has no merit, then some plants have distribution. Either one or both of these statements are true: medical symbols is the Guinea worm, or if waterfowls have (part) mouths, then phonograph isa machine. Once we know medical symbols is the Guinea worm, we also know that the claim that some plants have distribution has no merit. Once we know fast foods have a very high fat content with little nutritional value, we also know that if if waterfowls have (part) mouths, then phonograph isa machine, then the claim that some plants have distribution has no merit. It is fair to say that fast foods have a very high fat content with little nutritional value.
|
front yards are used for leisure.
|
Front yards are used for watering.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If (If [2], then [3].), then (Not [1].).
If [2], then [3]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Modus Tonens:
If (Not (If [2], then [3].).), then [4].
Not [4]. [SC2-3]
Therefore, If [2], then [3]..
[SC2-3]
Disjunction Elimination:
Either [5] or (If [6], then [7].).
If [5], then (Not [4].).
If (If [6], then [7].), then (Not [4].). [SC3-4]
Therefore, Not [4]..
[SC3-4]
Modus Ponens:
If [8], then (If (If [6], then [7].), then (Not [4].).).
[8]
Therefore, If (If [6], then [7].), then (Not [4].)..
|
{0: 'Front yards are used for leisure.', 1: 'Potassium behaves much like nitrogen, in that it dissolves quickly.', 2: 'Religious practice enhances spiritual growth.', 3: 'Most plants start roots.', 4: 'Some plants have distribution.', 5: 'Medical symbols is the Guinea worm.', 6: 'Waterfowls have (part) mouths.', 7: 'Phonograph isa machine.', 8: 'Fast foods have a very high fat content with little nutritional value.'}
| 5 |
4,246 |
['Provided that some people mistakenly believe that either earth is half of a double-planet system which has no true moons or most vital organs perform functions, we know that baths add cold water.', 'If some people mistakenly believe that either earth is half of a double-planet system which has no true moons or most vital organs perform functions, then the claim that baths add cold water does not reflect reality.', 'We know that either population densities reflect subterranean burrow wall surface areas and burrow water volumes or either a daguerreotype is a photograph or some narwhals produce noise.', 'Assuming either a daguerreotype is a photograph or some narwhals produce noise, we know that it is not true that earth is half of a double-planet system which has no true moons.', "Should it be the case that the statement 'if population densities reflect subterranean burrow wall surface areas and burrow water volumes, then it is not true that earth is half of a double-planet system which has no true moons' can be considered false, it follows that perception is reality, and everyone's perceptions are different.", "At least one of two things is true: all recessive alleles cause genetic disease, or some people mistakenly believe that perception is reality, and everyone's perceptions are different.", 'It is not the case that all recessive alleles cause genetic disease.']
|
Provided that some people mistakenly believe that either earth is half of a double-planet system which has no true moons or most vital organs perform functions, we know that baths add cold water. If some people mistakenly believe that either earth is half of a double-planet system which has no true moons or most vital organs perform functions, then the claim that baths add cold water does not reflect reality. We know that either population densities reflect subterranean burrow wall surface areas and burrow water volumes or either a daguerreotype is a photograph or some narwhals produce noise. Assuming either a daguerreotype is a photograph or some narwhals produce noise, we know that it is not true that earth is half of a double-planet system which has no true moons. Should it be the case that the statement 'if population densities reflect subterranean burrow wall surface areas and burrow water volumes, then it is not true that earth is half of a double-planet system which has no true moons' can be considered false, it follows that perception is reality, and everyone's perceptions are different. At least one of two things is true: all recessive alleles cause genetic disease, or some people mistakenly believe that perception is reality, and everyone's perceptions are different. It is not the case that all recessive alleles cause genetic disease.
|
It is the case that most vital organs perform functions.
|
It is the case that most vital organs perform functions.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or [0].).), then [5].
If (Not (Either [1] or [0].).), then (Not [5].).
Therefore, Either [1] or [0]..
[SC2-1]
Disjunction Elimination:
Either [2] or (Either [3] or [4].).
If [2], then (Not [1].). [SC2-2]
If (Either [3] or [4].), then (Not [1].).
Therefore, Not [1]..
[SC2-2]
Modus Tonens:
If (Not (If [2], then (Not [1].).).), then [6].
Not [6]. [SC2-3]
Therefore, If [2], then (Not [1].)..
[SC2-3]
Disjunctive Syllogism:
Either [7] or (Not [6].).
Not [7].
Therefore, Not [6]..
|
{0: 'Most vital organs perform functions.', 1: 'Earth is half of a double-planet system which has no true moons.', 2: 'Population densities reflect subterranean burrow wall surface areas and burrow water volumes.', 3: 'A daguerreotype is a photograph.', 4: 'Some narwhals produce noise.', 5: 'Baths add cold water.', 6: "Perception is reality, and everyone's perceptions are different.", 7: 'All recessive alleles cause genetic disease.'}
| 5 |
4,970 |
['It is a fact that either water molecules stick to each other through relatively weak bonds called hydrogen bonds or vitamin D prevents unwanted inflammation and helps bones in their absorption of calcium.', 'Provided that vitamin D prevents unwanted inflammation and helps bones in their absorption of calcium, we know that squash bugs are also present in many areas.', 'Assuming human beings are the caretakers of the planet, we know that squash bugs are also present in many areas.', 'At least one of two things is true: either forest roads are essential to many facets of forest management or spiders come from eggs, or if plants adapt their growth and development to their local environment, then breeds have sex.', 'If if plants adapt their growth and development to their local environment, then breeds have sex, then if water molecules stick to each other through relatively weak bonds called hydrogen bonds, then human beings are the caretakers of the planet.', 'It is true that people control animals.', "So long as people control animals, 'geysers are quite rare, requiring a combination of water , heat , and fortuitous plumbing ' is true.", 'One may reasonably assume that if geysers are quite rare, requiring a combination of water , heat , and fortuitous plumbing , then if either forest roads are essential to many facets of forest management or spiders come from eggs, then if water molecules stick to each other through relatively weak bonds called hydrogen bonds, then human beings are the caretakers of the planet.']
|
It is a fact that either water molecules stick to each other through relatively weak bonds called hydrogen bonds or vitamin D prevents unwanted inflammation and helps bones in their absorption of calcium. Provided that vitamin D prevents unwanted inflammation and helps bones in their absorption of calcium, we know that squash bugs are also present in many areas. Assuming human beings are the caretakers of the planet, we know that squash bugs are also present in many areas. At least one of two things is true: either forest roads are essential to many facets of forest management or spiders come from eggs, or if plants adapt their growth and development to their local environment, then breeds have sex. If if plants adapt their growth and development to their local environment, then breeds have sex, then if water molecules stick to each other through relatively weak bonds called hydrogen bonds, then human beings are the caretakers of the planet. It is true that people control animals. So long as people control animals, 'geysers are quite rare, requiring a combination of water , heat , and fortuitous plumbing ' is true. One may reasonably assume that if geysers are quite rare, requiring a combination of water , heat , and fortuitous plumbing , then if either forest roads are essential to many facets of forest management or spiders come from eggs, then if water molecules stick to each other through relatively weak bonds called hydrogen bonds, then human beings are the caretakers of the planet.
|
Those that suggest squash bugs are also present in many areas are right.
|
Squash bugs are serious pests of squash and pumpkins.
|
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 [3]. [SC1-2]
If [3], then [0].
Therefore, If [1], then [0]..
[SC1-2]
Disjunction Elimination:
Either (Either [4] or [5].) or (If [6], then [7].).
If (Either [4] or [5].), then (If [1], then [3].). [SC2-3]
If (If [6], then [7].), then (If [1], then [3].).
Therefore, If [1], then [3]..
[SC2-3]
Modus Ponens:
If [8], then (If (Either [4] or [5].), then (If [1], then [3].).). [SC1-4]
[8]
Therefore, If (Either [4] or [5].), then (If [1], then [3].)..
[SC1-4]
Hypothetical Syllogism:
If [8], then [9].
If [9], then (If (Either [4] or [5].), then (If [1], then [3].).).
Therefore, If [8], then (If (Either [4] or [5].), then (If [1], then [3].).)..
|
{0: 'Squash bugs are also present in many areas.', 1: 'Water molecules stick to each other through relatively weak bonds called hydrogen bonds.', 2: 'Vitamin D prevents unwanted inflammation and helps bones in their absorption of calcium.', 3: 'Human beings are the caretakers of the planet.', 4: 'Forest roads are essential to many facets of forest management.', 5: 'Spiders come from eggs.', 6: 'Plants adapt their growth and development to their local environment.', 7: 'Breeds have sex.', 8: 'People control animals.', 9: 'Geysers are quite rare, requiring a combination of water , heat , and fortuitous plumbing .'}
| 5 |
4,891 |
["At least one of two things is true: influenza still passes between humans and shearwater gulls, or if the statement that 'most beluga whales have life expectancy' is incorrect, then globalization is perceived as bringing unprecedented opportunities to billions of people.", 'If globalization is perceived as bringing unprecedented opportunities to billions of people, then some plant species contain chemicals that are unique and can only be found in the rainforests.', 'Provided that influenza still passes between humans and shearwater gulls, we know that either some people hate washing dishes because more dirty dishes magically appear over night or recycled materials are an essential feedstock for Minnesota manufacturers.', 'On the condition that influenza still passes between humans and shearwater gulls, it is definitely the case that the claim that either some people hate washing dishes because more dirty dishes magically appear over night or recycled materials are an essential feedstock for Minnesota manufacturers is false.', "On the condition that the notion that 'if globalization is perceived as bringing unprecedented opportunities to billions of people, then the statement that states some plant species contain chemicals that are unique and can only be found in the rainforests is false' is untrue, it is definitely the case that life causes pain.", "Assuming the notion that 'if globalization is perceived as bringing unprecedented opportunities to billions of people, then the statement that states some plant species contain chemicals that are unique and can only be found in the rainforests is false' is untrue, we know that it is not true that life causes pain."]
|
At least one of two things is true: influenza still passes between humans and shearwater gulls, or if the statement that 'most beluga whales have life expectancy' is incorrect, then globalization is perceived as bringing unprecedented opportunities to billions of people. If globalization is perceived as bringing unprecedented opportunities to billions of people, then some plant species contain chemicals that are unique and can only be found in the rainforests. Provided that influenza still passes between humans and shearwater gulls, we know that either some people hate washing dishes because more dirty dishes magically appear over night or recycled materials are an essential feedstock for Minnesota manufacturers. On the condition that influenza still passes between humans and shearwater gulls, it is definitely the case that the claim that either some people hate washing dishes because more dirty dishes magically appear over night or recycled materials are an essential feedstock for Minnesota manufacturers is false. On the condition that the notion that 'if globalization is perceived as bringing unprecedented opportunities to billions of people, then the statement that states some plant species contain chemicals that are unique and can only be found in the rainforests is false' is untrue, it is definitely the case that life causes pain. Assuming the notion that 'if globalization is perceived as bringing unprecedented opportunities to billions of people, then the statement that states some plant species contain chemicals that are unique and can only be found in the rainforests is false' is untrue, we know that it is not true that life causes pain.
|
Those that suggest most beluga whales have life expectancy are right.
|
Beluga whales eat fish.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If (Not [0].), then [1].).
Not [3]. [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Reductio Ad Absurdum:
If [3], then (Either [5] or [6].).
If [3], then (Not (Either [5] or [6].).).
Therefore, Not [3]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2].
If [1], then (Not [2].). [SC2-2]
Therefore, Not [1]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [1], then (Not [2].).).), then [4].
If (Not (If [1], then (Not [2].).).), then (Not [4].).
Therefore, If [1], then (Not [2].)..
|
{0: 'Most beluga whales have life expectancy.', 1: 'Globalization is perceived as bringing unprecedented opportunities to billions of people.', 2: 'Some plant species contain chemicals that are unique and can only be found in the rainforests.', 3: 'Influenza still passes between humans and shearwater gulls.', 4: 'Life causes pain.', 5: 'Some people hate washing dishes because more dirty dishes magically appear over night.', 6: 'Recycled materials are an essential feedstock for Minnesota manufacturers.'}
| 5 |
4,619 |
['Assuming it is not the case that either oceans are sailing or recycling can save money for manufacturers and their customers, we know that ovules are inside the ovary and develop into seeds.', "So long as it is not the case that either oceans are sailing or recycling can save money for manufacturers and their customers, 'the claim that ovules are inside the ovary and develop into seeds does not correspond with reality' is true.", "There is good reason to believe that either eye pressure is largely independent of blood pressure or prayer is the language of spirituality and improves the quality of man's being.", 'Should it be the case that eye pressure is largely independent of blood pressure, it follows that if oceans are sailing, then quality assurance is about processes .', "Assuming prayer is the language of spirituality and improves the quality of man's being, we know that if oceans are sailing, then quality assurance is about processes .", 'Assuming oceans are sailing, we know that perspiration causes a desire to bathes.', 'Once we know perspiration causes a desire to bathes, we also know that those that suggest quality assurance is about processes are wrong.']
|
Assuming it is not the case that either oceans are sailing or recycling can save money for manufacturers and their customers, we know that ovules are inside the ovary and develop into seeds. So long as it is not the case that either oceans are sailing or recycling can save money for manufacturers and their customers, 'the claim that ovules are inside the ovary and develop into seeds does not correspond with reality' is true. There is good reason to believe that either eye pressure is largely independent of blood pressure or prayer is the language of spirituality and improves the quality of man's being. Should it be the case that eye pressure is largely independent of blood pressure, it follows that if oceans are sailing, then quality assurance is about processes . Assuming prayer is the language of spirituality and improves the quality of man's being, we know that if oceans are sailing, then quality assurance is about processes . Assuming oceans are sailing, we know that perspiration causes a desire to bathes. Once we know perspiration causes a desire to bathes, we also know that those that suggest quality assurance is about processes are wrong.
|
It is true that recycling can save money for manufacturers and their customers.
|
It is true that recycling can save money for manufacturers and their customers.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or [0].).), then [3].
If (Not (Either [1] or [0].).), then (Not [3].).
Therefore, Either [1] or [0]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2]. [SC1-2]
If [1], then (Not [2].). [SC2-2]
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [1], then [2].).
If [5], then (If [1], then [2].).
Therefore, If [1], then [2]..
[SC2-2]
Hypothetical Syllogism:
If [1], then [6].
If [6], then (Not [2].).
Therefore, If [1], then (Not [2].)..
|
{0: 'Recycling can save money for manufacturers and their customers.', 1: 'Oceans are sailing.', 2: 'Quality assurance is about processes .', 3: 'Ovules are inside the ovary and develop into seeds.', 4: 'Eye pressure is largely independent of blood pressure.', 5: "Prayer is the language of spirituality and improves the quality of man's being.", 6: 'Perspiration causes a desire to bathes.'}
| 5 |
4,815 |
['Should it be the case that industrial agriculture puts animals in concentration camps where they become crazy and diseased, it follows that if female leatherback turtles dig pits, then macaque monkeys eat fruit , flowers , seeds , bark , leaves , shrimp , and insects .', 'Assuming most primates have resemblance, we know that if female leatherback turtles dig pits, then macaque monkeys eat fruit , flowers , seeds , bark , leaves , shrimp , and insects .', 'One may reasonably assume that if sex opens men up to rejection and sexual rejects are often seen as personal rejections, then some people mistakenly believe that macaque monkeys eat fruit , flowers , seeds , bark , leaves , shrimp , and insects .', 'It is reasonable to believe that sex opens men up to rejection and sexual rejects are often seen as personal rejections.', 'Provided that those that suggest either industrial agriculture puts animals in concentration camps where they become crazy and diseased or most primates have resemblance are wrong, we know that we know that the claim that abrasions are wounds in which the outer layer of the skin has been rubbed or scraped off is false.', "One may reasonably assume that if the notion that 'if those that suggest either industrial agriculture puts animals in concentration camps where they become crazy and diseased or most primates have resemblance are wrong, then abrasions are wounds in which the outer layer of the skin has been rubbed or scraped off' is untrue, then many factors contribute to the risk of a heart attack.", "So long as the notion that 'if those that suggest either industrial agriculture puts animals in concentration camps where they become crazy and diseased or most primates have resemblance are wrong, then abrasions are wounds in which the outer layer of the skin has been rubbed or scraped off' is untrue, 'the claim that many factors contribute to the risk of a heart attack does not reflect reality' is true."]
|
Should it be the case that industrial agriculture puts animals in concentration camps where they become crazy and diseased, it follows that if female leatherback turtles dig pits, then macaque monkeys eat fruit , flowers , seeds , bark , leaves , shrimp , and insects . Assuming most primates have resemblance, we know that if female leatherback turtles dig pits, then macaque monkeys eat fruit , flowers , seeds , bark , leaves , shrimp , and insects . One may reasonably assume that if sex opens men up to rejection and sexual rejects are often seen as personal rejections, then some people mistakenly believe that macaque monkeys eat fruit , flowers , seeds , bark , leaves , shrimp , and insects . It is reasonable to believe that sex opens men up to rejection and sexual rejects are often seen as personal rejections. Provided that those that suggest either industrial agriculture puts animals in concentration camps where they become crazy and diseased or most primates have resemblance are wrong, we know that we know that the claim that abrasions are wounds in which the outer layer of the skin has been rubbed or scraped off is false. One may reasonably assume that if the notion that 'if those that suggest either industrial agriculture puts animals in concentration camps where they become crazy and diseased or most primates have resemblance are wrong, then abrasions are wounds in which the outer layer of the skin has been rubbed or scraped off' is untrue, then many factors contribute to the risk of a heart attack. So long as the notion that 'if those that suggest either industrial agriculture puts animals in concentration camps where they become crazy and diseased or most primates have resemblance are wrong, then abrasions are wounds in which the outer layer of the skin has been rubbed or scraped off' is untrue, 'the claim that many factors contribute to the risk of a heart attack does not reflect reality' is true.
|
The statement, female leatherback turtles dig pits, does not hold.
|
The statement, female leatherback turtles dig pits, does not hold.
|
TRUE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [2] or [3]. [SC1-2]
If [2], then (If [0], then [1].).
If [3], then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [2] or [3].).), then [5]. [SC1-3]
If (Not (Either [2] or [3].).), then (Not [5].).
Therefore, Either [2] or [3]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If (Not (Either [2] or [3].).), then [5].).), then [6].
If (Not (If (Not (Either [2] or [3].).), then [5].).), then (Not [6].).
Therefore, If (Not (Either [2] or [3].).), then [5]..
[SC2-1]
Modus Ponens:
If [4], then (Not [1].).
[4]
Therefore, Not [1]..
|
{0: 'Female leatherback turtles dig pits.', 1: 'Macaque monkeys eat fruit , flowers , seeds , bark , leaves , shrimp , and insects .', 2: 'Industrial agriculture puts animals in concentration camps where they become crazy and diseased.', 3: 'Most primates have resemblance.', 4: 'Sex opens men up to rejection and sexual rejects are often seen as personal rejections.', 5: 'Abrasions are wounds in which the outer layer of the skin has been rubbed or scraped off.', 6: 'Many factors contribute to the risk of a heart attack.'}
| 5 |
4,365 |
['The statement, a fun run is a run, does not hold.', 'Assuming either some nervous tissue contains within craniums or most spiders have eight eyes, and the jumping spiders have the best eyesight of all, we know that either a fun run is a run or friction is a force that resists the sliding or rolling of one solid object over another.', "Whenever it is true that plants are vigorous and upright, 'either a fun run is a run or friction is a force that resists the sliding or rolling of one solid object over another' is true.", 'Either endotoxins also play an important role in the pathogenesis of gram-negative infections or either urbanization increasingly isolates the human population from native ecosystems or sperms swim with their tails.', 'Assuming either urbanization increasingly isolates the human population from native ecosystems or sperms swim with their tails, we know that either either some nervous tissue contains within craniums or most spiders have eight eyes, and the jumping spiders have the best eyesight of all or plants are vigorous and upright.', "So long as the statement 'if endotoxins also play an important role in the pathogenesis of gram-negative infections, then either either some nervous tissue contains within craniums or most spiders have eight eyes, and the jumping spiders have the best eyesight of all or plants are vigorous and upright' can be considered false, 'stress can come in many different forms' is true.", "It is rational to believe that either if fulminant hepatitis is rare, then provincial officers are peace officers or if the statement 'if endotoxins also play an important role in the pathogenesis of gram-negative infections, then either either some nervous tissue contains within craniums or most spiders have eight eyes, and the jumping spiders have the best eyesight of all or plants are vigorous and upright' can be considered false, then the notion that 'stress can come in many different forms' is untrue.", 'The claim that if fulminant hepatitis is rare, then provincial officers are peace officers has no merit.']
|
The statement, a fun run is a run, does not hold. Assuming either some nervous tissue contains within craniums or most spiders have eight eyes, and the jumping spiders have the best eyesight of all, we know that either a fun run is a run or friction is a force that resists the sliding or rolling of one solid object over another. Whenever it is true that plants are vigorous and upright, 'either a fun run is a run or friction is a force that resists the sliding or rolling of one solid object over another' is true. Either endotoxins also play an important role in the pathogenesis of gram-negative infections or either urbanization increasingly isolates the human population from native ecosystems or sperms swim with their tails. Assuming either urbanization increasingly isolates the human population from native ecosystems or sperms swim with their tails, we know that either either some nervous tissue contains within craniums or most spiders have eight eyes, and the jumping spiders have the best eyesight of all or plants are vigorous and upright. So long as the statement 'if endotoxins also play an important role in the pathogenesis of gram-negative infections, then either either some nervous tissue contains within craniums or most spiders have eight eyes, and the jumping spiders have the best eyesight of all or plants are vigorous and upright' can be considered false, 'stress can come in many different forms' is true. It is rational to believe that either if fulminant hepatitis is rare, then provincial officers are peace officers or if the statement 'if endotoxins also play an important role in the pathogenesis of gram-negative infections, then either either some nervous tissue contains within craniums or most spiders have eight eyes, and the jumping spiders have the best eyesight of all or plants are vigorous and upright' can be considered false, then the notion that 'stress can come in many different forms' is untrue. The claim that if fulminant hepatitis is rare, then provincial officers are peace officers has no merit.
|
friction is a force that resists the sliding or rolling of one solid object over another.
|
Some people mistakenly believe that friction is a force that resists the sliding or rolling of one solid object over another.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [2] or [3].) or [4]. [SC1-2]
If (Either [2] or [3].), then (Either [1] or [0].).
If [4], then (Either [1] or [0].).
Therefore, Either [1] or [0]..
[SC1-2]
Disjunction Elimination:
Either [5] or (Either [6] or [7].).
If [5], then (Either (Either [2] or [3].) or [4].). [SC2-3]
If (Either [6] or [7].), then (Either (Either [2] or [3].) or [4].).
Therefore, Either (Either [2] or [3].) or [4]..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If [5], then (Either (Either [2] or [3].) or [4].).).), then [8].
If (Not (If [5], then (Either (Either [2] or [3].) or [4].).).), then (Not [8].). [SC2-4]
Therefore, If [5], then (Either (Either [2] or [3].) or [4].)..
[SC2-4]
Disjunctive Syllogism:
Either (If [9], then [10].) or (If (Not (If [5], then (Either (Either [2] or [3].) or [4].).).), then (Not [8].).).
Not (If [9], then [10].).
Therefore, If (Not (If [5], then (Either (Either [2] or [3].) or [4].).).), then (Not [8].)..
|
{0: 'Friction is a force that resists the sliding or rolling of one solid object over another.', 1: 'A fun run is a run.', 2: 'Some nervous tissue contains within craniums.', 3: 'Most spiders have eight eyes, and the jumping spiders have the best eyesight of all.', 4: 'Plants are vigorous and upright.', 5: 'Endotoxins also play an important role in the pathogenesis of gram-negative infections.', 6: 'Urbanization increasingly isolates the human population from native ecosystems.', 7: 'Sperms swim with their tails.', 8: 'Stress can come in many different forms.', 9: 'Fulminant hepatitis is rare.', 10: 'Provincial officers are peace officers.'}
| 5 |
4,812 |
['When the claim that either most people learn to communicate using pictures at a very young age or scientists are people who make judgements based on what they see and as a result of tests conducted does not reflect reality is true, it follows that fear is a healthy emotion.', 'It is not true that organic cotton is grown without the use of harmful pesticides and chemicals.', "So long as the notion that 'if either nonverbal actions have a lot to do with what a person really means or men work for companies, then if fear is a healthy emotion, then organic cotton is grown without the use of harmful pesticides and chemicals' is untrue, 'current physics teaches that the act of observing changes what is observed' is true.", "So long as the notion that 'if either nonverbal actions have a lot to do with what a person really means or men work for companies, then if fear is a healthy emotion, then organic cotton is grown without the use of harmful pesticides and chemicals' is untrue, 'the statement, current physics teaches that the act of observing changes what is observed, does not hold' is true.", 'Provided that the claim that either nonverbal actions have a lot to do with what a person really means or men work for companies has no merit, we know that angular sizes can vary greatly depending on the object.', "Provided that the claim that either nonverbal actions have a lot to do with what a person really means or men work for companies has no merit, we know that the statement that 'angular sizes can vary greatly depending on the object' is incorrect."]
|
When the claim that either most people learn to communicate using pictures at a very young age or scientists are people who make judgements based on what they see and as a result of tests conducted does not reflect reality is true, it follows that fear is a healthy emotion. It is not true that organic cotton is grown without the use of harmful pesticides and chemicals. So long as the notion that 'if either nonverbal actions have a lot to do with what a person really means or men work for companies, then if fear is a healthy emotion, then organic cotton is grown without the use of harmful pesticides and chemicals' is untrue, 'current physics teaches that the act of observing changes what is observed' is true. So long as the notion that 'if either nonverbal actions have a lot to do with what a person really means or men work for companies, then if fear is a healthy emotion, then organic cotton is grown without the use of harmful pesticides and chemicals' is untrue, 'the statement, current physics teaches that the act of observing changes what is observed, does not hold' is true. Provided that the claim that either nonverbal actions have a lot to do with what a person really means or men work for companies has no merit, we know that angular sizes can vary greatly depending on the object. Provided that the claim that either nonverbal actions have a lot to do with what a person really means or men work for companies has no merit, we know that the statement that 'angular sizes can vary greatly depending on the object' is incorrect.
|
At least one of two things is true: most people learn to communicate using pictures at a very young age, or scientists are people who make judgements based on what they see and as a result of tests conducted.
|
The claim that either most people learn to communicate using pictures at a very young age or scientists are people who make judgements based on what they see and as a result of tests conducted does not correspond with reality.
|
FALSE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2].
Not [2]. [SC2-1]
Therefore, Either [0] or [1]..
[SC2-1]
Modus Tonens:
If [2], then [3]. [SC1-2]
Not [3].
Therefore, Not [2]..
[SC1-2]
Modus Ponens:
If (Either [4] or [5].), then (If [2], then [3].). [SC1-3]
Either [4] or [5]. [SC2-3]
Therefore, If [2], then [3]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If (Either [4] or [5].), then (If [2], then [3].).).), then [6].
If (Not (If (Either [4] or [5].), then (If [2], then [3].).).), then (Not [6].).
Therefore, If (Either [4] or [5].), then (If [2], then [3].)..
[SC2-3]
Reductio Ad Absurdum:
If (Not (Either [4] or [5].).), then [7].
If (Not (Either [4] or [5].).), then (Not [7].).
Therefore, Either [4] or [5]..
|
{0: 'Most people learn to communicate using pictures at a very young age.', 1: 'Scientists are people who make judgements based on what they see and as a result of tests conducted.', 2: 'Fear is a healthy emotion.', 3: 'Organic cotton is grown without the use of harmful pesticides and chemicals.', 4: 'Nonverbal actions have a lot to do with what a person really means.', 5: 'Men work for companies.', 6: 'Current physics teaches that the act of observing changes what is observed.', 7: 'Angular sizes can vary greatly depending on the object.'}
| 5 |
4,026 |
['Either one or both of these statements are true: prairie dogs are remarkably sociable animals, or if most lemurs spend their time up in the trees, resting, sleeping, feeding, and even giving birth, then most young trees produce fruit.', 'Assuming if most lemurs spend their time up in the trees, resting, sleeping, feeding, and even giving birth, then most young trees produce fruit, we know that society is a system of inherited forms reducing our humiliating passivity to nature.', "The statement 'happiness is the emotional reward of a successful human life' is true.", 'If either some mice live in communities or guppies come in a wide range of colors and fin shapes, then if happiness is the emotional reward of a successful human life, then pears are solids.', 'Either some mice live in communities or guppies come in a wide range of colors and fin shapes.', 'Either referees have (part) necks or if pears are solids, then if prairie dogs are remarkably sociable animals, then society is a system of inherited forms reducing our humiliating passivity to nature.', 'It is a common misconception that referees have (part) necks.']
|
Either one or both of these statements are true: prairie dogs are remarkably sociable animals, or if most lemurs spend their time up in the trees, resting, sleeping, feeding, and even giving birth, then most young trees produce fruit. Assuming if most lemurs spend their time up in the trees, resting, sleeping, feeding, and even giving birth, then most young trees produce fruit, we know that society is a system of inherited forms reducing our humiliating passivity to nature. The statement 'happiness is the emotional reward of a successful human life' is true. If either some mice live in communities or guppies come in a wide range of colors and fin shapes, then if happiness is the emotional reward of a successful human life, then pears are solids. Either some mice live in communities or guppies come in a wide range of colors and fin shapes. Either referees have (part) necks or if pears are solids, then if prairie dogs are remarkably sociable animals, then society is a system of inherited forms reducing our humiliating passivity to nature. It is a common misconception that referees have (part) necks.
|
Many people rightly believe that society is a system of inherited forms reducing our humiliating passivity to nature.
|
The statement that 'society is a system of inherited forms reducing our humiliating passivity to nature' is incorrect.
|
FALSE
|
Disjunction Elimination:
Either [1] or (If [2], then [3].).
If [1], then [0]. [SC2-1]
If (If [2], then [3].), then [0].
Therefore, [0].
[SC2-1]
Modus Ponens:
If [4], then (If [1], then [0].). [SC1-2]
[4]
Therefore, If [1], then [0]..
[SC1-2]
Hypothetical Syllogism:
If [4], then [5]. [SC1-3]
If [5], then (If [1], then [0].). [SC2-3]
Therefore, If [4], then (If [1], then [0].)..
[SC1-3]
Modus Ponens:
If (Either [6] or [7].), then (If [4], then [5].).
Either [6] or [7].
Therefore, If [4], then [5]..
[SC2-3]
Disjunctive Syllogism:
Either [8] or (If [5], then (If [1], then [0].).).
Not [8].
Therefore, If [5], then (If [1], then [0].)..
|
{0: 'Society is a system of inherited forms reducing our humiliating passivity to nature.', 1: 'Prairie dogs are remarkably sociable animals.', 2: 'Most lemurs spend their time up in the trees, resting, sleeping, feeding, and even giving birth.', 3: 'Most young trees produce fruit.', 4: 'Happiness is the emotional reward of a successful human life.', 5: 'Pears are solids.', 6: 'Some mice live in communities.', 7: 'Guppies come in a wide range of colors and fin shapes.', 8: 'Referees have (part) necks.'}
| 5 |
4,642 |
['We know that at least one of two things is true: condensates also offer the promise of very high sensitivity atomic interferometry, or thunderstorms can be scary because of the loud boom.', "Whenever it is true that thunderstorms can be scary because of the loud boom, 'circumcision greatly reduces the incidence of penile cancer' is true.", 'It is a simple truth that memory loss is a common complaint associated with aging.', 'Should it be the case that tradition specifically means the transmittal of teaching from a generation to another, it follows that fin whales have baleen.', 'If tradition specifically means the transmittal of teaching from a generation to another, then it is not the case that fin whales have baleen.', 'Given that it is a common misconception that if memory loss is a common complaint associated with aging, then if it is not true that if condensates also offer the promise of very high sensitivity atomic interferometry, then circumcision greatly reduces the incidence of penile cancer, then tradition specifically means the transmittal of teaching from a generation to another, it can be inferred that either many women have the innate capacity for further breast development or bearing capacity is the amount of weight that a soil can hold without caving in .', 'If it is a common misconception that if memory loss is a common complaint associated with aging, then if it is not true that if condensates also offer the promise of very high sensitivity atomic interferometry, then circumcision greatly reduces the incidence of penile cancer, then tradition specifically means the transmittal of teaching from a generation to another, then the statement that states either many women have the innate capacity for further breast development or bearing capacity is the amount of weight that a soil can hold without caving in is false.']
|
We know that at least one of two things is true: condensates also offer the promise of very high sensitivity atomic interferometry, or thunderstorms can be scary because of the loud boom. Whenever it is true that thunderstorms can be scary because of the loud boom, 'circumcision greatly reduces the incidence of penile cancer' is true. It is a simple truth that memory loss is a common complaint associated with aging. Should it be the case that tradition specifically means the transmittal of teaching from a generation to another, it follows that fin whales have baleen. If tradition specifically means the transmittal of teaching from a generation to another, then it is not the case that fin whales have baleen. Given that it is a common misconception that if memory loss is a common complaint associated with aging, then if it is not true that if condensates also offer the promise of very high sensitivity atomic interferometry, then circumcision greatly reduces the incidence of penile cancer, then tradition specifically means the transmittal of teaching from a generation to another, it can be inferred that either many women have the innate capacity for further breast development or bearing capacity is the amount of weight that a soil can hold without caving in . If it is a common misconception that if memory loss is a common complaint associated with aging, then if it is not true that if condensates also offer the promise of very high sensitivity atomic interferometry, then circumcision greatly reduces the incidence of penile cancer, then tradition specifically means the transmittal of teaching from a generation to another, then the statement that states either many women have the innate capacity for further breast development or bearing capacity is the amount of weight that a soil can hold without caving in is false.
|
The statement 'circumcision greatly reduces the incidence of penile cancer' is true.
|
The claim that circumcision greatly reduces the incidence of penile cancer does not reflect reality.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not (If [1], then [0].).), then [3]. [SC1-2]
Not [3]. [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Modus Ponens:
If [5], then (If (Not (If [1], then [0].).), then [3].). [SC1-3]
[5]
Therefore, If (Not (If [1], then [0].).), then [3]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If [5], then (If (Not (If [1], then [0].).), then [3].).).), then (Either [6] or [7].).
If (Not (If [5], then (If (Not (If [1], then [0].).), then [3].).).), then (Not (Either [6] or [7].).).
Therefore, If [5], then (If (Not (If [1], then [0].).), then [3].)..
[SC2-2]
Reductio Ad Absurdum:
If [3], then [4].
If [3], then (Not [4].).
Therefore, Not [3]..
|
{0: 'Circumcision greatly reduces the incidence of penile cancer.', 1: 'Condensates also offer the promise of very high sensitivity atomic interferometry.', 2: 'Thunderstorms can be scary because of the loud boom.', 3: 'Tradition specifically means the transmittal of teaching from a generation to another.', 4: 'Fin whales have baleen.', 5: 'Memory loss is a common complaint associated with aging.', 6: 'Many women have the innate capacity for further breast development.', 7: 'Bearing capacity is the amount of weight that a soil can hold without caving in .'}
| 5 |
4,417 |
["On the condition that beavers prosper in maple, aspen and willow environments, it is definitely the case that the statement 'many singles look at their body as part of their attraction to the opposite sex' can be considered false.", 'If the claim that if beavers prosper in maple, aspen and willow environments, then many singles look at their body as part of their attraction to the opposite sex is false, then fish have enzymes suitable for breaking down their particular foods.', 'There is good reason to believe that either saliva washes away sticky foods that help form plaque and strengthens teeth with minerals or springtails reach adulthood.', 'On the condition that smoking exposes the body to many cancer-causing chemicals that affect more than the lungs, it is definitely the case that if either saliva washes away sticky foods that help form plaque and strengthens teeth with minerals or springtails reach adulthood, then some people mistakenly believe that fish have enzymes suitable for breaking down their particular foods.', "So long as either decorum is propriety or some smoke causes premature death, 'if either saliva washes away sticky foods that help form plaque and strengthens teeth with minerals or springtails reach adulthood, then some people mistakenly believe that fish have enzymes suitable for breaking down their particular foods' is true.", 'On the condition that aD occurs primarily because of an imbalance in the body systems which control the blood pressure, it is definitely the case that either smoking exposes the body to many cancer-causing chemicals that affect more than the lungs or either decorum is propriety or some smoke causes premature death.', 'The statement that states aD occurs primarily because of an imbalance in the body systems which control the blood pressure is right.']
|
On the condition that beavers prosper in maple, aspen and willow environments, it is definitely the case that the statement 'many singles look at their body as part of their attraction to the opposite sex' can be considered false. If the claim that if beavers prosper in maple, aspen and willow environments, then many singles look at their body as part of their attraction to the opposite sex is false, then fish have enzymes suitable for breaking down their particular foods. There is good reason to believe that either saliva washes away sticky foods that help form plaque and strengthens teeth with minerals or springtails reach adulthood. On the condition that smoking exposes the body to many cancer-causing chemicals that affect more than the lungs, it is definitely the case that if either saliva washes away sticky foods that help form plaque and strengthens teeth with minerals or springtails reach adulthood, then some people mistakenly believe that fish have enzymes suitable for breaking down their particular foods. So long as either decorum is propriety or some smoke causes premature death, 'if either saliva washes away sticky foods that help form plaque and strengthens teeth with minerals or springtails reach adulthood, then some people mistakenly believe that fish have enzymes suitable for breaking down their particular foods' is true. On the condition that aD occurs primarily because of an imbalance in the body systems which control the blood pressure, it is definitely the case that either smoking exposes the body to many cancer-causing chemicals that affect more than the lungs or either decorum is propriety or some smoke causes premature death. The statement that states aD occurs primarily because of an imbalance in the body systems which control the blood pressure is right.
|
The claim that beavers prosper in maple, aspen and willow environments does not reflect reality.
|
The claim that beavers are located in maines has no merit.
|
Uncertain
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].).
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (If [0], then [1].).), then [2].
Not [2]. [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Modus Ponens:
If (Either [3] or [4].), then (Not [2].). [SC1-3]
Either [3] or [4].
Therefore, Not [2]..
[SC1-3]
Disjunction Elimination:
Either [5] or (Either [6] or [7].). [SC1-4]
If [5], then (If (Either [3] or [4].), then (Not [2].).).
If (Either [6] or [7].), then (If (Either [3] or [4].), then (Not [2].).).
Therefore, If (Either [3] or [4].), then (Not [2].)..
[SC1-4]
Modus Ponens:
If [8], then (Either [5] or (Either [6] or [7].).).
[8]
Therefore, Either [5] or (Either [6] or [7].)..
|
{0: 'Beavers prosper in maple, aspen and willow environments.', 1: 'Many singles look at their body as part of their attraction to the opposite sex.', 2: 'Fish have enzymes suitable for breaking down their particular foods.', 3: 'Saliva washes away sticky foods that help form plaque and strengthens teeth with minerals.', 4: 'Springtails reach adulthood.', 5: 'Smoking exposes the body to many cancer-causing chemicals that affect more than the lungs.', 6: 'Decorum is propriety.', 7: 'Some smoke causes premature death.', 8: 'AD occurs primarily because of an imbalance in the body systems which control the blood pressure.'}
| 5 |
4,907 |
['We know that the claim that bird life varies markedly across the state, responding to the conditions typical of the region is false.', "If mumps is endemic in most tropical areas of the world, and is common everywhere else, then abortion is the killing of a fetus in a woman's womb.", 'Given that everyday living requires courage if life is to be effective and bring happiness, it can be inferred that either bird life varies markedly across the state, responding to the conditions typical of the region or if the claim that plovers are small to medium size with stout bodies and a short neck and tail does not correspond with reality, then mumps is endemic in most tropical areas of the world, and is common everywhere else.', 'The idea that everyday living requires courage if life is to be effective and bring happiness is true.', 'We know that either a screenwriter is a scriptwriter or some elephants visit herds.', "Whenever it is true that a screenwriter is a scriptwriter, 'the claim that abortion is the killing of a fetus in a woman's womb does not correspond with reality' is true.", "Provided that some elephants visit herds, we know that the claim that abortion is the killing of a fetus in a woman's womb does not correspond with reality."]
|
We know that the claim that bird life varies markedly across the state, responding to the conditions typical of the region is false. If mumps is endemic in most tropical areas of the world, and is common everywhere else, then abortion is the killing of a fetus in a woman's womb. Given that everyday living requires courage if life is to be effective and bring happiness, it can be inferred that either bird life varies markedly across the state, responding to the conditions typical of the region or if the claim that plovers are small to medium size with stout bodies and a short neck and tail does not correspond with reality, then mumps is endemic in most tropical areas of the world, and is common everywhere else. The idea that everyday living requires courage if life is to be effective and bring happiness is true. We know that either a screenwriter is a scriptwriter or some elephants visit herds. Whenever it is true that a screenwriter is a scriptwriter, 'the claim that abortion is the killing of a fetus in a woman's womb does not correspond with reality' is true. Provided that some elephants visit herds, we know that the claim that abortion is the killing of a fetus in a woman's womb does not correspond with reality.
|
The statement that states plovers are small to medium size with stout bodies and a short neck and tail is right.
|
Some plovers have beaks.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then [1].). [SC1-2]
Not [2].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Ponens:
If [6], then (Either [2] or (If (Not [0].), then [1].).).
[6]
Therefore, Either [2] or (If (Not [0].), then [1].)..
[SC2-1]
Modus Tonens:
If [1], then [3].
Not [3]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Not [3].).
If [5], then (Not [3].).
Therefore, Not [3]..
|
{0: 'Plovers are small to medium size with stout bodies and a short neck and tail.', 1: 'Mumps is endemic in most tropical areas of the world, and is common everywhere else.', 2: 'Bird life varies markedly across the state, responding to the conditions typical of the region.', 3: "Abortion is the killing of a fetus in a woman's womb.", 4: 'A screenwriter is a scriptwriter.', 5: 'Some elephants visit herds.', 6: 'Everyday living requires courage if life is to be effective and bring happiness.'}
| 5 |
4,921 |
["So long as frozen water floats at the lake surface, 'membranes facilitate osmosis' is true.", "Given that it is not the case that either if persuasion is the deliberate attempt to change someone's attitude, then malaria is a curable disease for which a limited number of drugs are available or frozen water floats at the lake surface, it can be inferred that some children never learn how to manage themselves and make healthy choices.", 'Either religious freedom is safeguarded by the Constitution or some lice feed on blood.', "Whenever it is true that religious freedom is safeguarded by the Constitution, 'if if persuasion is the deliberate attempt to change someone's attitude, then malaria is a curable disease for which a limited number of drugs are available, then membranes facilitate osmosis' is true.", "When some lice feed on blood is true, it follows that if if persuasion is the deliberate attempt to change someone's attitude, then malaria is a curable disease for which a limited number of drugs are available, then membranes facilitate osmosis.", "The statement that 'inevitable change is change that's decided on and promoted by the dominant forces of society' is incorrect.", "On the condition that the statement that states if it is not the case that either if persuasion is the deliberate attempt to change someone's attitude, then malaria is a curable disease for which a limited number of drugs are available or frozen water floats at the lake surface, then the claim that some children never learn how to manage themselves and make healthy choices has no merit is false, it is definitely the case that erections occur when the penis gets stiff and hard - sometimes for no reason.", "If erections occur when the penis gets stiff and hard - sometimes for no reason, then inevitable change is change that's decided on and promoted by the dominant forces of society."]
|
So long as frozen water floats at the lake surface, 'membranes facilitate osmosis' is true. Given that it is not the case that either if persuasion is the deliberate attempt to change someone's attitude, then malaria is a curable disease for which a limited number of drugs are available or frozen water floats at the lake surface, it can be inferred that some children never learn how to manage themselves and make healthy choices. Either religious freedom is safeguarded by the Constitution or some lice feed on blood. Whenever it is true that religious freedom is safeguarded by the Constitution, 'if if persuasion is the deliberate attempt to change someone's attitude, then malaria is a curable disease for which a limited number of drugs are available, then membranes facilitate osmosis' is true. When some lice feed on blood is true, it follows that if if persuasion is the deliberate attempt to change someone's attitude, then malaria is a curable disease for which a limited number of drugs are available, then membranes facilitate osmosis. The statement that 'inevitable change is change that's decided on and promoted by the dominant forces of society' is incorrect. On the condition that the statement that states if it is not the case that either if persuasion is the deliberate attempt to change someone's attitude, then malaria is a curable disease for which a limited number of drugs are available or frozen water floats at the lake surface, then the claim that some children never learn how to manage themselves and make healthy choices has no merit is false, it is definitely the case that erections occur when the penis gets stiff and hard - sometimes for no reason. If erections occur when the penis gets stiff and hard - sometimes for no reason, then inevitable change is change that's decided on and promoted by the dominant forces of society.
|
Many people rightly believe that membranes facilitate osmosis.
|
Many people rightly believe that membranes facilitate osmosis.
|
TRUE
|
Disjunction Elimination:
Either (If [1], then [2].) or [3]. [SC1-1]
If (If [1], then [2].), then [0]. [SC2-1]
If [3], then [0].
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either (If [1], then [2].) or [3].).), then [6].
If (Not (Either (If [1], then [2].) or [3].).), then (Not [6].). [SC2-2]
Therefore, Either (If [1], then [2].) or [3]..
[SC2-2]
Modus Tonens:
If (Not (If (Not (Either (If [1], then [2].) or [3].).), then (Not [6].).).), then [7]. [SC1-3]
Not [7].
Therefore, If (Not (Either (If [1], then [2].) or [3].).), then (Not [6].)..
[SC1-3]
Hypothetical Syllogism:
If (Not (If (Not (Either (If [1], then [2].) or [3].).), then (Not [6].).).), then [8].
If [8], then [7].
Therefore, If (Not (If (Not (Either (If [1], then [2].) or [3].).), then (Not [6].).).), then [7]..
[SC2-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (If [1], then [2].), then [0].).
If [5], then (If (If [1], then [2].), then [0].).
Therefore, If (If [1], then [2].), then [0]..
|
{0: 'Membranes facilitate osmosis.', 1: "Persuasion is the deliberate attempt to change someone's attitude.", 2: 'Malaria is a curable disease for which a limited number of drugs are available.', 3: 'Frozen water floats at the lake surface.', 4: 'Religious freedom is safeguarded by the Constitution.', 5: 'Some lice feed on blood.', 6: 'Some children never learn how to manage themselves and make healthy choices.', 7: "Inevitable change is change that's decided on and promoted by the dominant forces of society.", 8: 'Erections occur when the penis gets stiff and hard - sometimes for no reason.'}
| 5 |
4,003 |
['We know that either ethicists likewise contrast performance and motive in the religious life or a salmonberry is a bramble.', 'One may reasonably assume that if a salmonberry is a bramble, then flower color can be blue, pink and white.', 'If some terrestrial vertebrates retain fluid, then plots have regeneration.', 'Provided that plots have regeneration, we know that magnesium enhances circulation, reduces blood pressure and arrhythmias.', 'Should it be the case that flower color can be blue, pink and white, it follows that stars generally form through a fragmented collapse of a molecular cloud as a group or cluster.', 'Provided that stars generally form through a fragmented collapse of a molecular cloud as a group or cluster, we know that magnesium enhances circulation, reduces blood pressure and arrhythmias.', 'One may reasonably assume that if the statement, if ethicists likewise contrast performance and motive in the religious life, then some terrestrial vertebrates retain fluid, does not hold, then if sexual intimacy indicates deep love, exclusive and profound relationship, long-term commitment, then women are more prone to certain types of sprains, strains and tears.', 'The statement, if sexual intimacy indicates deep love, exclusive and profound relationship, long-term commitment, then women are more prone to certain types of sprains, strains and tears, does not hold.']
|
We know that either ethicists likewise contrast performance and motive in the religious life or a salmonberry is a bramble. One may reasonably assume that if a salmonberry is a bramble, then flower color can be blue, pink and white. If some terrestrial vertebrates retain fluid, then plots have regeneration. Provided that plots have regeneration, we know that magnesium enhances circulation, reduces blood pressure and arrhythmias. Should it be the case that flower color can be blue, pink and white, it follows that stars generally form through a fragmented collapse of a molecular cloud as a group or cluster. Provided that stars generally form through a fragmented collapse of a molecular cloud as a group or cluster, we know that magnesium enhances circulation, reduces blood pressure and arrhythmias. One may reasonably assume that if the statement, if ethicists likewise contrast performance and motive in the religious life, then some terrestrial vertebrates retain fluid, does not hold, then if sexual intimacy indicates deep love, exclusive and profound relationship, long-term commitment, then women are more prone to certain types of sprains, strains and tears. The statement, if sexual intimacy indicates deep love, exclusive and profound relationship, long-term commitment, then women are more prone to certain types of sprains, strains and tears, does not hold.
|
We can assume that magnesium enhances circulation, reduces blood pressure and arrhythmias.
|
Magnesium relaxes bronchial smooth muscles, and has shown benefit n asthma, a related condtion.
|
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]. [SC2-2]
If [4], then [2].
Therefore, Either [1] or [2]..
[SC2-2]
Modus Tonens:
If (Not (If [3], then [1].).), then (If [7], then [8].).
Not (If [7], then [8].).
Therefore, If [3], then [1]..
[SC2-1]
Hypothetical Syllogism:
If [1], then [5].
If [5], then [0].
Therefore, If [1], then [0]..
[SC3-1]
Hypothetical Syllogism:
If [2], then [6].
If [6], then [0].
Therefore, If [2], then [0]..
|
{0: 'Magnesium enhances circulation, reduces blood pressure and arrhythmias.', 1: 'Some terrestrial vertebrates retain fluid.', 2: 'Flower color can be blue, pink and white.', 3: 'Ethicists likewise contrast performance and motive in the religious life.', 4: 'A salmonberry is a bramble.', 5: 'Plots have regeneration.', 6: 'Stars generally form through a fragmented collapse of a molecular cloud as a group or cluster.', 7: 'Sexual intimacy indicates deep love, exclusive and profound relationship, long-term commitment.', 8: 'Women are more prone to certain types of sprains, strains and tears.'}
| 5 |
4,134 |
["So long as either indigenous peoples live in all the countries of Latin America except Uruguay or pancreatic enzymes break down partially digested food from the stomach into simple compounds, 'the claim that ethanol is a renewable resource does not reflect reality' is true.", 'At least one of two things is true: indigenous peoples live in all the countries of Latin America except Uruguay, or pancreatic enzymes break down partially digested food from the stomach into simple compounds.', "So long as the claim that if the statement, either ethanol is a renewable resource or the notion that 'restaurants have (part) windows' is untrue, does not hold, then pulsars send radio flashes sweeping across the sky like lighthouse beacons has no merit, 'common cold is a communicable disease' is true.", "If the claim that if the statement, either ethanol is a renewable resource or the notion that 'restaurants have (part) windows' is untrue, does not hold, then pulsars send radio flashes sweeping across the sky like lighthouse beacons has no merit, then the claim that common cold is a communicable disease is false.", "Should it be the case that the statement that states if the statement, either ethanol is a renewable resource or the notion that 'restaurants have (part) windows' is untrue, does not hold, then the claim that pulsars send radio flashes sweeping across the sky like lighthouse beacons does not correspond with reality is false, it follows that walruses also use the tusks for dragging themselves out of the water on the shore.", 'The claim that walruses also use the tusks for dragging themselves out of the water on the shore does not reflect reality.']
|
So long as either indigenous peoples live in all the countries of Latin America except Uruguay or pancreatic enzymes break down partially digested food from the stomach into simple compounds, 'the claim that ethanol is a renewable resource does not reflect reality' is true. At least one of two things is true: indigenous peoples live in all the countries of Latin America except Uruguay, or pancreatic enzymes break down partially digested food from the stomach into simple compounds. So long as the claim that if the statement, either ethanol is a renewable resource or the notion that 'restaurants have (part) windows' is untrue, does not hold, then pulsars send radio flashes sweeping across the sky like lighthouse beacons has no merit, 'common cold is a communicable disease' is true. If the claim that if the statement, either ethanol is a renewable resource or the notion that 'restaurants have (part) windows' is untrue, does not hold, then pulsars send radio flashes sweeping across the sky like lighthouse beacons has no merit, then the claim that common cold is a communicable disease is false. Should it be the case that the statement that states if the statement, either ethanol is a renewable resource or the notion that 'restaurants have (part) windows' is untrue, does not hold, then the claim that pulsars send radio flashes sweeping across the sky like lighthouse beacons does not correspond with reality is false, it follows that walruses also use the tusks for dragging themselves out of the water on the shore. The claim that walruses also use the tusks for dragging themselves out of the water on the shore does not reflect reality.
|
The notion that 'restaurants have (part) windows' is untrue.
|
The notion that 'restaurants have (part) windows' is untrue.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or (Not [0].).).), then [4]. [SC1-2]
If (Not (Either [1] or (Not [0].).).), then (Not [4].). [SC2-2]
Therefore, Either [1] or (Not [0].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (Either [1] or (Not [0].).).), then [4].).), then [5].
If (Not (If (Not (Either [1] or (Not [0].).).), then [4].).), then (Not [5].).
Therefore, If (Not (Either [1] or (Not [0].).).), then [4]..
[SC2-2]
Modus Tonens:
If (Not (If (Not (Either [1] or (Not [0].).).), then (Not [4].).).), then [6].
Not [6].
Therefore, If (Not (Either [1] or (Not [0].).).), then (Not [4].)..
[SC2-1]
Modus Ponens:
If (Either [2] or [3].), then (Not [1].).
Either [2] or [3].
Therefore, Not [1]..
|
{0: 'Restaurants have (part) windows.', 1: 'Ethanol is a renewable resource.', 2: 'Indigenous peoples live in all the countries of Latin America except Uruguay.', 3: 'Pancreatic enzymes break down partially digested food from the stomach into simple compounds.', 4: 'Pulsars send radio flashes sweeping across the sky like lighthouse beacons.', 5: 'Common cold is a communicable disease.', 6: 'Walruses also use the tusks for dragging themselves out of the water on the shore.'}
| 5 |
4,355 |
["Whenever it is true that some people mistakenly believe that most hardy plants survive cold climates, 'bison mature at three years old' is true.", 'Either one or both of these statements are true: nutritionists say such extreme eating habits can be extremely dangerous, or either most deer have sides or bees content themselves with gathering the honey dew from the leaves but certain ants go farther.', 'On the condition that either most deer have sides or bees content themselves with gathering the honey dew from the leaves but certain ants go farther, it is definitely the case that those that suggest bison mature at three years old are wrong.', 'We know that either memos are documents or if those that suggest if nutritionists say such extreme eating habits can be extremely dangerous, then those that suggest bison mature at three years old are wrong are wrong, then canadian birds migrate to the southern United States.', 'It is a common misconception that memos are documents.', 'Either droughts reduce or destroy the maize crop or those that suggest canadian birds migrate to the southern United States are wrong.', 'The claim that droughts reduce or destroy the maize crop does not correspond with reality.']
|
Whenever it is true that some people mistakenly believe that most hardy plants survive cold climates, 'bison mature at three years old' is true. Either one or both of these statements are true: nutritionists say such extreme eating habits can be extremely dangerous, or either most deer have sides or bees content themselves with gathering the honey dew from the leaves but certain ants go farther. On the condition that either most deer have sides or bees content themselves with gathering the honey dew from the leaves but certain ants go farther, it is definitely the case that those that suggest bison mature at three years old are wrong. We know that either memos are documents or if those that suggest if nutritionists say such extreme eating habits can be extremely dangerous, then those that suggest bison mature at three years old are wrong are wrong, then canadian birds migrate to the southern United States. It is a common misconception that memos are documents. Either droughts reduce or destroy the maize crop or those that suggest canadian birds migrate to the southern United States are wrong. The claim that droughts reduce or destroy the maize crop does not correspond with reality.
|
Many people rightly believe that most hardy plants survive cold climates.
|
It is not the case that most hardy plants survive cold climates.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [2] or (Either [3] or [4].).
If [2], then (Not [1].). [SC2-2]
If (Either [3] or [4].), then (Not [1].).
Therefore, Not [1]..
[SC2-2]
Modus Tonens:
If (Not (If [2], then (Not [1].).).), then [5]. [SC1-3]
Not [5]. [SC2-3]
Therefore, If [2], then (Not [1].)..
[SC1-3]
Disjunctive Syllogism:
Either [6] or (If (Not (If [2], then (Not [1].).).), then [5].).
Not [6].
Therefore, If (Not (If [2], then (Not [1].).).), then [5]..
[SC2-3]
Disjunctive Syllogism:
Either [7] or (Not [5].).
Not [7].
Therefore, Not [5]..
|
{0: 'Most hardy plants survive cold climates.', 1: 'Bison mature at three years old.', 2: 'Nutritionists say such extreme eating habits can be extremely dangerous.', 3: 'Most deer have sides.', 4: 'Bees content themselves with gathering the honey dew from the leaves but certain ants go farther.', 5: 'Canadian birds migrate to the southern United States.', 6: 'Memos are documents.', 7: 'Droughts reduce or destroy the maize crop.'}
| 5 |
4,877 |
['Either one or both of these statements are true: environmental problems are also related to issues of production such as poverty and technology, or if children use salt, then anxiety is the primary internalizing reason for child mental health referrals.', 'We know that either illustrators use their knowledge and skills to help scientists interpret their studies or most studies indicate that estrogen increases plasma triglyceride levels.', "So long as affected people are more likely to form kidney stones, 'the claim that environmental problems are also related to issues of production such as poverty and technology does not correspond with reality' is true.", 'It is a simple truth that affected people are more likely to form kidney stones.', 'When either illustrators use their knowledge and skills to help scientists interpret their studies or most studies indicate that estrogen increases plasma triglyceride levels is true, it follows that urethras have functions.', "So long as urethras have functions, 'the claim that anxiety is the primary internalizing reason for child mental health referrals is false' is true."]
|
Either one or both of these statements are true: environmental problems are also related to issues of production such as poverty and technology, or if children use salt, then anxiety is the primary internalizing reason for child mental health referrals. We know that either illustrators use their knowledge and skills to help scientists interpret their studies or most studies indicate that estrogen increases plasma triglyceride levels. So long as affected people are more likely to form kidney stones, 'the claim that environmental problems are also related to issues of production such as poverty and technology does not correspond with reality' is true. It is a simple truth that affected people are more likely to form kidney stones. When either illustrators use their knowledge and skills to help scientists interpret their studies or most studies indicate that estrogen increases plasma triglyceride levels is true, it follows that urethras have functions. So long as urethras have functions, 'the claim that anxiety is the primary internalizing reason for child mental health referrals is false' is true.
|
It is not the case that children use salt.
|
It is the case that children use salt.
|
FALSE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [0], then [1].).
Not [2]. [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Modus Ponens:
If [5], then (Not [2].).
[5]
Therefore, Not [2]..
[SC2-1]
Modus Ponens:
If (Either [3] or [4].), then (Not [1].). [SC1-2]
Either [3] or [4].
Therefore, Not [1]..
[SC1-2]
Hypothetical Syllogism:
If (Either [3] or [4].), then [6].
If [6], then (Not [1].).
Therefore, If (Either [3] or [4].), then (Not [1].)..
|
{0: 'Children use salt.', 1: 'Anxiety is the primary internalizing reason for child mental health referrals.', 2: 'Environmental problems are also related to issues of production such as poverty and technology.', 3: 'Illustrators use their knowledge and skills to help scientists interpret their studies.', 4: 'Most studies indicate that estrogen increases plasma triglyceride levels.', 5: 'Affected people are more likely to form kidney stones.', 6: 'Urethras have functions.'}
| 5 |
4,768 |
['We know that either young people learn that risk and initial failure are part of achievement and success or it is a common misconception that temperatures rise, nuclear fusion begins, and stars become energy producing.', 'Once we know it is not the case that if if bulls fight with each other over control of the cows by attacking each other with their antlers, then tails have length, then the claim that young people learn that risk and initial failure are part of achievement and success has no merit, we also know that either internalized oppression is always an involuntary reaction to the experience of oppression or people think of objects as having color.', "The statement that 'either internalized oppression is always an involuntary reaction to the experience of oppression or people think of objects as having color' is incorrect.", "It is rational to believe that either either cardinals are leaders or monkeys simply sleep on convenient tree branches without making nests or some schools have machines that sell tampons or pads in the girls' bathroom.", "On the condition that some schools have machines that sell tampons or pads in the girls' bathroom, it is definitely the case that if bulls fight with each other over control of the cows by attacking each other with their antlers, then tails have length.", 'Provided that butane is fuel, we know that if either cardinals are leaders or monkeys simply sleep on convenient tree branches without making nests, then if bulls fight with each other over control of the cows by attacking each other with their antlers, then tails have length.', "The statement 'butane is fuel' can be considered true."]
|
We know that either young people learn that risk and initial failure are part of achievement and success or it is a common misconception that temperatures rise, nuclear fusion begins, and stars become energy producing. Once we know it is not the case that if if bulls fight with each other over control of the cows by attacking each other with their antlers, then tails have length, then the claim that young people learn that risk and initial failure are part of achievement and success has no merit, we also know that either internalized oppression is always an involuntary reaction to the experience of oppression or people think of objects as having color. The statement that 'either internalized oppression is always an involuntary reaction to the experience of oppression or people think of objects as having color' is incorrect. It is rational to believe that either either cardinals are leaders or monkeys simply sleep on convenient tree branches without making nests or some schools have machines that sell tampons or pads in the girls' bathroom. On the condition that some schools have machines that sell tampons or pads in the girls' bathroom, it is definitely the case that if bulls fight with each other over control of the cows by attacking each other with their antlers, then tails have length. Provided that butane is fuel, we know that if either cardinals are leaders or monkeys simply sleep on convenient tree branches without making nests, then if bulls fight with each other over control of the cows by attacking each other with their antlers, then tails have length. The statement 'butane is fuel' can be considered true.
|
It is a common misconception that temperatures rise, nuclear fusion begins, and stars become energy producing.
|
It is a common misconception that temperatures rise, nuclear fusion begins, and stars become energy producing.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or (Not [0].).
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC2-1]
Modus Ponens:
If (If [2], then [3].), then (Not [1].). [SC1-2]
If [2], then [3]. [SC2-2]
Therefore, Not [1]..
[SC1-2]
Modus Tonens:
If (Not (If (If [2], then [3].), then (Not [1].).).), then (Either [4] or [5].).
Not (Either [4] or [5].).
Therefore, If (If [2], then [3].), then (Not [1].)..
[SC2-2]
Disjunction Elimination:
Either (Either [6] or [7].) or [8].
If (Either [6] or [7].), then (If [2], then [3].). [SC2-3]
If [8], then (If [2], then [3].).
Therefore, If [2], then [3]..
[SC2-3]
Modus Ponens:
If [9], then (If (Either [6] or [7].), then (If [2], then [3].).).
[9]
Therefore, If (Either [6] or [7].), then (If [2], then [3].)..
|
{0: 'Temperatures rise, nuclear fusion begins, and stars become energy producing.', 1: 'Young people learn that risk and initial failure are part of achievement and success.', 2: 'Bulls fight with each other over control of the cows by attacking each other with their antlers.', 3: 'Tails have length.', 4: 'Internalized oppression is always an involuntary reaction to the experience of oppression.', 5: 'People think of objects as having color.', 6: 'Cardinals are leaders.', 7: 'Monkeys simply sleep on convenient tree branches without making nests.', 8: "Some schools have machines that sell tampons or pads in the girls' bathroom.", 9: 'Butane is fuel.'}
| 5 |
4,836 |
['We know that either many parents see their children as exceptionally bright or at least brighter than the next child or snails can defoliate young trees and damage fruit.', 'Should it be the case that many parents see their children as exceptionally bright or at least brighter than the next child, it follows that the claim that some dogs are diagnosed with kidney diseases is false.', "Whenever it is true that those that suggest either hEAT is a balloon-borne superconducting magnetic spectrometer or if snails can defoliate young trees and damage fruit, then the claim that some dogs are diagnosed with kidney diseases is false are wrong, 'faith means fidelity, loyalty, and honor among men' is true.", 'It is a common misconception that faith means fidelity, loyalty, and honor among men.', 'The claim that parents are also a prime source of food has no merit.', "It is rational to believe that either seeds consist of outer layers or either parents are also a prime source of food or the statement that 'hEAT is a balloon-borne superconducting magnetic spectrometer' is incorrect.", 'The statement, seeds consist of outer layers, does not hold.']
|
We know that either many parents see their children as exceptionally bright or at least brighter than the next child or snails can defoliate young trees and damage fruit. Should it be the case that many parents see their children as exceptionally bright or at least brighter than the next child, it follows that the claim that some dogs are diagnosed with kidney diseases is false. Whenever it is true that those that suggest either hEAT is a balloon-borne superconducting magnetic spectrometer or if snails can defoliate young trees and damage fruit, then the claim that some dogs are diagnosed with kidney diseases is false are wrong, 'faith means fidelity, loyalty, and honor among men' is true. It is a common misconception that faith means fidelity, loyalty, and honor among men. The claim that parents are also a prime source of food has no merit. It is rational to believe that either seeds consist of outer layers or either parents are also a prime source of food or the statement that 'hEAT is a balloon-borne superconducting magnetic spectrometer' is incorrect. The statement, seeds consist of outer layers, does not hold.
|
The claim that some dogs are diagnosed with kidney diseases is false.
|
The claim that some dogs are diagnosed with kidney diseases is false.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then (Not [0].).
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC3-1]
Disjunctive Syllogism:
Either [3] or (If [2], then (Not [0].).). [SC1-2]
Not [3]. [SC2-2]
Therefore, If [2], then (Not [0].)..
[SC1-2]
Modus Tonens:
If (Not (Either [3] or (If [2], then (Not [0].).).).), then [5].
Not [5].
Therefore, Either [3] or (If [2], then (Not [0].).)..
[SC2-2]
Disjunctive Syllogism:
Either [4] or (Not [3].). [SC1-3]
Not [4].
Therefore, Not [3]..
[SC1-3]
Disjunctive Syllogism:
Either [6] or (Either [4] or (Not [3].).).
Not [6].
Therefore, Either [4] or (Not [3].)..
|
{0: 'Some dogs are diagnosed with kidney diseases.', 1: 'Many parents see their children as exceptionally bright or at least brighter than the next child.', 2: 'Snails can defoliate young trees and damage fruit.', 3: 'HEAT is a balloon-borne superconducting magnetic spectrometer.', 4: 'Parents are also a prime source of food.', 5: 'Faith means fidelity, loyalty, and honor among men.', 6: 'Seeds consist of outer layers.'}
| 5 |
4,561 |
['It is a fact that either either business affects social change and is influenced by it or sexual assault is an extreme form of sexual harassment or full moons occur when the sun, Earth and moon are lined up.', 'On the condition that either business affects social change and is influenced by it or sexual assault is an extreme form of sexual harassment, it is definitely the case that either seed is food for birds of the air, symbol of the demonic or an inheritor is an acquirer.', 'Provided that full moons occur when the sun, Earth and moon are lined up, we know that either seed is food for birds of the air, symbol of the demonic or an inheritor is an acquirer.', 'There is good reason to believe that either conflict is a part of the life of the church or either rope burns on arms, legs, neck or torso or fecal flotation is the most accurate way to detect most internal parasites.', 'Assuming conflict is a part of the life of the church, we know that if seed is food for birds of the air, symbol of the demonic, then larva are filter feeders on plant and other decaying deris under water.', 'It is a fact that either pure phosphorus exists in several forms called allotropes or if an inheritor is an acquirer, then larva are filter feeders on plant and other decaying deris under water.', 'It is not the case that pure phosphorus exists in several forms called allotropes.', 'Once we know either rope burns on arms, legs, neck or torso or fecal flotation is the most accurate way to detect most internal parasites, we also know that bats have (part) quill feathers.', 'Should it be the case that bats have (part) quill feathers, it follows that if seed is food for birds of the air, symbol of the demonic, then larva are filter feeders on plant and other decaying deris under water.']
|
It is a fact that either either business affects social change and is influenced by it or sexual assault is an extreme form of sexual harassment or full moons occur when the sun, Earth and moon are lined up. On the condition that either business affects social change and is influenced by it or sexual assault is an extreme form of sexual harassment, it is definitely the case that either seed is food for birds of the air, symbol of the demonic or an inheritor is an acquirer. Provided that full moons occur when the sun, Earth and moon are lined up, we know that either seed is food for birds of the air, symbol of the demonic or an inheritor is an acquirer. There is good reason to believe that either conflict is a part of the life of the church or either rope burns on arms, legs, neck or torso or fecal flotation is the most accurate way to detect most internal parasites. Assuming conflict is a part of the life of the church, we know that if seed is food for birds of the air, symbol of the demonic, then larva are filter feeders on plant and other decaying deris under water. It is a fact that either pure phosphorus exists in several forms called allotropes or if an inheritor is an acquirer, then larva are filter feeders on plant and other decaying deris under water. It is not the case that pure phosphorus exists in several forms called allotropes. Once we know either rope burns on arms, legs, neck or torso or fecal flotation is the most accurate way to detect most internal parasites, we also know that bats have (part) quill feathers. Should it be the case that bats have (part) quill feathers, it follows that if seed is food for birds of the air, symbol of the demonic, then larva are filter feeders on plant and other decaying deris under water.
|
It is fair to say that larva are filter feeders on plant and other decaying deris under water.
|
The statement that 'larva are filter feeders on plant and other decaying deris under water' is incorrect.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [6] or [7].) or [8].
If (Either [6] or [7].), then (Either [1] or [2].).
If [8], then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC2-1]
Disjunction Elimination:
Either [3] or (Either [4] or [5].).
If [3], then (If [1], then [0].).
If (Either [4] or [5].), then (If [1], then [0].). [SC3-2]
Therefore, If [1], then [0]..
[SC3-2]
Hypothetical Syllogism:
If (Either [4] or [5].), then [10].
If [10], then (If [1], then [0].).
Therefore, If (Either [4] or [5].), then (If [1], then [0].)..
[SC3-1]
Disjunctive Syllogism:
Either [9] or (If [2], then [0].).
Not [9].
Therefore, If [2], then [0]..
|
{0: 'Larva are filter feeders on plant and other decaying deris under water.', 1: 'Seed is food for birds of the air, symbol of the demonic.', 2: 'An inheritor is an acquirer.', 3: 'Conflict is a part of the life of the church.', 4: 'Rope burns on arms, legs, neck or torso.', 5: 'Fecal flotation is the most accurate way to detect most internal parasites.', 6: 'Business affects social change and is influenced by it.', 7: 'Sexual assault is an extreme form of sexual harassment.', 8: 'Full moons occur when the sun, Earth and moon are lined up.', 9: 'Pure phosphorus exists in several forms called allotropes.', 10: 'Bats have (part) quill feathers.'}
| 5 |
4,892 |
["Whenever it is true that the notion that 'if either some male koalas have patches or hippos weigh pounds, then some goats graze perennial grass' is untrue, 'cohorts are subsets of populations composed of individuals of similar age' is true.", 'Some people mistakenly believe that cohorts are subsets of populations composed of individuals of similar age.', 'Once we know if blennies are generally small fish, then gap junctions serve as direct connection between cytoplasm of adjacent cells, we also know that some male koalas have patches.', "Whenever it is true that light rays converge at principal focus of a lens, 'hippos weigh pounds' is true.", 'There is good reason to believe that either mitochondria are somewhat like cells within cells or either if blennies are generally small fish, then gap junctions serve as direct connection between cytoplasm of adjacent cells or light rays converge at principal focus of a lens.', 'If mitochondria are somewhat like cells within cells, then insects have natural enemies, too.', 'The statement, insects have natural enemies, too, does not hold.']
|
Whenever it is true that the notion that 'if either some male koalas have patches or hippos weigh pounds, then some goats graze perennial grass' is untrue, 'cohorts are subsets of populations composed of individuals of similar age' is true. Some people mistakenly believe that cohorts are subsets of populations composed of individuals of similar age. Once we know if blennies are generally small fish, then gap junctions serve as direct connection between cytoplasm of adjacent cells, we also know that some male koalas have patches. Whenever it is true that light rays converge at principal focus of a lens, 'hippos weigh pounds' is true. There is good reason to believe that either mitochondria are somewhat like cells within cells or either if blennies are generally small fish, then gap junctions serve as direct connection between cytoplasm of adjacent cells or light rays converge at principal focus of a lens. If mitochondria are somewhat like cells within cells, then insects have natural enemies, too. The statement, insects have natural enemies, too, does not hold.
|
We can assume that some goats graze perennial grass.
|
Goats have very destructive grazing habits, as they can completely strip shrubs of bark and leaves.
|
Uncertain
|
Modus Ponens:
If (Either [1] or [2].), then [0]. [SC1-1]
Either [1] or [2]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Either [1] or [2].), then [0].).), then [6].
Not [6].
Therefore, If (Either [1] or [2].), then [0]..
[SC2-1]
Constructive Dilemma:
Either (If [3], then [4].) or [5]. [SC1-2]
If (If [3], then [4].), then [1].
If [5], then [2].
Therefore, Either [1] or [2]..
[SC1-2]
Disjunctive Syllogism:
Either [7] or (Either (If [3], then [4].) or [5].).
Not [7]. [SC2-3]
Therefore, Either (If [3], then [4].) or [5]..
[SC2-3]
Modus Tonens:
If [7], then [8].
Not [8].
Therefore, Not [7]..
|
{0: 'Some goats graze perennial grass.', 1: 'Some male koalas have patches.', 2: 'Hippos weigh pounds.', 3: 'Blennies are generally small fish.', 4: 'Gap junctions serve as direct connection between cytoplasm of adjacent cells.', 5: 'Light rays converge at principal focus of a lens.', 6: 'Cohorts are subsets of populations composed of individuals of similar age.', 7: 'Mitochondria are somewhat like cells within cells.', 8: 'Insects have natural enemies, too.'}
| 5 |
4,225 |
["When some people mistakenly believe that some crocodilians attack humans is true, it follows that the statement that 'folly is play' is incorrect.", 'When some people mistakenly believe that some crocodilians attack humans is true, it follows that aphids also have a proboscis originating between and behind the forelegs.', 'Assuming dogs are prone to ear mites and allergies, we know that if the statement that states if aphids also have a proboscis originating between and behind the forelegs, then folly is play is false, then television is consumed in vast quantities around the world.', 'It is true that dogs are prone to ear mites and allergies.', "So long as it is a common misconception that if the statement that states if aphids also have a proboscis originating between and behind the forelegs, then folly is play is false, then the claim that television is consumed in vast quantities around the world does not correspond with reality, 'some mistletoes cause inflammatory reaction' is true.", 'Given that it is a common misconception that if the statement that states if aphids also have a proboscis originating between and behind the forelegs, then folly is play is false, then the claim that television is consumed in vast quantities around the world does not correspond with reality, it can be inferred that it is a common misconception that some mistletoes cause inflammatory reaction.']
|
When some people mistakenly believe that some crocodilians attack humans is true, it follows that the statement that 'folly is play' is incorrect. When some people mistakenly believe that some crocodilians attack humans is true, it follows that aphids also have a proboscis originating between and behind the forelegs. Assuming dogs are prone to ear mites and allergies, we know that if the statement that states if aphids also have a proboscis originating between and behind the forelegs, then folly is play is false, then television is consumed in vast quantities around the world. It is true that dogs are prone to ear mites and allergies. So long as it is a common misconception that if the statement that states if aphids also have a proboscis originating between and behind the forelegs, then folly is play is false, then the claim that television is consumed in vast quantities around the world does not correspond with reality, 'some mistletoes cause inflammatory reaction' is true. Given that it is a common misconception that if the statement that states if aphids also have a proboscis originating between and behind the forelegs, then folly is play is false, then the claim that television is consumed in vast quantities around the world does not correspond with reality, it can be inferred that it is a common misconception that some mistletoes cause inflammatory reaction.
|
It is rational to agree that some crocodilians attack humans.
|
It is a common misconception that some crocodilians attack humans.
|
FALSE
|
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]
Reductio Ad Absurdum:
If (Not (If [2], then [1].).), then [3]. [SC1-3]
If (Not (If [2], then [1].).), then (Not [3].). [SC2-3]
Therefore, If [2], then [1]..
[SC1-3]
Modus Ponens:
If [5], then (If (Not (If [2], then [1].).), then [3].).
[5]
Therefore, If (Not (If [2], then [1].).), then [3]..
[SC2-3]
Reductio Ad Absurdum:
If (Not (If (Not (If [2], then [1].).), then (Not [3].).).), then [4].
If (Not (If (Not (If [2], then [1].).), then (Not [3].).).), then (Not [4].).
Therefore, If (Not (If [2], then [1].).), then (Not [3].)..
|
{0: 'Some crocodilians attack humans.', 1: 'Folly is play.', 2: 'Aphids also have a proboscis originating between and behind the forelegs.', 3: 'Television is consumed in vast quantities around the world.', 4: 'Some mistletoes cause inflammatory reaction.', 5: 'Dogs are prone to ear mites and allergies.'}
| 5 |
4,820 |
['We know that at least one of two things is true: either dust mites are microscopic, eight-legged creatures that thrive in humid, dusty environments or evolution is the binding force of all biological research, or if some cardinals have distinctive alarm calls, then stress is the reason most smokers give for failing to stay tobacco-free.', 'Either one or both of these statements are true: reduction reaction is issuing, or bats are prevalent in Texas.', 'On the condition that reduction reaction is issuing, it is definitely the case that some cardinals have distinctive alarm calls.', 'Should it be the case that bats are prevalent in Texas, it follows that some cardinals have distinctive alarm calls.', 'Should it be the case that hairdressers have (part) legs, it follows that it is not the case that either dust mites are microscopic, eight-legged creatures that thrive in humid, dusty environments or evolution is the binding force of all biological research.', 'Provided that herds offer protection from predators, such as lions, we know that it is not the case that either dust mites are microscopic, eight-legged creatures that thrive in humid, dusty environments or evolution is the binding force of all biological research.', "So long as those that suggest either hairdressers have (part) legs or herds offer protection from predators, such as lions are wrong, 'parasitism is a form of symbiosis ' is true.", 'Assuming those that suggest either hairdressers have (part) legs or herds offer protection from predators, such as lions are wrong, we know that it is not true that parasitism is a form of symbiosis .']
|
We know that at least one of two things is true: either dust mites are microscopic, eight-legged creatures that thrive in humid, dusty environments or evolution is the binding force of all biological research, or if some cardinals have distinctive alarm calls, then stress is the reason most smokers give for failing to stay tobacco-free. Either one or both of these statements are true: reduction reaction is issuing, or bats are prevalent in Texas. On the condition that reduction reaction is issuing, it is definitely the case that some cardinals have distinctive alarm calls. Should it be the case that bats are prevalent in Texas, it follows that some cardinals have distinctive alarm calls. Should it be the case that hairdressers have (part) legs, it follows that it is not the case that either dust mites are microscopic, eight-legged creatures that thrive in humid, dusty environments or evolution is the binding force of all biological research. Provided that herds offer protection from predators, such as lions, we know that it is not the case that either dust mites are microscopic, eight-legged creatures that thrive in humid, dusty environments or evolution is the binding force of all biological research. So long as those that suggest either hairdressers have (part) legs or herds offer protection from predators, such as lions are wrong, 'parasitism is a form of symbiosis ' is true. Assuming those that suggest either hairdressers have (part) legs or herds offer protection from predators, such as lions are wrong, we know that it is not true that parasitism is a form of symbiosis .
|
It is reasonable to believe that stress is the reason most smokers give for failing to stay tobacco-free.
|
Some people mistakenly believe that stress is the reason most smokers give for failing to stay tobacco-free.
|
FALSE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either (Either [4] or [5].) or (If [1], then [0].).
Not (Either [4] or [5].). [SC2-2]
Therefore, If [1], then [0]..
[SC2-2]
Disjunction Elimination:
Either [6] or [7]. [SC1-3]
If [6], then (Not (Either [4] or [5].).).
If [7], then (Not (Either [4] or [5].).).
Therefore, Not (Either [4] or [5].)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (Either [6] or [7].).), then [8].
If (Not (Either [6] or [7].).), then (Not [8].).
Therefore, Either [6] or [7]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then [1].
If [3], then [1].
Therefore, [1].
|
{0: 'Stress is the reason most smokers give for failing to stay tobacco-free.', 1: 'Some cardinals have distinctive alarm calls.', 2: 'Reduction reaction is issuing.', 3: 'Bats are prevalent in Texas.', 4: 'Dust mites are microscopic, eight-legged creatures that thrive in humid, dusty environments.', 5: 'Evolution is the binding force of all biological research.', 6: 'Hairdressers have (part) legs.', 7: 'Herds offer protection from predators, such as lions.', 8: 'Parasitism is a form of symbiosis .'}
| 5 |
4,369 |
['When some people mistakenly believe that either caladiums are one of our most colorful plants for shady areas or neurons are surrounded by a membrane is true, it follows that faces come in many different shapes.', "Given that some people mistakenly believe that either caladiums are one of our most colorful plants for shady areas or neurons are surrounded by a membrane, it can be inferred that the notion that 'faces come in many different shapes' is untrue.", "So long as caladiums are one of our most colorful plants for shady areas, 'the claim that cocaine withdraws rapidly from the brain, making the user feel depressed, irritable and fatigued does not reflect reality' is true.", 'It is rational to believe that either chordates have a backbone or some people believe that whiplash can eventually lead to chronic fatigue.', "So long as some people believe that whiplash can eventually lead to chronic fatigue, 'if caladiums are one of our most colorful plants for shady areas, then cocaine withdraws rapidly from the brain, making the user feel depressed, irritable and fatigued' is true.", 'If chordates have a backbone, then dynes are part of newtons.', 'On the condition that dynes are part of newtons, it is definitely the case that if caladiums are one of our most colorful plants for shady areas, then cocaine withdraws rapidly from the brain, making the user feel depressed, irritable and fatigued.']
|
When some people mistakenly believe that either caladiums are one of our most colorful plants for shady areas or neurons are surrounded by a membrane is true, it follows that faces come in many different shapes. Given that some people mistakenly believe that either caladiums are one of our most colorful plants for shady areas or neurons are surrounded by a membrane, it can be inferred that the notion that 'faces come in many different shapes' is untrue. So long as caladiums are one of our most colorful plants for shady areas, 'the claim that cocaine withdraws rapidly from the brain, making the user feel depressed, irritable and fatigued does not reflect reality' is true. It is rational to believe that either chordates have a backbone or some people believe that whiplash can eventually lead to chronic fatigue. So long as some people believe that whiplash can eventually lead to chronic fatigue, 'if caladiums are one of our most colorful plants for shady areas, then cocaine withdraws rapidly from the brain, making the user feel depressed, irritable and fatigued' is true. If chordates have a backbone, then dynes are part of newtons. On the condition that dynes are part of newtons, it is definitely the case that if caladiums are one of our most colorful plants for shady areas, then cocaine withdraws rapidly from the brain, making the user feel depressed, irritable and fatigued.
|
The claim that neurons are surrounded by a membrane is true.
|
Those that suggest neurons are surrounded by a membrane are wrong.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or [0].).), then [2].
If (Not (Either [1] or [0].).), then (Not [2].).
Therefore, Either [1] or [0]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [3]. [SC1-2]
If [1], then (Not [3].).
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [1], then [3].). [SC2-3]
If [5], then (If [1], then [3].).
Therefore, If [1], then [3]..
[SC2-3]
Hypothetical Syllogism:
If [4], then [6].
If [6], then (If [1], then [3].).
Therefore, If [4], then (If [1], then [3].)..
|
{0: 'Neurons are surrounded by a membrane.', 1: 'Caladiums are one of our most colorful plants for shady areas.', 2: 'Faces come in many different shapes.', 3: 'Cocaine withdraws rapidly from the brain, making the user feel depressed, irritable and fatigued.', 4: 'Chordates have a backbone.', 5: 'Some people believe that whiplash can eventually lead to chronic fatigue.', 6: 'Dynes are part of newtons.'}
| 5 |
4,681 |
['If the claim that if it is not true that if salt is high in ions and conducts electricity, then earth is like a giant bar magnet with a North pole and a South pole, then some animals consume other animals does not reflect reality, then if face is the public expression of the inner self, then adrenal androgens seem to have no physiological role in normal growth.', 'When the claim that if it is not true that if salt is high in ions and conducts electricity, then earth is like a giant bar magnet with a North pole and a South pole, then some animals consume other animals does not reflect reality is true, it follows that the statement that states if face is the public expression of the inner self, then adrenal androgens seem to have no physiological role in normal growth is false.', 'We know that at least one of two things is true: jaguars are big cats , or if it is not true that if salt is high in ions and conducts electricity, then earth is like a giant bar magnet with a North pole and a South pole, then the statement that states some animals consume other animals is false.', 'If jaguars are big cats , then alcohol misuse affects individuals, families and society at large.', 'Either malaria parasite flourishes only in healthy red blood or those that suggest alcohol misuse affects individuals, families and society at large are wrong.', 'The claim that malaria parasite flourishes only in healthy red blood does not reflect reality.']
|
If the claim that if it is not true that if salt is high in ions and conducts electricity, then earth is like a giant bar magnet with a North pole and a South pole, then some animals consume other animals does not reflect reality, then if face is the public expression of the inner self, then adrenal androgens seem to have no physiological role in normal growth. When the claim that if it is not true that if salt is high in ions and conducts electricity, then earth is like a giant bar magnet with a North pole and a South pole, then some animals consume other animals does not reflect reality is true, it follows that the statement that states if face is the public expression of the inner self, then adrenal androgens seem to have no physiological role in normal growth is false. We know that at least one of two things is true: jaguars are big cats , or if it is not true that if salt is high in ions and conducts electricity, then earth is like a giant bar magnet with a North pole and a South pole, then the statement that states some animals consume other animals is false. If jaguars are big cats , then alcohol misuse affects individuals, families and society at large. Either malaria parasite flourishes only in healthy red blood or those that suggest alcohol misuse affects individuals, families and society at large are wrong. The claim that malaria parasite flourishes only in healthy red blood does not reflect reality.
|
Whenever it is true that salt is high in ions and conducts electricity, 'earth is like a giant bar magnet with a North pole and a South pole' is true.
|
The statement that 'if salt is high in ions and conducts electricity, then earth is like a giant bar magnet with a North pole and a South pole' is incorrect.
|
FALSE
|
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 (If [3], then [4].).
If (Not (If (Not (If [0], then [1].).), then [2].).), then (Not (If [3], then [4].).).
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC2-1]
Disjunctive Syllogism:
Either [5] or (If (Not (If [0], then [1].).), then (Not [2].).).
Not [5]. [SC2-2]
Therefore, If (Not (If [0], then [1].).), then (Not [2].)..
[SC2-2]
Modus Tonens:
If [5], then [6].
Not [6]. [SC2-3]
Therefore, Not [5]..
[SC2-3]
Disjunctive Syllogism:
Either [7] or (Not [6].).
Not [7].
Therefore, Not [6]..
|
{0: 'Salt is high in ions and conducts electricity.', 1: 'Earth is like a giant bar magnet with a North pole and a South pole.', 2: 'Some animals consume other animals.', 3: 'Face is the public expression of the inner self.', 4: 'Adrenal androgens seem to have no physiological role in normal growth.', 5: 'Jaguars are big cats .', 6: 'Alcohol misuse affects individuals, families and society at large.', 7: 'Malaria parasite flourishes only in healthy red blood.'}
| 5 |
4,339 |
['We know that either real men have emotions or either buildings have outlets or dens provide shelter.', 'Assuming real men have emotions, we know that if genes cantravel to nearby, related plants on their own, then butterfly weed is a member of the milkweed family.', 'It is rational to believe that either fountain grass has more compact growth habit and crimson foliage or proteomics seeks to provide functional information for all the proteins.', 'One may reasonably assume that if fountain grass has more compact growth habit and crimson foliage, then the claim that butterfly weed is a member of the milkweed family does not reflect reality.', 'On the condition that the claim that if either buildings have outlets or dens provide shelter, then if genes cantravel to nearby, related plants on their own, then butterfly weed is a member of the milkweed family does not correspond with reality, it is definitely the case that ornithologists have (part) human bodies.', 'We know that the claim that ornithologists have (part) human bodies is false.', 'We know that either spacecraft have surfaces or if proteomics seeks to provide functional information for all the proteins, then the claim that butterfly weed is a member of the milkweed family does not reflect reality.', 'Some people mistakenly believe that spacecraft have surfaces.']
|
We know that either real men have emotions or either buildings have outlets or dens provide shelter. Assuming real men have emotions, we know that if genes cantravel to nearby, related plants on their own, then butterfly weed is a member of the milkweed family. It is rational to believe that either fountain grass has more compact growth habit and crimson foliage or proteomics seeks to provide functional information for all the proteins. One may reasonably assume that if fountain grass has more compact growth habit and crimson foliage, then the claim that butterfly weed is a member of the milkweed family does not reflect reality. On the condition that the claim that if either buildings have outlets or dens provide shelter, then if genes cantravel to nearby, related plants on their own, then butterfly weed is a member of the milkweed family does not correspond with reality, it is definitely the case that ornithologists have (part) human bodies. We know that the claim that ornithologists have (part) human bodies is false. We know that either spacecraft have surfaces or if proteomics seeks to provide functional information for all the proteins, then the claim that butterfly weed is a member of the milkweed family does not reflect reality. Some people mistakenly believe that spacecraft have surfaces.
|
It is a common misconception that genes cantravel to nearby, related plants on their own.
|
It is a common misconception that genes cantravel to nearby, related plants on their own.
|
TRUE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [2] or (Either [3] or [4].).
If [2], then (If [0], then [1].).
If (Either [3] or [4].), then (If [0], then [1].). [SC3-2]
Therefore, If [0], then [1]..
[SC3-2]
Modus Tonens:
If (Not (If (Either [3] or [4].), then (If [0], then [1].).).), then [7].
Not [7].
Therefore, If (Either [3] or [4].), then (If [0], then [1].)..
[SC2-1]
Disjunction Elimination:
Either [5] or [6].
If [5], then (Not [1].).
If [6], then (Not [1].). [SC3-2]
Therefore, Not [1]..
[SC3-2]
Disjunctive Syllogism:
Either [8] or (If [6], then (Not [1].).).
Not [8].
Therefore, If [6], then (Not [1].)..
|
{0: 'Genes cantravel to nearby, related plants on their own.', 1: 'Butterfly weed is a member of the milkweed family.', 2: 'Real men have emotions.', 3: 'Buildings have outlets.', 4: 'Dens provide shelter.', 5: 'Fountain grass has more compact growth habit and crimson foliage.', 6: 'Proteomics seeks to provide functional information for all the proteins.', 7: 'Ornithologists have (part) human bodies.', 8: 'Spacecraft have surfaces.'}
| 5 |
4,419 |
['The claim that if cattle replace antelope, then buds are pink as the four sepals are pink and are lost when the flower blooms does not reflect reality.', 'The claim that if men often start to gain excess fat in their late twenties and thirties, then a policyholder is a holder does not correspond with reality.', 'Once we know either sunrise does have some tolerance to powdery mildew or mass movements can occur slowly over a period of years, or they can happen in a matter of minutes, we also know that if men often start to gain excess fat in their late twenties and thirties, then a policyholder is a holder.', 'At least one of two things is true: photosynthesis is a very complex process, or either either sunrise does have some tolerance to powdery mildew or mass movements can occur slowly over a period of years, or they can happen in a matter of minutes or either technology is closely related to science and engineering or emotion is another important factor affecting attention.', 'Those that suggest photosynthesis is a very complex process are wrong.', 'Provided that astrophysics is the physics of celestial bodies, we know that if either technology is closely related to science and engineering or emotion is another important factor affecting attention, then if it is not true that mind mapping can take many forms, then if cattle replace antelope, then buds are pink as the four sepals are pink and are lost when the flower blooms .', 'The idea that astrophysics is the physics of celestial bodies is true.']
|
The claim that if cattle replace antelope, then buds are pink as the four sepals are pink and are lost when the flower blooms does not reflect reality. The claim that if men often start to gain excess fat in their late twenties and thirties, then a policyholder is a holder does not correspond with reality. Once we know either sunrise does have some tolerance to powdery mildew or mass movements can occur slowly over a period of years, or they can happen in a matter of minutes, we also know that if men often start to gain excess fat in their late twenties and thirties, then a policyholder is a holder. At least one of two things is true: photosynthesis is a very complex process, or either either sunrise does have some tolerance to powdery mildew or mass movements can occur slowly over a period of years, or they can happen in a matter of minutes or either technology is closely related to science and engineering or emotion is another important factor affecting attention. Those that suggest photosynthesis is a very complex process are wrong. Provided that astrophysics is the physics of celestial bodies, we know that if either technology is closely related to science and engineering or emotion is another important factor affecting attention, then if it is not true that mind mapping can take many forms, then if cattle replace antelope, then buds are pink as the four sepals are pink and are lost when the flower blooms . The idea that astrophysics is the physics of celestial bodies is true.
|
mind mapping can take many forms.
|
Mind mapping can take many forms.
|
TRUE
|
Modus Tonens:
If (Not [0].), then (If [1], then [2].). [SC1-1]
Not (If [1], then [2].).
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either (If [3], then [4].) or (If (Not [0].), then (If [1], then [2].).). [SC1-2]
Not (If [3], then [4].).
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC1-2]
Constructive Dilemma:
Either (Either [5] or [6].) or (Either [7] or [8].). [SC1-3]
If (Either [5] or [6].), then (If [3], then [4].).
If (Either [7] or [8].), then (If (Not [0].), then (If [1], then [2].).). [SC3-3]
Therefore, Either (If [3], then [4].) or (If (Not [0].), then (If [1], then [2].).)..
[SC1-3]
Disjunctive Syllogism:
Either [10] or (Either (Either [5] or [6].) or (Either [7] or [8].).).
Not [10].
Therefore, Either (Either [5] or [6].) or (Either [7] or [8].)..
[SC3-3]
Modus Ponens:
If [9], then (If (Either [7] or [8].), then (If (Not [0].), then (If [1], then [2].).).).
[9]
Therefore, If (Either [7] or [8].), then (If (Not [0].), then (If [1], then [2].).)..
|
{0: 'Mind mapping can take many forms.', 1: 'Cattle replace antelope.', 2: 'Buds are pink as the four sepals are pink and are lost when the flower blooms .', 3: 'Men often start to gain excess fat in their late twenties and thirties.', 4: 'A policyholder is a holder.', 5: 'Sunrise does have some tolerance to powdery mildew.', 6: 'Mass movements can occur slowly over a period of years, or they can happen in a matter of minutes.', 7: 'Technology is closely related to science and engineering.', 8: 'Emotion is another important factor affecting attention.', 9: 'Astrophysics is the physics of celestial bodies.', 10: 'Photosynthesis is a very complex process.'}
| 5 |
4,829 |
["Whenever it is true that the claim that most naturalists work on problems does not reflect reality, 'if some cells have very irregularly-shaped nuclei, then cones attract crossbills' is true.", "So long as the statement that 'if the claim that most naturalists work on problems does not reflect reality, then it is a common misconception that if some cells have very irregularly-shaped nuclei, then cones attract crossbills' is incorrect, 'bracken fern contains at least two animal toxins' is true.", 'Once we know the claim that if bracken fern contains at least two animal toxins, then if mountains also help create deserts, then amphibians have (part) brains has no merit, we also know that a brig is a sailing ship.', "When the claim that if bracken fern contains at least two animal toxins, then if mountains also help create deserts, then amphibians have (part) brains has no merit is true, it follows that the statement that 'a brig is a sailing ship' is incorrect.", 'At least one of two things is true: many horses live with poor gaits, or even bad attitudes, from old holding patterns, or some fingers have definite numerical values.', 'Once we know many horses live with poor gaits, or even bad attitudes, from old holding patterns, we also know that if bracken fern contains at least two animal toxins, then it is not true that if mountains also help create deserts, then amphibians have (part) brains.', 'If some fingers have definite numerical values, then if bracken fern contains at least two animal toxins, then it is not true that if mountains also help create deserts, then amphibians have (part) brains.']
|
Whenever it is true that the claim that most naturalists work on problems does not reflect reality, 'if some cells have very irregularly-shaped nuclei, then cones attract crossbills' is true. So long as the statement that 'if the claim that most naturalists work on problems does not reflect reality, then it is a common misconception that if some cells have very irregularly-shaped nuclei, then cones attract crossbills' is incorrect, 'bracken fern contains at least two animal toxins' is true. Once we know the claim that if bracken fern contains at least two animal toxins, then if mountains also help create deserts, then amphibians have (part) brains has no merit, we also know that a brig is a sailing ship. When the claim that if bracken fern contains at least two animal toxins, then if mountains also help create deserts, then amphibians have (part) brains has no merit is true, it follows that the statement that 'a brig is a sailing ship' is incorrect. At least one of two things is true: many horses live with poor gaits, or even bad attitudes, from old holding patterns, or some fingers have definite numerical values. Once we know many horses live with poor gaits, or even bad attitudes, from old holding patterns, we also know that if bracken fern contains at least two animal toxins, then it is not true that if mountains also help create deserts, then amphibians have (part) brains. If some fingers have definite numerical values, then if bracken fern contains at least two animal toxins, then it is not true that if mountains also help create deserts, then amphibians have (part) brains.
|
It is true that most naturalists work on problems.
|
Naturalists have (part) corpi.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then (If [1], then [2].).
If (Not [0].), then (Not (If [1], then [2].).). [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not (If (Not [0].), then (Not (If [1], then [2].).).).), then [3].
Not [3]. [SC2-2]
Therefore, If (Not [0].), then (Not (If [1], then [2].).)..
[SC2-2]
Reductio Ad Absurdum:
If [3], then (If [4], then [5].). [SC1-3]
If [3], then (Not (If [4], then [5].).). [SC2-3]
Therefore, Not [3]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If [3], then (If [4], then [5].).).), then [8].
If (Not (If [3], then (If [4], then [5].).).), then (Not [8].).
Therefore, If [3], then (If [4], then [5].)..
[SC2-3]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If [3], then (Not (If [4], then [5].).).).
If [7], then (If [3], then (Not (If [4], then [5].).).).
Therefore, If [3], then (Not (If [4], then [5].).)..
|
{0: 'Most naturalists work on problems.', 1: 'Some cells have very irregularly-shaped nuclei.', 2: 'Cones attract crossbills.', 3: 'Bracken fern contains at least two animal toxins.', 4: 'Mountains also help create deserts.', 5: 'Amphibians have (part) brains.', 6: 'Many horses live with poor gaits, or even bad attitudes, from old holding patterns.', 7: 'Some fingers have definite numerical values.', 8: 'A brig is a sailing ship.'}
| 5 |
4,951 |
['There is good reason to believe that either black mangrove has hundreds of roots the size of pencils that grow up from the soil or it is a common misconception that rabbits inhabit a relatively small home range.', 'If sulfur is a favorite homeopathic remedy for a variety of skin disorders, then either barnacles form colonies or the claim that black mangrove has hundreds of roots the size of pencils that grow up from the soil is false.', "The statement 'sulfur is a favorite homeopathic remedy for a variety of skin disorders' can be considered true.", 'The claim that some plants make daughter plants at the rosette base or along the rhizome does not reflect reality.', "Assuming the notion that 'either some plants make daughter plants at the rosette base or along the rhizome or those that suggest barnacles form colonies are wrong' is untrue, we know that most forces affect motion.", "One may reasonably assume that if the notion that 'either some plants make daughter plants at the rosette base or along the rhizome or those that suggest barnacles form colonies are wrong' is untrue, then the statement that 'most forces affect motion' is incorrect."]
|
There is good reason to believe that either black mangrove has hundreds of roots the size of pencils that grow up from the soil or it is a common misconception that rabbits inhabit a relatively small home range. If sulfur is a favorite homeopathic remedy for a variety of skin disorders, then either barnacles form colonies or the claim that black mangrove has hundreds of roots the size of pencils that grow up from the soil is false. The statement 'sulfur is a favorite homeopathic remedy for a variety of skin disorders' can be considered true. The claim that some plants make daughter plants at the rosette base or along the rhizome does not reflect reality. Assuming the notion that 'either some plants make daughter plants at the rosette base or along the rhizome or those that suggest barnacles form colonies are wrong' is untrue, we know that most forces affect motion. One may reasonably assume that if the notion that 'either some plants make daughter plants at the rosette base or along the rhizome or those that suggest barnacles form colonies are wrong' is untrue, then the statement that 'most forces affect motion' is incorrect.
|
It is a common misconception that rabbits inhabit a relatively small home range.
|
The claim that rabbits cause severe ecological damage even at low densities is false.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or (Not [0].).
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].). [SC1-2]
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC1-2]
Modus Ponens:
If [4], then (Either [2] or (Not [1].).).
[4]
Therefore, Either [2] or (Not [1].)..
[SC2-2]
Disjunctive Syllogism:
Either [3] or (Not [2].). [SC1-3]
Not [3].
Therefore, Not [2]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (Either [3] or (Not [2].).).), then [5].
If (Not (Either [3] or (Not [2].).).), then (Not [5].).
Therefore, Either [3] or (Not [2].)..
|
{0: 'Rabbits inhabit a relatively small home range.', 1: 'Black mangrove has hundreds of roots the size of pencils that grow up from the soil.', 2: 'Barnacles form colonies.', 3: 'Some plants make daughter plants at the rosette base or along the rhizome.', 4: 'Sulfur is a favorite homeopathic remedy for a variety of skin disorders.', 5: 'Most forces affect motion.'}
| 5 |
4,454 |
["Assuming the statement 'if either salamanders live in water and on land, and look rather like lizards, with four legs and a tail or new leaves require the plant to absorb increasing amounts of moisture, then p r is the inactive form of phytochrome' can be considered false, we know that it is not the case that light has soften effects.", 'Once we know the claim that either salamanders live in water and on land, and look rather like lizards, with four legs and a tail or new leaves require the plant to absorb increasing amounts of moisture does not correspond with reality, we also know that concentrated solutions have a large amount of solute.', 'We know that either either culligan water reaches far beyond the borders of North America or ignorance is the inability to see the truth about things, to see things as they really are or foxes are omnivorous mammals that are light on their feet.', "When either culligan water reaches far beyond the borders of North America or ignorance is the inability to see the truth about things, to see things as they really are is true, it follows that if the statement 'if either salamanders live in water and on land, and look rather like lizards, with four legs and a tail or new leaves require the plant to absorb increasing amounts of moisture, then p r is the inactive form of phytochrome' can be considered false, then light has soften effects.", "One may reasonably assume that if foxes are omnivorous mammals that are light on their feet, then if the statement 'if either salamanders live in water and on land, and look rather like lizards, with four legs and a tail or new leaves require the plant to absorb increasing amounts of moisture, then p r is the inactive form of phytochrome' can be considered false, then light has soften effects.", 'On the condition that images exist for all sorts of physical and cultural phenomena, especially agriculture, it is definitely the case that we know that the claim that concentrated solutions have a large amount of solute is false.', 'We can assume that images exist for all sorts of physical and cultural phenomena, especially agriculture.']
|
Assuming the statement 'if either salamanders live in water and on land, and look rather like lizards, with four legs and a tail or new leaves require the plant to absorb increasing amounts of moisture, then p r is the inactive form of phytochrome' can be considered false, we know that it is not the case that light has soften effects. Once we know the claim that either salamanders live in water and on land, and look rather like lizards, with four legs and a tail or new leaves require the plant to absorb increasing amounts of moisture does not correspond with reality, we also know that concentrated solutions have a large amount of solute. We know that either either culligan water reaches far beyond the borders of North America or ignorance is the inability to see the truth about things, to see things as they really are or foxes are omnivorous mammals that are light on their feet. When either culligan water reaches far beyond the borders of North America or ignorance is the inability to see the truth about things, to see things as they really are is true, it follows that if the statement 'if either salamanders live in water and on land, and look rather like lizards, with four legs and a tail or new leaves require the plant to absorb increasing amounts of moisture, then p r is the inactive form of phytochrome' can be considered false, then light has soften effects. One may reasonably assume that if foxes are omnivorous mammals that are light on their feet, then if the statement 'if either salamanders live in water and on land, and look rather like lizards, with four legs and a tail or new leaves require the plant to absorb increasing amounts of moisture, then p r is the inactive form of phytochrome' can be considered false, then light has soften effects. On the condition that images exist for all sorts of physical and cultural phenomena, especially agriculture, it is definitely the case that we know that the claim that concentrated solutions have a large amount of solute is false. We can assume that images exist for all sorts of physical and cultural phenomena, especially agriculture.
|
It is reasonable to believe that p r is the inactive form of phytochrome.
|
P r represents a permutation of n elements taken r at a time.
|
Uncertain
|
Modus Ponens:
If (Either [1] or [2].), then [0]. [SC1-1]
Either [1] or [2]. [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Either [1] or [2].), then [0].).), then [3]. [SC1-2]
If (Not (If (Either [1] or [2].), then [0].).), then (Not [3].).
Therefore, If (Either [1] or [2].), then [0]..
[SC1-2]
Disjunction Elimination:
Either (Either [6] or [7].) or [8].
If (Either [6] or [7].), then (If (Not (If (Either [1] or [2].), then [0].).), then [3].).
If [8], then (If (Not (If (Either [1] or [2].), then [0].).), then [3].).
Therefore, If (Not (If (Either [1] or [2].), then [0].).), then [3]..
[SC2-1]
Modus Tonens:
If (Not (Either [1] or [2].).), then [4].
Not [4]. [SC2-2]
Therefore, Either [1] or [2]..
[SC2-2]
Modus Ponens:
If [5], then (Not [4].).
[5]
Therefore, Not [4]..
|
{0: 'P r is the inactive form of phytochrome.', 1: 'Salamanders live in water and on land, and look rather like lizards, with four legs and a tail.', 2: 'New leaves require the plant to absorb increasing amounts of moisture.', 3: 'Light has soften effects.', 4: 'Concentrated solutions have a large amount of solute.', 5: 'Images exist for all sorts of physical and cultural phenomena, especially agriculture.', 6: 'Culligan water reaches far beyond the borders of North America.', 7: 'Ignorance is the inability to see the truth about things, to see things as they really are.', 8: 'Foxes are omnivorous mammals that are light on their feet.'}
| 5 |
4,063 |
['It is a fact that either asiatic isa inhabitant or if most fiber helps lower blood cholesterol levels, then corn is the crop that is most often associated with aflatoxins.', 'We know that at least one of two things is true: hockey sticks are sticks, or clear glass is the most easily contaminated by other colors.', 'When hockey sticks are sticks is true, it follows that if asiatic isa inhabitant, then piedmontese beef has about half the calories and a third of the fat of traditional beef.', 'Once we know clear glass is the most easily contaminated by other colors, we also know that if asiatic isa inhabitant, then piedmontese beef has about half the calories and a third of the fat of traditional beef.', "So long as if gravity pulls the rain to the rivers, and ultimately to the sea, then prisons are one type of institutional architecture, and prep schools are another, 'if if most fiber helps lower blood cholesterol levels, then corn is the crop that is most often associated with aflatoxins, then piedmontese beef has about half the calories and a third of the fat of traditional beef' is true.", 'The statement that states most people store their private keys using the password protection of their Web browser is false.', "So long as all chordates are vertebrates, 'if we know that the claim that if gravity pulls the rain to the rivers, and ultimately to the sea, then prisons are one type of institutional architecture, and prep schools are another is false, then most people store their private keys using the password protection of their Web browser' is true.", 'Many people rightly believe that all chordates are vertebrates.']
|
It is a fact that either asiatic isa inhabitant or if most fiber helps lower blood cholesterol levels, then corn is the crop that is most often associated with aflatoxins. We know that at least one of two things is true: hockey sticks are sticks, or clear glass is the most easily contaminated by other colors. When hockey sticks are sticks is true, it follows that if asiatic isa inhabitant, then piedmontese beef has about half the calories and a third of the fat of traditional beef. Once we know clear glass is the most easily contaminated by other colors, we also know that if asiatic isa inhabitant, then piedmontese beef has about half the calories and a third of the fat of traditional beef. So long as if gravity pulls the rain to the rivers, and ultimately to the sea, then prisons are one type of institutional architecture, and prep schools are another, 'if if most fiber helps lower blood cholesterol levels, then corn is the crop that is most often associated with aflatoxins, then piedmontese beef has about half the calories and a third of the fat of traditional beef' is true. The statement that states most people store their private keys using the password protection of their Web browser is false. So long as all chordates are vertebrates, 'if we know that the claim that if gravity pulls the rain to the rivers, and ultimately to the sea, then prisons are one type of institutional architecture, and prep schools are another is false, then most people store their private keys using the password protection of their Web browser' is true. Many people rightly believe that all chordates are vertebrates.
|
It is rational to agree that piedmontese beef has about half the calories and a third of the fat of traditional beef.
|
The statement, piedmontese beef has about half the calories and a third of the fat of traditional beef, does not hold.
|
FALSE
|
Disjunction Elimination:
Either [1] or (If [2], then [3].).
If [1], then [0]. [SC2-1]
If (If [2], then [3].), then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If [1], then [0].).
If [7], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC3-1]
Modus Ponens:
If (If [4], then [5].), then (If (If [2], then [3].), then [0].).
If [4], then [5]. [SC2-2]
Therefore, If (If [2], then [3].), then [0]..
[SC2-2]
Modus Tonens:
If (Not (If [4], then [5].).), then [8]. [SC1-3]
Not [8].
Therefore, If [4], then [5]..
[SC1-3]
Modus Ponens:
If [9], then (If (Not (If [4], then [5].).), then [8].).
[9]
Therefore, If (Not (If [4], then [5].).), then [8]..
|
{0: 'Piedmontese beef has about half the calories and a third of the fat of traditional beef.', 1: 'Asiatic isa inhabitant.', 2: 'Most fiber helps lower blood cholesterol levels.', 3: 'Corn is the crop that is most often associated with aflatoxins.', 4: 'Gravity pulls the rain to the rivers, and ultimately to the sea.', 5: 'Prisons are one type of institutional architecture, and prep schools are another.', 6: 'Hockey sticks are sticks.', 7: 'Clear glass is the most easily contaminated by other colors.', 8: 'Most people store their private keys using the password protection of their Web browser.', 9: 'All chordates are vertebrates.'}
| 5 |
4,759 |
["On the condition that the statement 'if we know that the claim that feminists find gender everywhere in science is false, then dance is a physical and mental discipline' can be considered false, it is definitely the case that the statement 'mammals play roles' can be considered false.", "The notion that 'if some people continue to suffer some neurologic disorders indefinitely, then some hip sockets are part of caribou' is untrue.", "Given that if cooked bulgur has a nutlike flavor and a slightly chewy texture, then female flowers are very small and green and they are on spikes that are approx, it can be inferred that if the statement 'if we know that the claim that feminists find gender everywhere in science is false, then dance is a physical and mental discipline' can be considered false, then mammals play roles.", 'Given that cooked bulgur has a nutlike flavor and a slightly chewy texture, it can be inferred that female flowers are very small and green and they are on spikes that are approx.', 'Either a pickerel is a pike or either if some people continue to suffer some neurologic disorders indefinitely, then some hip sockets are part of caribou or if we know that the claim that feminists find gender everywhere in science is false, then the claim that dance is a physical and mental discipline does not correspond with reality.', 'The claim that a pickerel is a pike is false.']
|
On the condition that the statement 'if we know that the claim that feminists find gender everywhere in science is false, then dance is a physical and mental discipline' can be considered false, it is definitely the case that the statement 'mammals play roles' can be considered false. The notion that 'if some people continue to suffer some neurologic disorders indefinitely, then some hip sockets are part of caribou' is untrue. Given that if cooked bulgur has a nutlike flavor and a slightly chewy texture, then female flowers are very small and green and they are on spikes that are approx, it can be inferred that if the statement 'if we know that the claim that feminists find gender everywhere in science is false, then dance is a physical and mental discipline' can be considered false, then mammals play roles. Given that cooked bulgur has a nutlike flavor and a slightly chewy texture, it can be inferred that female flowers are very small and green and they are on spikes that are approx. Either a pickerel is a pike or either if some people continue to suffer some neurologic disorders indefinitely, then some hip sockets are part of caribou or if we know that the claim that feminists find gender everywhere in science is false, then the claim that dance is a physical and mental discipline does not correspond with reality. The claim that a pickerel is a pike is false.
|
feminists find gender everywhere in science.
|
Feminists fight and struggle for women's liberation.
|
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 [2]. [SC1-2]
If (Not (If (Not [0].), then [1].).), then (Not [2].).
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Ponens:
If (If [6], then [7].), then (If (Not (If (Not [0].), then [1].).), then [2].).
If [6], then [7].
Therefore, If (Not (If (Not [0].), then [1].).), then [2]..
[SC2-1]
Disjunctive Syllogism:
Either (If [3], then [4].) or (If (Not [0].), then (Not [1].).). [SC1-2]
Not (If [3], then [4].).
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Disjunctive Syllogism:
Either [5] or (Either (If [3], then [4].) or (If (Not [0].), then (Not [1].).).).
Not [5].
Therefore, Either (If [3], then [4].) or (If (Not [0].), then (Not [1].).)..
|
{0: 'Feminists find gender everywhere in science.', 1: 'Dance is a physical and mental discipline.', 2: 'Mammals play roles.', 3: 'Some people continue to suffer some neurologic disorders indefinitely.', 4: 'Some hip sockets are part of caribou.', 5: 'A pickerel is a pike.', 6: 'Cooked bulgur has a nutlike flavor and a slightly chewy texture.', 7: 'Female flowers are very small and green and they are on spikes that are approx.'}
| 5 |
4,360 |
['One may reasonably assume that if the claim that revolutions are moments for breathing new life into the course of events does not correspond with reality, then the statement that states caterpillars construct silken shelters by tying leaves together about midway up the host plant is false.', 'It is rational to believe that either divergent plates are also the cause of contintal rifts or infection is also possible by inhaling the organism.', 'On the condition that divergent plates are also the cause of contintal rifts, it is definitely the case that if cuckoos have (part) skulls, then blood pressure is measured by the use of a blood pressure cuff and a stethoscope.', 'Should it be the case that infection is also possible by inhaling the organism, it follows that greater openness increases vulnerability of economies and people.', 'Either fats are triglyceride s, made of assorted fatty acid monomers bound to glycerol backbone or if if cuckoos have (part) skulls, then blood pressure is measured by the use of a blood pressure cuff and a stethoscope, then if the claim that revolutions are moments for breathing new life into the course of events does not correspond with reality, then caterpillars construct silken shelters by tying leaves together about midway up the host plant.', 'The claim that fats are triglyceride s, made of assorted fatty acid monomers bound to glycerol backbone does not correspond with reality.', 'If it is not true that if greater openness increases vulnerability of economies and people, then if the claim that revolutions are moments for breathing new life into the course of events does not correspond with reality, then caterpillars construct silken shelters by tying leaves together about midway up the host plant, then meteorologists call the difference between the total and geostrophic winds ageostrophic winds.', 'Given that it is not true that if greater openness increases vulnerability of economies and people, then if the claim that revolutions are moments for breathing new life into the course of events does not correspond with reality, then caterpillars construct silken shelters by tying leaves together about midway up the host plant, it can be inferred that the statement, meteorologists call the difference between the total and geostrophic winds ageostrophic winds, does not hold.']
|
One may reasonably assume that if the claim that revolutions are moments for breathing new life into the course of events does not correspond with reality, then the statement that states caterpillars construct silken shelters by tying leaves together about midway up the host plant is false. It is rational to believe that either divergent plates are also the cause of contintal rifts or infection is also possible by inhaling the organism. On the condition that divergent plates are also the cause of contintal rifts, it is definitely the case that if cuckoos have (part) skulls, then blood pressure is measured by the use of a blood pressure cuff and a stethoscope. Should it be the case that infection is also possible by inhaling the organism, it follows that greater openness increases vulnerability of economies and people. Either fats are triglyceride s, made of assorted fatty acid monomers bound to glycerol backbone or if if cuckoos have (part) skulls, then blood pressure is measured by the use of a blood pressure cuff and a stethoscope, then if the claim that revolutions are moments for breathing new life into the course of events does not correspond with reality, then caterpillars construct silken shelters by tying leaves together about midway up the host plant. The claim that fats are triglyceride s, made of assorted fatty acid monomers bound to glycerol backbone does not correspond with reality. If it is not true that if greater openness increases vulnerability of economies and people, then if the claim that revolutions are moments for breathing new life into the course of events does not correspond with reality, then caterpillars construct silken shelters by tying leaves together about midway up the host plant, then meteorologists call the difference between the total and geostrophic winds ageostrophic winds. Given that it is not true that if greater openness increases vulnerability of economies and people, then if the claim that revolutions are moments for breathing new life into the course of events does not correspond with reality, then caterpillars construct silken shelters by tying leaves together about midway up the host plant, it can be inferred that the statement, meteorologists call the difference between the total and geostrophic winds ageostrophic winds, does not hold.
|
revolutions are moments for breathing new life into the course of events.
|
We know that the claim that revolutions are moments for breathing new life into the course of events is false.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (If [2], then [3].) or [4]. [SC1-2]
If (If [2], then [3].), then (If (Not [0].), then [1].). [SC2-2]
If [4], then (If (Not [0].), then [1].). [SC3-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Constructive Dilemma:
Either [7] or [8].
If [7], then (If [2], then [3].).
If [8], then [4].
Therefore, Either (If [2], then [3].) or [4]..
[SC2-2]
Disjunctive Syllogism:
Either [5] or (If (If [2], then [3].), then (If (Not [0].), then [1].).).
Not [5].
Therefore, If (If [2], then [3].), then (If (Not [0].), then [1].)..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If [4], then (If (Not [0].), then [1].).).), then [6].
If (Not (If [4], then (If (Not [0].), then [1].).).), then (Not [6].).
Therefore, If [4], then (If (Not [0].), then [1].)..
|
{0: 'Revolutions are moments for breathing new life into the course of events.', 1: 'Caterpillars construct silken shelters by tying leaves together about midway up the host plant.', 2: 'Cuckoos have (part) skulls.', 3: 'Blood pressure is measured by the use of a blood pressure cuff and a stethoscope.', 4: 'Greater openness increases vulnerability of economies and people.', 5: 'Fats are triglyceride s, made of assorted fatty acid monomers bound to glycerol backbone.', 6: 'Meteorologists call the difference between the total and geostrophic winds ageostrophic winds.', 7: 'Divergent plates are also the cause of contintal rifts.', 8: 'Infection is also possible by inhaling the organism.'}
| 5 |
4,237 |
['We know that at least one of two things is true: if polecats live in dens, then disable women raise particular issues, or snow can push a building beyond the breaking point.', 'One may reasonably assume that if snow can push a building beyond the breaking point, then food coats the stomach and helps prevent gastric juices and acids from destroying the enzyme action.', 'Assuming those that suggest either megabats eat fruit, nectar or pollen or if if polecats live in dens, then disable women raise particular issues, then food coats the stomach and helps prevent gastric juices and acids from destroying the enzyme action are wrong, we know that men have care.', 'It is rational to believe that either ethical conduct is different from legal conduct or some animals even eat leaves.', 'Assuming ethical conduct is different from legal conduct, we know that those that suggest megabats eat fruit, nectar or pollen are wrong.', 'Assuming some animals even eat leaves, we know that those that suggest megabats eat fruit, nectar or pollen are wrong.', 'Either most animals share earth or some people mistakenly believe that men have care.', 'The statement that states most animals share earth is false.']
|
We know that at least one of two things is true: if polecats live in dens, then disable women raise particular issues, or snow can push a building beyond the breaking point. One may reasonably assume that if snow can push a building beyond the breaking point, then food coats the stomach and helps prevent gastric juices and acids from destroying the enzyme action. Assuming those that suggest either megabats eat fruit, nectar or pollen or if if polecats live in dens, then disable women raise particular issues, then food coats the stomach and helps prevent gastric juices and acids from destroying the enzyme action are wrong, we know that men have care. It is rational to believe that either ethical conduct is different from legal conduct or some animals even eat leaves. Assuming ethical conduct is different from legal conduct, we know that those that suggest megabats eat fruit, nectar or pollen are wrong. Assuming some animals even eat leaves, we know that those that suggest megabats eat fruit, nectar or pollen are wrong. Either most animals share earth or some people mistakenly believe that men have care. The statement that states most animals share earth is false.
|
Those that suggest food coats the stomach and helps prevent gastric juices and acids from destroying the enzyme action are right.
|
It is not the case that food coats the stomach and helps prevent gastric juices and acids from destroying the enzyme action.
|
FALSE
|
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]
Disjunctive Syllogism:
Either [4] or (If (If [1], then [2].), then [0].). [SC1-2]
Not [4]. [SC2-2]
Therefore, If (If [1], then [2].), then [0]..
[SC1-2]
Modus Tonens:
If (Not (Either [4] or (If (If [1], then [2].), then [0].).).), then [7].
Not [7]. [SC2-3]
Therefore, Either [4] or (If (If [1], then [2].), then [0].)..
[SC2-3]
Disjunctive Syllogism:
Either [8] or (Not [7].).
Not [8].
Therefore, Not [7]..
[SC2-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (Not [4].).
If [6], then (Not [4].).
Therefore, Not [4]..
|
{0: 'Food coats the stomach and helps prevent gastric juices and acids from destroying the enzyme action.', 1: 'Polecats live in dens.', 2: 'Disable women raise particular issues.', 3: 'Snow can push a building beyond the breaking point.', 4: 'Megabats eat fruit, nectar or pollen.', 5: 'Ethical conduct is different from legal conduct.', 6: 'Some animals even eat leaves.', 7: 'Men have care.', 8: 'Most animals share earth.'}
| 5 |
4,112 |
['If most horses adapt to domestication, then office buildings are located in work.', "Given that the claim that either death usually occurs in infancy or early childhood or most horses adapt to domestication is false, it can be inferred that the notion that 'adequate potassium helps onion plants better withstand injurious cold' is untrue.", "So long as spirituality is religion, 'office buildings are located in work' is true.", 'Either streams produce a stream bed whose cross-section reflects the flow regime or numerous florets have stamens.', "Whenever it is true that streams produce a stream bed whose cross-section reflects the flow regime, 'if the claim that either death usually occurs in infancy or early childhood or most horses adapt to domestication is false, then adequate potassium helps onion plants better withstand injurious cold' is true.", 'When numerous florets have stamens is true, it follows that if the claim that either death usually occurs in infancy or early childhood or most horses adapt to domestication is false, then adequate potassium helps onion plants better withstand injurious cold.', 'Given that death usually occurs in infancy or early childhood, it can be inferred that if fall leafs are located in lawns, then internet technology is different from that of advertising media.', 'Once we know if fall leafs are located in lawns, then internet technology is different from that of advertising media, we also know that spirituality is religion.']
|
If most horses adapt to domestication, then office buildings are located in work. Given that the claim that either death usually occurs in infancy or early childhood or most horses adapt to domestication is false, it can be inferred that the notion that 'adequate potassium helps onion plants better withstand injurious cold' is untrue. So long as spirituality is religion, 'office buildings are located in work' is true. Either streams produce a stream bed whose cross-section reflects the flow regime or numerous florets have stamens. Whenever it is true that streams produce a stream bed whose cross-section reflects the flow regime, 'if the claim that either death usually occurs in infancy or early childhood or most horses adapt to domestication is false, then adequate potassium helps onion plants better withstand injurious cold' is true. When numerous florets have stamens is true, it follows that if the claim that either death usually occurs in infancy or early childhood or most horses adapt to domestication is false, then adequate potassium helps onion plants better withstand injurious cold. Given that death usually occurs in infancy or early childhood, it can be inferred that if fall leafs are located in lawns, then internet technology is different from that of advertising media. Once we know if fall leafs are located in lawns, then internet technology is different from that of advertising media, we also know that spirituality is religion.
|
office buildings are located in work.
|
Office buildings are located in work.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or [2].).), then [4]. [SC1-2]
If (Not (Either [1] or [2].).), then (Not [4].).
Therefore, Either [1] or [2]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Not (Either [1] or [2].).), then [4].).
If [6], then (If (Not (Either [1] or [2].).), then [4].).
Therefore, If (Not (Either [1] or [2].).), then [4]..
[SC2-1]
Hypothetical Syllogism:
If [1], then [3]. [SC1-2]
If [3], then [0].
Therefore, If [1], then [0]..
[SC1-2]
Hypothetical Syllogism:
If [1], then (If [7], then [8].).
If (If [7], then [8].), then [3].
Therefore, If [1], then [3]..
|
{0: 'Office buildings are located in work.', 1: 'Death usually occurs in infancy or early childhood.', 2: 'Most horses adapt to domestication.', 3: 'Spirituality is religion.', 4: 'Adequate potassium helps onion plants better withstand injurious cold.', 5: 'Streams produce a stream bed whose cross-section reflects the flow regime.', 6: 'Numerous florets have stamens.', 7: 'Fall leafs are located in lawns.', 8: 'Internet technology is different from that of advertising media.'}
| 5 |
4,640 |
["Whenever it is true that either astronomers use measurements of the red shift of stars and galaxies as a distance indicator or most countries are strong in some aspects of internal security but weak in others, 'some tracts cause pain' is true.", 'The claim that either mitosis consists of four stages or some food is eaten by elands does not reflect reality.', 'If the claim that if phosphoric acid contains three hydrogen ions, then some tracts cause pain does not reflect reality, then aliens have rich dream lives, in which they dream vivid, color images.', "One may reasonably assume that if the claim that if the notion that 'either phosphoric acid contains three hydrogen ions or either astronomers use measurements of the red shift of stars and galaxies as a distance indicator or most countries are strong in some aspects of internal security but weak in others' is untrue, then either mitosis consists of four stages or some food is eaten by elands does not reflect reality, then animals become restless and irritable and are hyperresponsive to auditory and visual stimuli.", 'Some people mistakenly believe that animals become restless and irritable and are hyperresponsive to auditory and visual stimuli.', "Whenever it is true that all catalysts are enzymes, 'if the claim that if phosphoric acid contains three hydrogen ions, then some tracts cause pain does not reflect reality, then it is not true that aliens have rich dream lives, in which they dream vivid, color images' is true.", 'It is the case that all catalysts are enzymes.']
|
Whenever it is true that either astronomers use measurements of the red shift of stars and galaxies as a distance indicator or most countries are strong in some aspects of internal security but weak in others, 'some tracts cause pain' is true. The claim that either mitosis consists of four stages or some food is eaten by elands does not reflect reality. If the claim that if phosphoric acid contains three hydrogen ions, then some tracts cause pain does not reflect reality, then aliens have rich dream lives, in which they dream vivid, color images. One may reasonably assume that if the claim that if the notion that 'either phosphoric acid contains three hydrogen ions or either astronomers use measurements of the red shift of stars and galaxies as a distance indicator or most countries are strong in some aspects of internal security but weak in others' is untrue, then either mitosis consists of four stages or some food is eaten by elands does not reflect reality, then animals become restless and irritable and are hyperresponsive to auditory and visual stimuli. Some people mistakenly believe that animals become restless and irritable and are hyperresponsive to auditory and visual stimuli. Whenever it is true that all catalysts are enzymes, 'if the claim that if phosphoric acid contains three hydrogen ions, then some tracts cause pain does not reflect reality, then it is not true that aliens have rich dream lives, in which they dream vivid, color images' is true. It is the case that all catalysts are enzymes.
|
The statement 'some tracts cause pain' can be considered true.
|
The statement that 'some tracts cause pain' is incorrect.
|
FALSE
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].). [SC1-1]
If [1], then [0]. [SC2-1]
If (Either [2] or [3].), then [0].
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either [1] or (Either [2] or [3].).).), then (Either [4] or [5].). [SC1-2]
Not (Either [4] or [5].).
Therefore, Either [1] or (Either [2] or [3].)..
[SC1-2]
Modus Tonens:
If (Not (If (Not (Either [1] or (Either [2] or [3].).).), then (Either [4] or [5].).).), then [7].
Not [7].
Therefore, If (Not (Either [1] or (Either [2] or [3].).).), then (Either [4] or [5].)..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [1], then [0].).), then [6].
If (Not (If [1], then [0].).), then (Not [6].). [SC2-2]
Therefore, If [1], then [0]..
[SC2-2]
Modus Ponens:
If [8], then (If (Not (If [1], then [0].).), then (Not [6].).).
[8]
Therefore, If (Not (If [1], then [0].).), then (Not [6].)..
|
{0: 'Some tracts cause pain.', 1: 'Phosphoric acid contains three hydrogen ions.', 2: 'Astronomers use measurements of the red shift of stars and galaxies as a distance indicator.', 3: 'Most countries are strong in some aspects of internal security but weak in others.', 4: 'Mitosis consists of four stages.', 5: 'Some food is eaten by elands.', 6: 'Aliens have rich dream lives, in which they dream vivid, color images.', 7: 'Animals become restless and irritable and are hyperresponsive to auditory and visual stimuli.', 8: 'All catalysts are enzymes.'}
| 5 |
4,532 |
['water is able to diffuse freely between the two cells.', 'When the claim that if water is able to diffuse freely between the two cells, then pelicans are large birds with large pouched bills does not reflect reality is true, it follows that those that suggest vacuoles also regulate the water content of certain one-celled animals are wrong.', 'If either most multicellular organisms display some form of symmetry or technology companies produce real unit growth every year, with stable or declining prices, then if the claim that if water is able to diffuse freely between the two cells, then pelicans are large birds with large pouched bills does not reflect reality, then vacuoles also regulate the water content of certain one-celled animals.', 'Once we know if timelines represent information that proceeds in temporal order, then water helps restore lost fluids and keeps mucus thin and flowing, we also know that if the claim that if water is able to diffuse freely between the two cells, then pelicans are large birds with large pouched bills does not reflect reality, then vacuoles also regulate the water content of certain one-celled animals.', 'We know that at least one of two things is true: people learn languages, like anything else, in different ways, or a gaslight is light.', "Whenever it is true that a gaslight is light, 'either either most multicellular organisms display some form of symmetry or technology companies produce real unit growth every year, with stable or declining prices or if timelines represent information that proceeds in temporal order, then water helps restore lost fluids and keeps mucus thin and flowing' is true.", 'Should it be the case that the statement that states if people learn languages, like anything else, in different ways, then either either most multicellular organisms display some form of symmetry or technology companies produce real unit growth every year, with stable or declining prices or if timelines represent information that proceeds in temporal order, then water helps restore lost fluids and keeps mucus thin and flowing is false, it follows that electrons are found in clouds that surround the nucleus of an atom.', "So long as the statement that states if people learn languages, like anything else, in different ways, then either either most multicellular organisms display some form of symmetry or technology companies produce real unit growth every year, with stable or declining prices or if timelines represent information that proceeds in temporal order, then water helps restore lost fluids and keeps mucus thin and flowing is false, 'the notion that 'electrons are found in clouds that surround the nucleus of an atom' is untrue' is true."]
|
water is able to diffuse freely between the two cells. When the claim that if water is able to diffuse freely between the two cells, then pelicans are large birds with large pouched bills does not reflect reality is true, it follows that those that suggest vacuoles also regulate the water content of certain one-celled animals are wrong. If either most multicellular organisms display some form of symmetry or technology companies produce real unit growth every year, with stable or declining prices, then if the claim that if water is able to diffuse freely between the two cells, then pelicans are large birds with large pouched bills does not reflect reality, then vacuoles also regulate the water content of certain one-celled animals. Once we know if timelines represent information that proceeds in temporal order, then water helps restore lost fluids and keeps mucus thin and flowing, we also know that if the claim that if water is able to diffuse freely between the two cells, then pelicans are large birds with large pouched bills does not reflect reality, then vacuoles also regulate the water content of certain one-celled animals. We know that at least one of two things is true: people learn languages, like anything else, in different ways, or a gaslight is light. Whenever it is true that a gaslight is light, 'either either most multicellular organisms display some form of symmetry or technology companies produce real unit growth every year, with stable or declining prices or if timelines represent information that proceeds in temporal order, then water helps restore lost fluids and keeps mucus thin and flowing' is true. Should it be the case that the statement that states if people learn languages, like anything else, in different ways, then either either most multicellular organisms display some form of symmetry or technology companies produce real unit growth every year, with stable or declining prices or if timelines represent information that proceeds in temporal order, then water helps restore lost fluids and keeps mucus thin and flowing is false, it follows that electrons are found in clouds that surround the nucleus of an atom. So long as the statement that states if people learn languages, like anything else, in different ways, then either either most multicellular organisms display some form of symmetry or technology companies produce real unit growth every year, with stable or declining prices or if timelines represent information that proceeds in temporal order, then water helps restore lost fluids and keeps mucus thin and flowing is false, 'the notion that 'electrons are found in clouds that surround the nucleus of an atom' is untrue' is true.
|
It is a simple truth that pelicans are large birds with large pouched bills.
|
We know that the claim that pelicans are large birds with large pouched bills is false.
|
FALSE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [1], then [0].).), then [2]. [SC1-2]
If (Not (If [1], then [0].).), then (Not [2].).
Therefore, If [1], then [0]..
[SC1-2]
Disjunction Elimination:
Either (Either [3] or [4].) or (If [5], then [6].). [SC1-3]
If (Either [3] or [4].), then (If (Not (If [1], then [0].).), then [2].).
If (If [5], then [6].), then (If (Not (If [1], then [0].).), then [2].).
Therefore, If (Not (If [1], then [0].).), then [2]..
[SC1-3]
Disjunction Elimination:
Either [7] or [8].
If [7], then (Either (Either [3] or [4].) or (If [5], then [6].).). [SC2-4]
If [8], then (Either (Either [3] or [4].) or (If [5], then [6].).).
Therefore, Either (Either [3] or [4].) or (If [5], then [6].)..
[SC2-4]
Reductio Ad Absurdum:
If (Not (If [7], then (Either (Either [3] or [4].) or (If [5], then [6].).).).), then [9].
If (Not (If [7], then (Either (Either [3] or [4].) or (If [5], then [6].).).).), then (Not [9].).
Therefore, If [7], then (Either (Either [3] or [4].) or (If [5], then [6].).)..
|
{0: 'Pelicans are large birds with large pouched bills.', 1: 'Water is able to diffuse freely between the two cells.', 2: 'Vacuoles also regulate the water content of certain one-celled animals.', 3: 'Most multicellular organisms display some form of symmetry.', 4: 'Technology companies produce real unit growth every year, with stable or declining prices.', 5: 'Timelines represent information that proceeds in temporal order.', 6: 'Water helps restore lost fluids and keeps mucus thin and flowing.', 7: 'People learn languages, like anything else, in different ways.', 8: 'A gaslight is light.', 9: 'Electrons are found in clouds that surround the nucleus of an atom.'}
| 5 |
4,126 |
["So long as the notion that 'either either pinworms thrive on sugar and refined carbohydrates or hagfishes have (part) brains or the statement 'time management is one of the keys to success in college and throughout life' can be considered false' is untrue, 'sunflowers grow in ranges' is true.", 'We know that the claim that sunflowers grow in ranges is false.', 'Given that either pinworms thrive on sugar and refined carbohydrates or hagfishes have (part) brains, it can be inferred that management is the process of coordinating various resources to achieve organizational objectives.', 'One may reasonably assume that if management is the process of coordinating various resources to achieve organizational objectives, then if faculty provides plant materials, then apoptosis is increased in diabetic rat retinas.', 'Provided that the claim that if either pinworms thrive on sugar and refined carbohydrates or hagfishes have (part) brains, then the claim that if faculty provides plant materials, then apoptosis is increased in diabetic rat retinas does not reflect reality does not correspond with reality, we know that bulls grow darker with age and become black about the head and neck.', 'Some people mistakenly believe that bulls grow darker with age and become black about the head and neck.']
|
So long as the notion that 'either either pinworms thrive on sugar and refined carbohydrates or hagfishes have (part) brains or the statement 'time management is one of the keys to success in college and throughout life' can be considered false' is untrue, 'sunflowers grow in ranges' is true. We know that the claim that sunflowers grow in ranges is false. Given that either pinworms thrive on sugar and refined carbohydrates or hagfishes have (part) brains, it can be inferred that management is the process of coordinating various resources to achieve organizational objectives. One may reasonably assume that if management is the process of coordinating various resources to achieve organizational objectives, then if faculty provides plant materials, then apoptosis is increased in diabetic rat retinas. Provided that the claim that if either pinworms thrive on sugar and refined carbohydrates or hagfishes have (part) brains, then the claim that if faculty provides plant materials, then apoptosis is increased in diabetic rat retinas does not reflect reality does not correspond with reality, we know that bulls grow darker with age and become black about the head and neck. Some people mistakenly believe that bulls grow darker with age and become black about the head and neck.
|
The statement 'time management is one of the keys to success in college and throughout life' can be considered false.
|
The statement 'time management is one of the keys to success in college and throughout life' can be considered false.
|
TRUE
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or (Not [0].). [SC1-1]
Not (Either [1] or [2].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (Either (Either [1] or [2].) or (Not [0].).).), then [3].
Not [3].
Therefore, Either (Either [1] or [2].) or (Not [0].)..
[SC2-1]
Reductio Ad Absurdum:
If (Either [1] or [2].), then (If [4], then [5].). [SC1-2]
If (Either [1] or [2].), then (Not (If [4], then [5].).). [SC2-2]
Therefore, Not (Either [1] or [2].)..
[SC1-2]
Hypothetical Syllogism:
If (Either [1] or [2].), then [6].
If [6], then (If [4], then [5].).
Therefore, If (Either [1] or [2].), then (If [4], then [5].)..
[SC2-2]
Modus Tonens:
If (Not (If (Either [1] or [2].), then (Not (If [4], then [5].).).).), then [7].
Not [7].
Therefore, If (Either [1] or [2].), then (Not (If [4], then [5].).)..
|
{0: 'Time management is one of the keys to success in college and throughout life.', 1: 'Pinworms thrive on sugar and refined carbohydrates.', 2: 'Hagfishes have (part) brains.', 3: 'Sunflowers grow in ranges.', 4: 'Faculty provides plant materials.', 5: 'Apoptosis is increased in diabetic rat retinas.', 6: 'Management is the process of coordinating various resources to achieve organizational objectives.', 7: 'Bulls grow darker with age and become black about the head and neck.'}
| 5 |
4,259 |
["Provided that the claim that if the statement that 'yield refers to grain yield unless otherwise noted' is incorrect, then nematodes lack circulatory systems is false, we know that stains have pigments that can settle out quickly, especially in dark colors.", "The statement that 'stains have pigments that can settle out quickly, especially in dark colors' is incorrect.", "So long as some people mistakenly believe that if nematodes lack circulatory systems, then some temperature causes explosions, 'if neutrinos are neutral electron-like particles that originate from the sun or cosmic rays in space, then carabaos weigh kgs' is true.", 'Those that suggest if neutrinos are neutral electron-like particles that originate from the sun or cosmic rays in space, then carabaos weigh kgs are wrong.', "On the condition that some people mistakenly believe that if nematodes lack circulatory systems, then the notion that 'some temperature causes explosions' is untrue, it is definitely the case that stress comes in all the different forms.", "The notion that 'stress comes in all the different forms' is untrue."]
|
Provided that the claim that if the statement that 'yield refers to grain yield unless otherwise noted' is incorrect, then nematodes lack circulatory systems is false, we know that stains have pigments that can settle out quickly, especially in dark colors. The statement that 'stains have pigments that can settle out quickly, especially in dark colors' is incorrect. So long as some people mistakenly believe that if nematodes lack circulatory systems, then some temperature causes explosions, 'if neutrinos are neutral electron-like particles that originate from the sun or cosmic rays in space, then carabaos weigh kgs' is true. Those that suggest if neutrinos are neutral electron-like particles that originate from the sun or cosmic rays in space, then carabaos weigh kgs are wrong. On the condition that some people mistakenly believe that if nematodes lack circulatory systems, then the notion that 'some temperature causes explosions' is untrue, it is definitely the case that stress comes in all the different forms. The notion that 'stress comes in all the different forms' is untrue.
|
It is fair to say that yield refers to grain yield unless otherwise noted.
|
It is fair to say that yield refers to grain yield unless otherwise noted.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Not [0].), then [1].).), then [3].
Not [3].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2]. [SC1-2]
If [1], then (Not [2].). [SC2-2]
Therefore, Not [1]..
[SC1-2]
Modus Tonens:
If (Not (If [1], then [2].).), then (If [5], then [6].).
Not (If [5], then [6].).
Therefore, If [1], then [2]..
[SC2-2]
Modus Tonens:
If (Not (If [1], then (Not [2].).).), then [4].
Not [4].
Therefore, If [1], then (Not [2].)..
|
{0: 'Yield refers to grain yield unless otherwise noted.', 1: 'Nematodes lack circulatory systems.', 2: 'Some temperature causes explosions.', 3: 'Stains have pigments that can settle out quickly, especially in dark colors.', 4: 'Stress comes in all the different forms.', 5: 'Neutrinos are neutral electron-like particles that originate from the sun or cosmic rays in space.', 6: 'Carabaos weigh kgs.'}
| 5 |
4,742 |
["The statement that 'grace always promotes holiness of faith and holiness of life' is incorrect.", "Given that the statement 'if fin whales are the loudest animal on earth, then if it is not true that mexican has (part) corpi, then grace always promotes holiness of faith and holiness of life' can be considered false, it can be inferred that either vicarious reinforcement represents a kind of self-reinforcement or some equations govern theories.", 'The claim that either vicarious reinforcement represents a kind of self-reinforcement or some equations govern theories does not reflect reality.', 'We know that the claim that if chemicals contaminate drink water, then wildfires occur both on private and government property is false.', 'If it is not true that either if chemicals contaminate drink water, then wildfires occur both on private and government property or fin whales are the loudest animal on earth, then most brown bears have senses.', 'The claim that most brown bears have senses does not reflect reality.']
|
The statement that 'grace always promotes holiness of faith and holiness of life' is incorrect. Given that the statement 'if fin whales are the loudest animal on earth, then if it is not true that mexican has (part) corpi, then grace always promotes holiness of faith and holiness of life' can be considered false, it can be inferred that either vicarious reinforcement represents a kind of self-reinforcement or some equations govern theories. The claim that either vicarious reinforcement represents a kind of self-reinforcement or some equations govern theories does not reflect reality. We know that the claim that if chemicals contaminate drink water, then wildfires occur both on private and government property is false. If it is not true that either if chemicals contaminate drink water, then wildfires occur both on private and government property or fin whales are the loudest animal on earth, then most brown bears have senses. The claim that most brown bears have senses does not reflect reality.
|
mexican has (part) corpi.
|
Mexican has (part) plasma membranes.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (If (Not [0].), then [1].). [SC1-2]
[2] [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Tonens:
If (Not (If [2], then (If (Not [0].), then [1].).).), then (Either [3] or [4].).
Not (Either [3] or [4].).
Therefore, If [2], then (If (Not [0].), then [1].)..
[SC2-2]
Disjunctive Syllogism:
Either (If [5], then [6].) or [2]. [SC1-3]
Not (If [5], then [6].).
Therefore, [2].
[SC1-3]
Modus Tonens:
If (Not (Either (If [5], then [6].) or [2].).), then [7].
Not [7].
Therefore, Either (If [5], then [6].) or [2]..
|
{0: 'Mexican has (part) corpi.', 1: 'Grace always promotes holiness of faith and holiness of life.', 2: 'Fin whales are the loudest animal on earth.', 3: 'Vicarious reinforcement represents a kind of self-reinforcement.', 4: 'Some equations govern theories.', 5: 'Chemicals contaminate drink water.', 6: 'Wildfires occur both on private and government property.', 7: 'Most brown bears have senses.'}
| 5 |
4,761 |
['Assuming butterflies use nectar and pollen, we know that roofs are part of cars.', "So long as some vegetarians are vegans, 'cockroaches are inside habitats' is true.", "Once we know the notion that 'if if butterflies use nectar and pollen, then roofs are part of cars, then if it is not the case that some diarrhea develops in terminal stages, then some vegetarians are vegans' is untrue, we also know that functionality is practicality.", 'The claim that functionality is practicality does not correspond with reality.', 'We know that at least one of two things is true: breathing can make people feel calm and happy, or it is a common misconception that cockroaches are inside habitats.', 'We know that the claim that breathing can make people feel calm and happy is false.']
|
Assuming butterflies use nectar and pollen, we know that roofs are part of cars. So long as some vegetarians are vegans, 'cockroaches are inside habitats' is true. Once we know the notion that 'if if butterflies use nectar and pollen, then roofs are part of cars, then if it is not the case that some diarrhea develops in terminal stages, then some vegetarians are vegans' is untrue, we also know that functionality is practicality. The claim that functionality is practicality does not correspond with reality. We know that at least one of two things is true: breathing can make people feel calm and happy, or it is a common misconception that cockroaches are inside habitats. We know that the claim that breathing can make people feel calm and happy is false.
|
The statement that states some diarrhea develops in terminal stages is right.
|
The statement that states some diarrhea develops in terminal stages is right.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If (If [3], then [4].), then (If (Not [0].), then [1].). [SC1-2]
If [3], then [4].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Tonens:
If (Not (If (If [3], then [4].), then (If (Not [0].), then [1].).).), then [6].
Not [6].
Therefore, If (If [3], then [4].), then (If (Not [0].), then [1].)..
[SC2-1]
Modus Tonens:
If [1], then [2].
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Disjunctive Syllogism:
Either [5] or (Not [2].).
Not [5].
Therefore, Not [2]..
|
{0: 'Some diarrhea develops in terminal stages.', 1: 'Some vegetarians are vegans.', 2: 'Cockroaches are inside habitats.', 3: 'Butterflies use nectar and pollen.', 4: 'Roofs are part of cars.', 5: 'Breathing can make people feel calm and happy.', 6: 'Functionality is practicality.'}
| 5 |
4,137 |
["So long as the claim that water is a common substance but one with special properties has no merit, 'dogs are proverbially and in fact much better at odor detection than humans are' is true.", 'It is fair to say that most snakes possess venom.', 'There is good reason to believe that either pregnancy discrimination is illegal under the Saskatchewan Human Rights Code or synchrotrons are cyclotrons.', "Given that synchrotrons are cyclotrons, it can be inferred that if most snakes possess venom, then the statement that 'dogs are proverbially and in fact much better at odor detection than humans are' is incorrect.", "One may reasonably assume that if it is not true that if pregnancy discrimination is illegal under the Saskatchewan Human Rights Code, then if most snakes possess venom, then the statement that 'dogs are proverbially and in fact much better at odor detection than humans are' is incorrect, then most insect neurons are monopolar.", "If rodents reach maturity, then the statement that 'most insect neurons are monopolar' is incorrect.", 'The statement that states rodents reach maturity is right.']
|
So long as the claim that water is a common substance but one with special properties has no merit, 'dogs are proverbially and in fact much better at odor detection than humans are' is true. It is fair to say that most snakes possess venom. There is good reason to believe that either pregnancy discrimination is illegal under the Saskatchewan Human Rights Code or synchrotrons are cyclotrons. Given that synchrotrons are cyclotrons, it can be inferred that if most snakes possess venom, then the statement that 'dogs are proverbially and in fact much better at odor detection than humans are' is incorrect. One may reasonably assume that if it is not true that if pregnancy discrimination is illegal under the Saskatchewan Human Rights Code, then if most snakes possess venom, then the statement that 'dogs are proverbially and in fact much better at odor detection than humans are' is incorrect, then most insect neurons are monopolar. If rodents reach maturity, then the statement that 'most insect neurons are monopolar' is incorrect. The statement that states rodents reach maturity is right.
|
It is reasonable to believe that water is a common substance but one with special properties.
|
It is not true that water is a common substance but one with special properties.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [2], then (Not [1].). [SC1-2]
[2]
Therefore, Not [1]..
[SC1-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If [2], then (Not [1].).). [SC2-3]
If [4], then (If [2], then (Not [1].).).
Therefore, If [2], then (Not [1].)..
[SC2-3]
Modus Tonens:
If (Not (If [3], then (If [2], then (Not [1].).).).), then [5].
Not [5]. [SC2-4]
Therefore, If [3], then (If [2], then (Not [1].).)..
[SC2-4]
Modus Ponens:
If [6], then (Not [5].).
[6]
Therefore, Not [5]..
|
{0: 'Water is a common substance but one with special properties.', 1: 'Dogs are proverbially and in fact much better at odor detection than humans are.', 2: 'Most snakes possess venom.', 3: 'Pregnancy discrimination is illegal under the Saskatchewan Human Rights Code.', 4: 'Synchrotrons are cyclotrons.', 5: 'Most insect neurons are monopolar.', 6: 'Rodents reach maturity.'}
| 5 |
4,007 |
['The statement, carnivores swallow prey, does not hold.', 'On the condition that it is not true that either illuminated letters are calligraphic letters which are embellished or most excellent climbers have toes, it is definitely the case that infants means persons under one year of age.', 'The claim that infants means persons under one year of age is false.', 'Either either muskrats continue to live in large grous even when fighting and cannibalism occur in high rates or advent is a period marked by waiting, anticipating something to happen or if illuminated letters are calligraphic letters which are embellished, then either carnivores swallow prey or paintballs have (part) sections.', 'The statement that states either muskrats continue to live in large grous even when fighting and cannibalism occur in high rates or advent is a period marked by waiting, anticipating something to happen is false.', 'Should it be the case that it is a common misconception that if most excellent climbers have toes, then either carnivores swallow prey or paintballs have (part) sections, it follows that if most enzymes break down skin, then yeast is used as a model to teach some of the more actively researched areas of cell biology.', "Whenever it is true that it is a common misconception that if most excellent climbers have toes, then either carnivores swallow prey or paintballs have (part) sections, 'the claim that if most enzymes break down skin, then yeast is used as a model to teach some of the more actively researched areas of cell biology is false' is true."]
|
The statement, carnivores swallow prey, does not hold. On the condition that it is not true that either illuminated letters are calligraphic letters which are embellished or most excellent climbers have toes, it is definitely the case that infants means persons under one year of age. The claim that infants means persons under one year of age is false. Either either muskrats continue to live in large grous even when fighting and cannibalism occur in high rates or advent is a period marked by waiting, anticipating something to happen or if illuminated letters are calligraphic letters which are embellished, then either carnivores swallow prey or paintballs have (part) sections. The statement that states either muskrats continue to live in large grous even when fighting and cannibalism occur in high rates or advent is a period marked by waiting, anticipating something to happen is false. Should it be the case that it is a common misconception that if most excellent climbers have toes, then either carnivores swallow prey or paintballs have (part) sections, it follows that if most enzymes break down skin, then yeast is used as a model to teach some of the more actively researched areas of cell biology. Whenever it is true that it is a common misconception that if most excellent climbers have toes, then either carnivores swallow prey or paintballs have (part) sections, 'the claim that if most enzymes break down skin, then yeast is used as a model to teach some of the more actively researched areas of cell biology is false' is true.
|
It is reasonable to believe that paintballs have (part) sections.
|
It is reasonable to believe that paintballs have (part) sections.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [2] or [3]. [SC1-2]
If [2], then (Either [1] or [0].). [SC2-2]
If [3], then (Either [1] or [0].). [SC3-2]
Therefore, Either [1] or [0]..
[SC1-2]
Modus Tonens:
If (Not (Either [2] or [3].).), then [8].
Not [8].
Therefore, Either [2] or [3]..
[SC2-2]
Disjunctive Syllogism:
Either (Either [4] or [5].) or (If [2], then (Either [1] or [0].).).
Not (Either [4] or [5].).
Therefore, If [2], then (Either [1] or [0].)..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If [3], then (Either [1] or [0].).).), then (If [6], then [7].).
If (Not (If [3], then (Either [1] or [0].).).), then (Not (If [6], then [7].).).
Therefore, If [3], then (Either [1] or [0].)..
|
{0: 'Paintballs have (part) sections.', 1: 'Carnivores swallow prey.', 2: 'Illuminated letters are calligraphic letters which are embellished.', 3: 'Most excellent climbers have toes.', 4: 'Muskrats continue to live in large grous even when fighting and cannibalism occur in high rates.', 5: 'Advent is a period marked by waiting, anticipating something to happen.', 6: 'Most enzymes break down skin.', 7: 'Yeast is used as a model to teach some of the more actively researched areas of cell biology.', 8: 'Infants means persons under one year of age.'}
| 5 |
4,502 |
['Assuming some dogs kill mammals, we know that either either a plea bargaining is a bargaining or saltwater is denser than fresh water, and everything floats more easily in denser water or political parties choose the man or woman they feel best represents their views.', 'It is the case that some dogs kill mammals.', 'When some people mistakenly believe that if either a plea bargaining is a bargaining or saltwater is denser than fresh water, and everything floats more easily in denser water, then most minerals make components is true, it follows that covalent bonds tend to form between elements in the middle.', 'When some people mistakenly believe that if either a plea bargaining is a bargaining or saltwater is denser than fresh water, and everything floats more easily in denser water, then most minerals make components is true, it follows that the claim that covalent bonds tend to form between elements in the middle does not correspond with reality.', "When the statement that states if political parties choose the man or woman they feel best represents their views, then most minerals make components is false is true, it follows that giant kelp forms undersea forests in the cool waters of many of the world's oceans.", "If giant kelp forms undersea forests in the cool waters of many of the world's oceans, then gnomes are similar to both fighters and magic-users.", 'It is not the case that gnomes are similar to both fighters and magic-users.']
|
Assuming some dogs kill mammals, we know that either either a plea bargaining is a bargaining or saltwater is denser than fresh water, and everything floats more easily in denser water or political parties choose the man or woman they feel best represents their views. It is the case that some dogs kill mammals. When some people mistakenly believe that if either a plea bargaining is a bargaining or saltwater is denser than fresh water, and everything floats more easily in denser water, then most minerals make components is true, it follows that covalent bonds tend to form between elements in the middle. When some people mistakenly believe that if either a plea bargaining is a bargaining or saltwater is denser than fresh water, and everything floats more easily in denser water, then most minerals make components is true, it follows that the claim that covalent bonds tend to form between elements in the middle does not correspond with reality. When the statement that states if political parties choose the man or woman they feel best represents their views, then most minerals make components is false is true, it follows that giant kelp forms undersea forests in the cool waters of many of the world's oceans. If giant kelp forms undersea forests in the cool waters of many of the world's oceans, then gnomes are similar to both fighters and magic-users. It is not the case that gnomes are similar to both fighters and magic-users.
|
The statement 'most minerals make components' can be considered true.
|
Minerals play a very important role in estrous cycle function and conception.
|
Uncertain
|
Disjunction Elimination:
Either (Either [1] or [2].) or [3]. [SC1-1]
If (Either [1] or [2].), then [0]. [SC2-1]
If [3], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [5], then (Either (Either [1] or [2].) or [3].).
[5]
Therefore, Either (Either [1] or [2].) or [3]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (Either [1] or [2].), then [0].).), then [6].
If (Not (If (Either [1] or [2].), then [0].).), then (Not [6].).
Therefore, If (Either [1] or [2].), then [0]..
[SC3-1]
Modus Tonens:
If (Not (If [3], then [0].).), then [4].
Not [4]. [SC2-2]
Therefore, If [3], then [0]..
[SC2-2]
Modus Tonens:
If [4], then [7].
Not [7].
Therefore, Not [4]..
|
{0: 'Most minerals make components.', 1: 'A plea bargaining is a bargaining.', 2: 'Saltwater is denser than fresh water, and everything floats more easily in denser water.', 3: 'Political parties choose the man or woman they feel best represents their views.', 4: "Giant kelp forms undersea forests in the cool waters of many of the world's oceans.", 5: 'Some dogs kill mammals.', 6: 'Covalent bonds tend to form between elements in the middle.', 7: 'Gnomes are similar to both fighters and magic-users.'}
| 5 |
4,831 |
['Given that most fish have swim behavior, it can be inferred that tuberculosis is one of the oldest diseases of humans.', 'The statement, polymers typically exhibit complex behavior, including rate-dependence and inelasticity, does not hold.', 'We know that either lyrics are capable of poems or either baseball moves faster than cricket or every human being has a positive attribute.', 'Once we know lyrics are capable of poems, we also know that if if some midges drink water, then loons spend the winter season along the Atlantic, Pacific, and Gulf coasts, then tuberculosis is one of the oldest diseases of humans.', 'One may reasonably assume that if the statement that states either polymers typically exhibit complex behavior, including rate-dependence and inelasticity or either if some midges drink water, then loons spend the winter season along the Atlantic, Pacific, and Gulf coasts or most fish have swim behavior is false, then if seagulls seek food, then fireballs can be green, yellow, orange, blue, red, as well as brilliant white.', 'Provided that the statement that states either polymers typically exhibit complex behavior, including rate-dependence and inelasticity or either if some midges drink water, then loons spend the winter season along the Atlantic, Pacific, and Gulf coasts or most fish have swim behavior is false, we know that those that suggest if seagulls seek food, then fireballs can be green, yellow, orange, blue, red, as well as brilliant white are wrong.', 'On the condition that the claim that if either baseball moves faster than cricket or every human being has a positive attribute, then if if some midges drink water, then loons spend the winter season along the Atlantic, Pacific, and Gulf coasts, then tuberculosis is one of the oldest diseases of humans does not reflect reality, it is definitely the case that symptoms include muscle pain.', 'Provided that the claim that if either baseball moves faster than cricket or every human being has a positive attribute, then if if some midges drink water, then loons spend the winter season along the Atlantic, Pacific, and Gulf coasts, then tuberculosis is one of the oldest diseases of humans does not reflect reality, we know that the statement, symptoms include muscle pain, does not hold.']
|
Given that most fish have swim behavior, it can be inferred that tuberculosis is one of the oldest diseases of humans. The statement, polymers typically exhibit complex behavior, including rate-dependence and inelasticity, does not hold. We know that either lyrics are capable of poems or either baseball moves faster than cricket or every human being has a positive attribute. Once we know lyrics are capable of poems, we also know that if if some midges drink water, then loons spend the winter season along the Atlantic, Pacific, and Gulf coasts, then tuberculosis is one of the oldest diseases of humans. One may reasonably assume that if the statement that states either polymers typically exhibit complex behavior, including rate-dependence and inelasticity or either if some midges drink water, then loons spend the winter season along the Atlantic, Pacific, and Gulf coasts or most fish have swim behavior is false, then if seagulls seek food, then fireballs can be green, yellow, orange, blue, red, as well as brilliant white. Provided that the statement that states either polymers typically exhibit complex behavior, including rate-dependence and inelasticity or either if some midges drink water, then loons spend the winter season along the Atlantic, Pacific, and Gulf coasts or most fish have swim behavior is false, we know that those that suggest if seagulls seek food, then fireballs can be green, yellow, orange, blue, red, as well as brilliant white are wrong. On the condition that the claim that if either baseball moves faster than cricket or every human being has a positive attribute, then if if some midges drink water, then loons spend the winter season along the Atlantic, Pacific, and Gulf coasts, then tuberculosis is one of the oldest diseases of humans does not reflect reality, it is definitely the case that symptoms include muscle pain. Provided that the claim that if either baseball moves faster than cricket or every human being has a positive attribute, then if if some midges drink water, then loons spend the winter season along the Atlantic, Pacific, and Gulf coasts, then tuberculosis is one of the oldest diseases of humans does not reflect reality, we know that the statement, symptoms include muscle pain, does not hold.
|
The claim that tuberculosis is one of the oldest diseases of humans is true.
|
The claim that tuberculosis is one of the oldest diseases of humans is false.
|
FALSE
|
Disjunction Elimination:
Either (If [1], then [2].) or [3]. [SC1-1]
If (If [1], then [2].), then [0]. [SC2-1]
If [3], then [0].
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [7] or (Either (If [1], then [2].) or [3].). [SC1-2]
Not [7].
Therefore, Either (If [1], then [2].) or [3]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [7] or (Either (If [1], then [2].) or [3].).).), then (If [8], then [9].).
If (Not (Either [7] or (Either (If [1], then [2].) or [3].).).), then (Not (If [8], then [9].).).
Therefore, Either [7] or (Either (If [1], then [2].) or [3].)..
[SC2-1]
Disjunction Elimination:
Either [4] or (Either [5] or [6].).
If [4], then (If (If [1], then [2].), then [0].).
If (Either [5] or [6].), then (If (If [1], then [2].), then [0].). [SC3-2]
Therefore, If (If [1], then [2].), then [0]..
[SC3-2]
Reductio Ad Absurdum:
If (Not (If (Either [5] or [6].), then (If (If [1], then [2].), then [0].).).), then [10].
If (Not (If (Either [5] or [6].), then (If (If [1], then [2].), then [0].).).), then (Not [10].).
Therefore, If (Either [5] or [6].), then (If (If [1], then [2].), then [0].)..
|
{0: 'Tuberculosis is one of the oldest diseases of humans.', 1: 'Some midges drink water.', 2: 'Loons spend the winter season along the Atlantic, Pacific, and Gulf coasts.', 3: 'Most fish have swim behavior.', 4: 'Lyrics are capable of poems.', 5: 'Baseball moves faster than cricket.', 6: 'Every human being has a positive attribute.', 7: 'Polymers typically exhibit complex behavior, including rate-dependence and inelasticity.', 8: 'Seagulls seek food.', 9: 'Fireballs can be green, yellow, orange, blue, red, as well as brilliant white.', 10: 'Symptoms include muscle pain.'}
| 5 |
4,762 |
['At least one of two things is true: flooding occurs in low-lying areas of South Carolina such as river basins and coastal areas, or either adders have (part) vacuoles or cats tend to be more independent and sleep more as adults.', "So long as flooding occurs in low-lying areas of South Carolina such as river basins and coastal areas, 'ascendency takes place in space' is true.", 'Either milk has many nutrients to help babies grow and be healthy or if either adders have (part) vacuoles or cats tend to be more independent and sleep more as adults, then ascendency takes place in space.', 'Should it be the case that milk has many nutrients to help babies grow and be healthy, it follows that oral languages consist of sounds joined together in ways specified by grammar rules.', "Whenever it is true that oral languages consist of sounds joined together in ways specified by grammar rules, 'some children die before birthdays' is true.", "Whenever it is true that some children die before birthdays, 'deer chew cuds' is true.", "Whenever it is true that some children die before birthdays, 'the statement 'deer chew cuds' can be considered false' is true."]
|
At least one of two things is true: flooding occurs in low-lying areas of South Carolina such as river basins and coastal areas, or either adders have (part) vacuoles or cats tend to be more independent and sleep more as adults. So long as flooding occurs in low-lying areas of South Carolina such as river basins and coastal areas, 'ascendency takes place in space' is true. Either milk has many nutrients to help babies grow and be healthy or if either adders have (part) vacuoles or cats tend to be more independent and sleep more as adults, then ascendency takes place in space. Should it be the case that milk has many nutrients to help babies grow and be healthy, it follows that oral languages consist of sounds joined together in ways specified by grammar rules. Whenever it is true that oral languages consist of sounds joined together in ways specified by grammar rules, 'some children die before birthdays' is true. Whenever it is true that some children die before birthdays, 'deer chew cuds' is true. Whenever it is true that some children die before birthdays, 'the statement 'deer chew cuds' can be considered false' is true.
|
The idea that ascendency takes place in space is true.
|
The idea that ascendency takes place in space is true.
|
TRUE
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].).
If [1], then [0].
If (Either [2] or [3].), then [0]. [SC3-1]
Therefore, [0].
[SC3-1]
Disjunctive Syllogism:
Either [4] or (If (Either [2] or [3].), then [0].).
Not [4]. [SC2-2]
Therefore, If (Either [2] or [3].), then [0]..
[SC2-2]
Modus Tonens:
If [4], then [5]. [SC1-3]
Not [5]. [SC2-3]
Therefore, Not [4]..
[SC1-3]
Hypothetical Syllogism:
If [4], then [7].
If [7], then [5].
Therefore, If [4], then [5]..
[SC2-3]
Reductio Ad Absurdum:
If [5], then [6].
If [5], then (Not [6].).
Therefore, Not [5]..
|
{0: 'Ascendency takes place in space.', 1: 'Flooding occurs in low-lying areas of South Carolina such as river basins and coastal areas.', 2: 'Adders have (part) vacuoles.', 3: 'Cats tend to be more independent and sleep more as adults.', 4: 'Milk has many nutrients to help babies grow and be healthy.', 5: 'Some children die before birthdays.', 6: 'Deer chew cuds.', 7: 'Oral languages consist of sounds joined together in ways specified by grammar rules.'}
| 5 |
4,851 |
['Given that it is a common misconception that either most diesel locomotives use water as coolant or chilli is hot pepper, it can be inferred that most medical scientists become scientists.', 'It is not the case that young grubs feed within the crown area of the plant and kill it.', "Assuming infarction means death of a tissue or organ, we know that the statement 'most medical scientists become scientists' can be considered false.", "The statement 'infarction means death of a tissue or organ' is true.", 'We know that either eukaryotic chromosomes are linear, with the double helix sealing up at the two distant ends or if most diesel locomotives use water as coolant, then young grubs feed within the crown area of the plant and kill it.', 'The statement that states eukaryotic chromosomes are linear, with the double helix sealing up at the two distant ends is false.']
|
Given that it is a common misconception that either most diesel locomotives use water as coolant or chilli is hot pepper, it can be inferred that most medical scientists become scientists. It is not the case that young grubs feed within the crown area of the plant and kill it. Assuming infarction means death of a tissue or organ, we know that the statement 'most medical scientists become scientists' can be considered false. The statement 'infarction means death of a tissue or organ' is true. We know that either eukaryotic chromosomes are linear, with the double helix sealing up at the two distant ends or if most diesel locomotives use water as coolant, then young grubs feed within the crown area of the plant and kill it. The statement that states eukaryotic chromosomes are linear, with the double helix sealing up at the two distant ends is false.
|
The statement 'chilli is hot pepper' can be considered true.
|
Chillies range from large to small, and colours include green, white, purple, pink, and red.
|
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 [3].
Not [3]. [SC2-2]
Therefore, Either [1] or [0]..
[SC2-2]
Modus Ponens:
If [4], then (Not [3].).
[4]
Therefore, Not [3]..
[SC2-1]
Modus Tonens:
If [1], then [2]. [SC1-2]
Not [2].
Therefore, Not [1]..
[SC1-2]
Disjunctive Syllogism:
Either [5] or (If [1], then [2].).
Not [5].
Therefore, If [1], then [2]..
|
{0: 'Chilli is hot pepper.', 1: 'Most diesel locomotives use water as coolant.', 2: 'Young grubs feed within the crown area of the plant and kill it.', 3: 'Most medical scientists become scientists.', 4: 'Infarction means death of a tissue or organ.', 5: 'Eukaryotic chromosomes are linear, with the double helix sealing up at the two distant ends.'}
| 5 |
4,407 |
['Given that the claim that african lore is filled with stories of hunters being trampled to death because their bullets failed has no merit, it can be inferred that the claim that obesity can cause fatty deposits in the liver, leading to inflammation has no merit.', 'Given that we know that the claim that if the claim that african lore is filled with stories of hunters being trampled to death because their bullets failed has no merit, then obesity can cause fatty deposits in the liver, leading to inflammation is false, it can be inferred that if aerobic exercises work the heart and lungs as well as the muscles, and can improve overall health, then care is protection.', 'Should it be the case that amides are non-migratory slip additives, it follows that if if aerobic exercises work the heart and lungs as well as the muscles, and can improve overall health, then care is protection, then many factors can modify our genetic and metabolic propensity for illness and disease states.', 'The claim that amides are non-migratory slip additives is true.', 'Assuming many factors can modify our genetic and metabolic propensity for illness and disease states, we know that low power is a relative term.', 'The statement that states low power is a relative term is false.']
|
Given that the claim that african lore is filled with stories of hunters being trampled to death because their bullets failed has no merit, it can be inferred that the claim that obesity can cause fatty deposits in the liver, leading to inflammation has no merit. Given that we know that the claim that if the claim that african lore is filled with stories of hunters being trampled to death because their bullets failed has no merit, then obesity can cause fatty deposits in the liver, leading to inflammation is false, it can be inferred that if aerobic exercises work the heart and lungs as well as the muscles, and can improve overall health, then care is protection. Should it be the case that amides are non-migratory slip additives, it follows that if if aerobic exercises work the heart and lungs as well as the muscles, and can improve overall health, then care is protection, then many factors can modify our genetic and metabolic propensity for illness and disease states. The claim that amides are non-migratory slip additives is true. Assuming many factors can modify our genetic and metabolic propensity for illness and disease states, we know that low power is a relative term. The statement that states low power is a relative term is false.
|
The statement 'african lore is filled with stories of hunters being trampled to death because their bullets failed' can be considered true.
|
Some psychiatrists specialize in group therapy or individual counseling.
|
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 (If [2], then [3].).
Not (If [2], then [3].). [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Modus Tonens:
If (If [2], then [3].), then [4]. [SC1-3]
Not [4]. [SC2-3]
Therefore, Not (If [2], then [3].)..
[SC1-3]
Modus Ponens:
If [5], then (If (If [2], then [3].), then [4].).
[5]
Therefore, If (If [2], then [3].), then [4]..
[SC2-3]
Modus Tonens:
If [4], then [6].
Not [6].
Therefore, Not [4]..
|
{0: 'African lore is filled with stories of hunters being trampled to death because their bullets failed.', 1: 'Obesity can cause fatty deposits in the liver, leading to inflammation.', 2: 'Aerobic exercises work the heart and lungs as well as the muscles, and can improve overall health.', 3: 'Care is protection.', 4: 'Many factors can modify our genetic and metabolic propensity for illness and disease states.', 5: 'Amides are non-migratory slip additives.', 6: 'Low power is a relative term.'}
| 5 |
4,692 |
["Whenever it is true that long tentacles dangle from the four corners of the sea wasp's body, 'either air conditioning is widespread in cars, restaurants, shops and motels in the USA and Canada or health research is the foundation of public health and the treatment of disease' is true.", "Once we know energy efficiency works when our customers understand our programs, we also know that the statement that 'either air conditioning is widespread in cars, restaurants, shops and motels in the USA and Canada or health research is the foundation of public health and the treatment of disease' is incorrect.", 'We know that the claim that water appears murky or turbid due to suspended matter is false.', 'When legal immigrants have no constitutional rights whatsoever is true, it follows that water appears murky or turbid due to suspended matter.', "Whenever it is true that the statement 'if the claim that if long tentacles dangle from the four corners of the sea wasp's body, then energy efficiency works when our customers understand our programs is false, then legal immigrants have no constitutional rights whatsoever' can be considered false, 'either test tubes contain mixture or community building requires times when all gather to raise a barn together' is true.", "On the condition that the statement 'if the claim that if long tentacles dangle from the four corners of the sea wasp's body, then energy efficiency works when our customers understand our programs is false, then legal immigrants have no constitutional rights whatsoever' can be considered false, it is definitely the case that the statement, either test tubes contain mixture or community building requires times when all gather to raise a barn together, does not hold."]
|
Whenever it is true that long tentacles dangle from the four corners of the sea wasp's body, 'either air conditioning is widespread in cars, restaurants, shops and motels in the USA and Canada or health research is the foundation of public health and the treatment of disease' is true. Once we know energy efficiency works when our customers understand our programs, we also know that the statement that 'either air conditioning is widespread in cars, restaurants, shops and motels in the USA and Canada or health research is the foundation of public health and the treatment of disease' is incorrect. We know that the claim that water appears murky or turbid due to suspended matter is false. When legal immigrants have no constitutional rights whatsoever is true, it follows that water appears murky or turbid due to suspended matter. Whenever it is true that the statement 'if the claim that if long tentacles dangle from the four corners of the sea wasp's body, then energy efficiency works when our customers understand our programs is false, then legal immigrants have no constitutional rights whatsoever' can be considered false, 'either test tubes contain mixture or community building requires times when all gather to raise a barn together' is true. On the condition that the statement 'if the claim that if long tentacles dangle from the four corners of the sea wasp's body, then energy efficiency works when our customers understand our programs is false, then legal immigrants have no constitutional rights whatsoever' can be considered false, it is definitely the case that the statement, either test tubes contain mixture or community building requires times when all gather to raise a barn together, does not hold.
|
The claim that long tentacles dangle from the four corners of the sea wasp's body is false.
|
The claim that long tentacles dangle from the four corners of the sea wasp's body is false.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then (Either [1] or [2].).
If [0], then (Not (Either [1] or [2].).). [SC2-1]
Therefore, Not [0]..
[SC2-1]
Hypothetical Syllogism:
If [0], then [3]. [SC1-2]
If [3], then (Not (Either [1] or [2].).).
Therefore, If [0], then (Not (Either [1] or [2].).)..
[SC1-2]
Modus Tonens:
If (Not (If [0], then [3].).), then [4]. [SC1-3]
Not [4].
Therefore, If [0], then [3]..
[SC1-3]
Hypothetical Syllogism:
If (Not (If [0], then [3].).), then [5]. [SC1-4]
If [5], then [4].
Therefore, If (Not (If [0], then [3].).), then [4]..
[SC1-4]
Reductio Ad Absurdum:
If (Not (If (Not (If [0], then [3].).), then [5].).), then (Either [6] or [7].).
If (Not (If (Not (If [0], then [3].).), then [5].).), then (Not (Either [6] or [7].).).
Therefore, If (Not (If [0], then [3].).), then [5]..
|
{0: "Long tentacles dangle from the four corners of the sea wasp's body.", 1: 'Air conditioning is widespread in cars, restaurants, shops and motels in the USA and Canada.', 2: 'Health research is the foundation of public health and the treatment of disease.', 3: 'Energy efficiency works when our customers understand our programs.', 4: 'Water appears murky or turbid due to suspended matter.', 5: 'Legal immigrants have no constitutional rights whatsoever.', 6: 'Test tubes contain mixture.', 7: 'Community building requires times when all gather to raise a barn together.'}
| 5 |
4,353 |
['At least one of two things is true: either offspring reach reproductive maturity or film making is the art of storytelling with pictures, or wasps can also damage fruit when they create holes by eating the flesh.', 'It is a fact that either hickories are common in the broadleaf forests of the eastern and central parts of the United States or charismatic authority stems from the personal qualities of an individual.', 'When charismatic authority stems from the personal qualities of an individual is true, it follows that if either offspring reach reproductive maturity or film making is the art of storytelling with pictures, then heather works well in rock gardens.', 'It is a fact that either mulattoes often own slaves and plantations, learn trades or if wasps can also damage fruit when they create holes by eating the flesh, then heather works well in rock gardens.', 'The statement that states mulattoes often own slaves and plantations, learn trades is false.', 'Should it be the case that hickories are common in the broadleaf forests of the eastern and central parts of the United States, it follows that nutrient deficiencies can cause discolored or stunted foliage.', 'Provided that nutrient deficiencies can cause discolored or stunted foliage, we know that food colouring is used to colour food, but some foods have natural colourings, like beta carotene.', 'On the condition that food colouring is used to colour food, but some foods have natural colourings, like beta carotene, it is definitely the case that if either offspring reach reproductive maturity or film making is the art of storytelling with pictures, then heather works well in rock gardens.']
|
At least one of two things is true: either offspring reach reproductive maturity or film making is the art of storytelling with pictures, or wasps can also damage fruit when they create holes by eating the flesh. It is a fact that either hickories are common in the broadleaf forests of the eastern and central parts of the United States or charismatic authority stems from the personal qualities of an individual. When charismatic authority stems from the personal qualities of an individual is true, it follows that if either offspring reach reproductive maturity or film making is the art of storytelling with pictures, then heather works well in rock gardens. It is a fact that either mulattoes often own slaves and plantations, learn trades or if wasps can also damage fruit when they create holes by eating the flesh, then heather works well in rock gardens. The statement that states mulattoes often own slaves and plantations, learn trades is false. Should it be the case that hickories are common in the broadleaf forests of the eastern and central parts of the United States, it follows that nutrient deficiencies can cause discolored or stunted foliage. Provided that nutrient deficiencies can cause discolored or stunted foliage, we know that food colouring is used to colour food, but some foods have natural colourings, like beta carotene. On the condition that food colouring is used to colour food, but some foods have natural colourings, like beta carotene, it is definitely the case that if either offspring reach reproductive maturity or film making is the art of storytelling with pictures, then heather works well in rock gardens.
|
heather works well in rock gardens.
|
Heather works with the belief that every part of a person's life has an effect on their health.
|
Uncertain
|
Disjunction Elimination:
Either (Either [1] or [2].) or [3].
If (Either [1] or [2].), then [0]. [SC2-1]
If [3], then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Either [1] or [2].), then [0].). [SC2-2]
If [6], then (If (Either [1] or [2].), then [0].).
Therefore, If (Either [1] or [2].), then [0]..
[SC2-2]
Hypothetical Syllogism:
If [5], then [7].
If [7], then (If (Either [1] or [2].), then [0].). [SC2-3]
Therefore, If [5], then (If (Either [1] or [2].), then [0].)..
[SC2-3]
Hypothetical Syllogism:
If [7], then [8].
If [8], then (If (Either [1] or [2].), then [0].).
Therefore, If [7], then (If (Either [1] or [2].), then [0].)..
[SC3-1]
Disjunctive Syllogism:
Either [4] or (If [3], then [0].).
Not [4].
Therefore, If [3], then [0]..
|
{0: 'Heather works well in rock gardens.', 1: 'Offspring reach reproductive maturity.', 2: 'Film making is the art of storytelling with pictures.', 3: 'Wasps can also damage fruit when they create holes by eating the flesh.', 4: 'Mulattoes often own slaves and plantations, learn trades.', 5: 'Hickories are common in the broadleaf forests of the eastern and central parts of the United States.', 6: 'Charismatic authority stems from the personal qualities of an individual.', 7: 'Nutrient deficiencies can cause discolored or stunted foliage.', 8: 'Food colouring is used to colour food, but some foods have natural colourings, like beta carotene.'}
| 5 |
4,153 |
["Either sex helps prevention and recovery from aging or if bookcase isa furniture, then cynicism is intellectual dandyism without the coxcomb's feathers.", 'We know that at least one of two things is true: some people use adaptive technology with their computer to access the Web, or if sex helps prevention and recovery from aging, then conduction is also a common way of transferring heat through gases.', 'Given that plants contain fiber, it can be inferred that conduction is also a common way of transferring heat through gases.', 'It is rational to believe that either ecstasy breaks down mental and emotional inhibitions or the statement, some people use adaptive technology with their computer to access the Web, does not hold.', 'The claim that ecstasy breaks down mental and emotional inhibitions is false.', "Assuming either cannabis can also interfere with ovulation in women or female blossoms are easy to spot, because they have tiny pumpkins at their base, we know that if if bookcase isa furniture, then cynicism is intellectual dandyism without the coxcomb's feathers, then plants contain fiber.", 'It is a fact that either cannabis can also interfere with ovulation in women or female blossoms are easy to spot, because they have tiny pumpkins at their base.']
|
Either sex helps prevention and recovery from aging or if bookcase isa furniture, then cynicism is intellectual dandyism without the coxcomb's feathers. We know that at least one of two things is true: some people use adaptive technology with their computer to access the Web, or if sex helps prevention and recovery from aging, then conduction is also a common way of transferring heat through gases. Given that plants contain fiber, it can be inferred that conduction is also a common way of transferring heat through gases. It is rational to believe that either ecstasy breaks down mental and emotional inhibitions or the statement, some people use adaptive technology with their computer to access the Web, does not hold. The claim that ecstasy breaks down mental and emotional inhibitions is false. Assuming either cannabis can also interfere with ovulation in women or female blossoms are easy to spot, because they have tiny pumpkins at their base, we know that if if bookcase isa furniture, then cynicism is intellectual dandyism without the coxcomb's feathers, then plants contain fiber. It is a fact that either cannabis can also interfere with ovulation in women or female blossoms are easy to spot, because they have tiny pumpkins at their base.
|
It is the case that conduction is also a common way of transferring heat through gases.
|
Conduction carries heat.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (If [2], then [3].).
If [1], then [0]. [SC2-1]
If (If [2], then [3].), then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [4] or (If [1], then [0].).
Not [4]. [SC2-2]
Therefore, If [1], then [0]..
[SC2-2]
Disjunctive Syllogism:
Either [6] or (Not [4].).
Not [6].
Therefore, Not [4]..
[SC3-1]
Hypothetical Syllogism:
If (If [2], then [3].), then [5]. [SC1-2]
If [5], then [0].
Therefore, If (If [2], then [3].), then [0]..
[SC1-2]
Modus Ponens:
If (Either [7] or [8].), then (If (If [2], then [3].), then [5].).
Either [7] or [8].
Therefore, If (If [2], then [3].), then [5]..
|
{0: 'Conduction is also a common way of transferring heat through gases.', 1: 'Sex helps prevention and recovery from aging.', 2: 'Bookcase isa furniture.', 3: "Cynicism is intellectual dandyism without the coxcomb's feathers.", 4: 'Some people use adaptive technology with their computer to access the Web.', 5: 'Plants contain fiber.', 6: 'Ecstasy breaks down mental and emotional inhibitions.', 7: 'Cannabis can also interfere with ovulation in women.', 8: 'Female blossoms are easy to spot, because they have tiny pumpkins at their base.'}
| 5 |
4,566 |
["Should it be the case that those that suggest if the statement 'dendrites are branches in axons' can be considered false, then hot flashes occur sporadically and often start several years before other signs of menopause are wrong, it follows that the notion that 'either supraglacial lakes form early in the melt season before the englacial system opens up or plants need red light' is untrue.", 'Assuming hot flashes occur sporadically and often start several years before other signs of menopause, we know that either relatives can have consequences or rheas are omnivorous, preferring broad-leafed plants and clover.', 'Provided that hot flashes occur sporadically and often start several years before other signs of menopause, we know that the claim that either relatives can have consequences or rheas are omnivorous, preferring broad-leafed plants and clover has no merit.', "If the statement 'if those that suggest if the statement 'dendrites are branches in axons' can be considered false, then hot flashes occur sporadically and often start several years before other signs of menopause are wrong, then either supraglacial lakes form early in the melt season before the englacial system opens up or plants need red light' can be considered false, then the statement, most citrus pests have natural enemies that keep down their numbers, does not hold.", 'Either rabies can infect any warm blooded animal or lorikeets feed on pollen.', "Assuming rabies can infect any warm blooded animal, we know that if the statement 'if those that suggest if the statement 'dendrites are branches in axons' can be considered false, then hot flashes occur sporadically and often start several years before other signs of menopause are wrong, then either supraglacial lakes form early in the melt season before the englacial system opens up or plants need red light' can be considered false, then most citrus pests have natural enemies that keep down their numbers.", "Given that lorikeets feed on pollen, it can be inferred that if the statement 'if those that suggest if the statement 'dendrites are branches in axons' can be considered false, then hot flashes occur sporadically and often start several years before other signs of menopause are wrong, then either supraglacial lakes form early in the melt season before the englacial system opens up or plants need red light' can be considered false, then most citrus pests have natural enemies that keep down their numbers."]
|
Should it be the case that those that suggest if the statement 'dendrites are branches in axons' can be considered false, then hot flashes occur sporadically and often start several years before other signs of menopause are wrong, it follows that the notion that 'either supraglacial lakes form early in the melt season before the englacial system opens up or plants need red light' is untrue. Assuming hot flashes occur sporadically and often start several years before other signs of menopause, we know that either relatives can have consequences or rheas are omnivorous, preferring broad-leafed plants and clover. Provided that hot flashes occur sporadically and often start several years before other signs of menopause, we know that the claim that either relatives can have consequences or rheas are omnivorous, preferring broad-leafed plants and clover has no merit. If the statement 'if those that suggest if the statement 'dendrites are branches in axons' can be considered false, then hot flashes occur sporadically and often start several years before other signs of menopause are wrong, then either supraglacial lakes form early in the melt season before the englacial system opens up or plants need red light' can be considered false, then the statement, most citrus pests have natural enemies that keep down their numbers, does not hold. Either rabies can infect any warm blooded animal or lorikeets feed on pollen. Assuming rabies can infect any warm blooded animal, we know that if the statement 'if those that suggest if the statement 'dendrites are branches in axons' can be considered false, then hot flashes occur sporadically and often start several years before other signs of menopause are wrong, then either supraglacial lakes form early in the melt season before the englacial system opens up or plants need red light' can be considered false, then most citrus pests have natural enemies that keep down their numbers. Given that lorikeets feed on pollen, it can be inferred that if the statement 'if those that suggest if the statement 'dendrites are branches in axons' can be considered false, then hot flashes occur sporadically and often start several years before other signs of menopause are wrong, then either supraglacial lakes form early in the melt season before the englacial system opens up or plants need red light' can be considered false, then most citrus pests have natural enemies that keep down their numbers.
|
Many people rightly believe that dendrites are branches in axons.
|
Dendrites receive impulses that are conducted to the cell body.
|
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 (Either [2] or [3].). [SC1-2]
If (Not (If (Not [0].), then [1].).), then (Not (Either [2] or [3].).).
Therefore, If (Not [0].), then [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].).).), then [6]. [SC1-3]
If (Not (If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].).).), then (Not [6].).
Therefore, If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].)..
[SC1-3]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If (Not (If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].).).), then [6].).
If [8], then (If (Not (If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].).).), then [6].).
Therefore, If (Not (If (Not (If (Not [0].), then [1].).), then (Either [2] or [3].).).), then [6]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then (Either [4] or [5].).
If [1], then (Not (Either [4] or [5].).).
Therefore, Not [1]..
|
{0: 'Dendrites are branches in axons.', 1: 'Hot flashes occur sporadically and often start several years before other signs of menopause.', 2: 'Supraglacial lakes form early in the melt season before the englacial system opens up.', 3: 'Plants need red light.', 4: 'Relatives can have consequences.', 5: 'Rheas are omnivorous, preferring broad-leafed plants and clover.', 6: 'Most citrus pests have natural enemies that keep down their numbers.', 7: 'Rabies can infect any warm blooded animal.', 8: 'Lorikeets feed on pollen.'}
| 5 |
4,542 |
["The statement 'if shrews sometimes conflict with humans, however, then responsiveness is sensitivity' can be considered false.", 'There is good reason to believe that either most animals live for months or sleep is a restful time when our bodies replentish themselves and prepare for the next day.', 'If most animals live for months, then the claim that tests help physicians does not correspond with reality.', 'One may reasonably assume that if sleep is a restful time when our bodies replentish themselves and prepare for the next day, then the claim that tests help physicians does not correspond with reality.', 'It is not true that stalks provide food.', "So long as the statement, if the claim that either if shrews sometimes conflict with humans, however, then responsiveness is sensitivity or if the notion that 'either injuries caused by vehicle accidents are a very common type of personal injury or a rain barrel is a cistern' is untrue, then tests help physicians has no merit, then stalks provide food, does not hold, 'some phenomena involve electric charge' is true.", "Given that the statement, if the claim that either if shrews sometimes conflict with humans, however, then responsiveness is sensitivity or if the notion that 'either injuries caused by vehicle accidents are a very common type of personal injury or a rain barrel is a cistern' is untrue, then tests help physicians has no merit, then stalks provide food, does not hold, it can be inferred that it is not true that some phenomena involve electric charge."]
|
The statement 'if shrews sometimes conflict with humans, however, then responsiveness is sensitivity' can be considered false. There is good reason to believe that either most animals live for months or sleep is a restful time when our bodies replentish themselves and prepare for the next day. If most animals live for months, then the claim that tests help physicians does not correspond with reality. One may reasonably assume that if sleep is a restful time when our bodies replentish themselves and prepare for the next day, then the claim that tests help physicians does not correspond with reality. It is not true that stalks provide food. So long as the statement, if the claim that either if shrews sometimes conflict with humans, however, then responsiveness is sensitivity or if the notion that 'either injuries caused by vehicle accidents are a very common type of personal injury or a rain barrel is a cistern' is untrue, then tests help physicians has no merit, then stalks provide food, does not hold, 'some phenomena involve electric charge' is true. Given that the statement, if the claim that either if shrews sometimes conflict with humans, however, then responsiveness is sensitivity or if the notion that 'either injuries caused by vehicle accidents are a very common type of personal injury or a rain barrel is a cistern' is untrue, then tests help physicians has no merit, then stalks provide food, does not hold, it can be inferred that it is not true that some phenomena involve electric charge.
|
Either injuries caused by vehicle accidents are a very common type of personal injury or a rain barrel is a cistern.
|
Either injuries caused by vehicle accidents are a very common type of personal injury or a rain barrel is a cistern.
|
TRUE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Disjunctive Syllogism:
Either (If [5], then [6].) or (If (Not (Either [0] or [1].).), then [2].). [SC1-2]
Not (If [5], then [6].).
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC1-2]
Modus Tonens:
If (Not (Either (If [5], then [6].) or (If (Not (Either [0] or [1].).), then [2].).).), then [7]. [SC1-3]
Not [7].
Therefore, Either (If [5], then [6].) or (If (Not (Either [0] or [1].).), then [2].)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If (Not (Either (If [5], then [6].) or (If (Not (Either [0] or [1].).), then [2].).).), then [7].).), then [8].
If (Not (If (Not (Either (If [5], then [6].) or (If (Not (Either [0] or [1].).), then [2].).).), then [7].).), then (Not [8].).
Therefore, If (Not (Either (If [5], then [6].) or (If (Not (Either [0] or [1].).), then [2].).).), then [7]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not [2].).
If [4], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Injuries caused by vehicle accidents are a very common type of personal injury.', 1: 'A rain barrel is a cistern.', 2: 'Tests help physicians.', 3: 'Most animals live for months.', 4: 'Sleep is a restful time when our bodies replentish themselves and prepare for the next day.', 5: 'Shrews sometimes conflict with humans, however.', 6: 'Responsiveness is sensitivity.', 7: 'Stalks provide food.', 8: 'Some phenomena involve electric charge.'}
| 5 |
4,343 |
['There is good reason to believe that either if most government agencies run private businesses in order to raise funds, then regeneration is a gradual process taking many years, involving effort, love, good works or a khan is a ruler.', "When if most government agencies run private businesses in order to raise funds, then regeneration is a gradual process taking many years, involving effort, love, good works is true, it follows that if the statement that 'either residual risk is the risk that remains given current levels of environmental regulation and control or countries create opportunity' is incorrect, then statutes are laws which have been enacted by a vote of the legislature.", 'Once we know statutes are laws which have been enacted by a vote of the legislature, we also know that either reflective tape increases nighttime visibility or occasional storms move waves and sand with such great force that beaches and shorelines change.', 'When a khan is a ruler is true, it follows that true nightmares occur in the non- dream phase of sleep, and have little remembered content.', "If true nightmares occur in the non- dream phase of sleep, and have little remembered content, then if the statement that 'either residual risk is the risk that remains given current levels of environmental regulation and control or countries create opportunity' is incorrect, then statutes are laws which have been enacted by a vote of the legislature.", 'It is rational to believe that either some soy interferes with protein digestion or brains actually start developing before birth.', 'Should it be the case that some soy interferes with protein digestion, it follows that if statutes are laws which have been enacted by a vote of the legislature, then the claim that either reflective tape increases nighttime visibility or occasional storms move waves and sand with such great force that beaches and shorelines change does not reflect reality.', 'On the condition that brains actually start developing before birth, it is definitely the case that if statutes are laws which have been enacted by a vote of the legislature, then the claim that either reflective tape increases nighttime visibility or occasional storms move waves and sand with such great force that beaches and shorelines change does not reflect reality.']
|
There is good reason to believe that either if most government agencies run private businesses in order to raise funds, then regeneration is a gradual process taking many years, involving effort, love, good works or a khan is a ruler. When if most government agencies run private businesses in order to raise funds, then regeneration is a gradual process taking many years, involving effort, love, good works is true, it follows that if the statement that 'either residual risk is the risk that remains given current levels of environmental regulation and control or countries create opportunity' is incorrect, then statutes are laws which have been enacted by a vote of the legislature. Once we know statutes are laws which have been enacted by a vote of the legislature, we also know that either reflective tape increases nighttime visibility or occasional storms move waves and sand with such great force that beaches and shorelines change. When a khan is a ruler is true, it follows that true nightmares occur in the non- dream phase of sleep, and have little remembered content. If true nightmares occur in the non- dream phase of sleep, and have little remembered content, then if the statement that 'either residual risk is the risk that remains given current levels of environmental regulation and control or countries create opportunity' is incorrect, then statutes are laws which have been enacted by a vote of the legislature. It is rational to believe that either some soy interferes with protein digestion or brains actually start developing before birth. Should it be the case that some soy interferes with protein digestion, it follows that if statutes are laws which have been enacted by a vote of the legislature, then the claim that either reflective tape increases nighttime visibility or occasional storms move waves and sand with such great force that beaches and shorelines change does not reflect reality. On the condition that brains actually start developing before birth, it is definitely the case that if statutes are laws which have been enacted by a vote of the legislature, then the claim that either reflective tape increases nighttime visibility or occasional storms move waves and sand with such great force that beaches and shorelines change does not reflect reality.
|
At least one of two things is true: residual risk is the risk that remains given current levels of environmental regulation and control, or countries create opportunity.
|
At least one of two things is true: residual risk is the risk that remains given current levels of environmental regulation and control, or countries create opportunity.
|
TRUE
|
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 [3], then [4].) or [5].
If (If [3], then [4].), then (If (Not (Either [0] or [1].).), then [2].).
If [5], then (If (Not (Either [0] or [1].).), then [2].). [SC3-2]
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC3-2]
Hypothetical Syllogism:
If [5], then [8].
If [8], then (If (Not (Either [0] or [1].).), then [2].).
Therefore, If [5], then (If (Not (Either [0] or [1].).), then [2].)..
[SC2-1]
Reductio Ad Absurdum:
If [2], then (Either [6] or [7].).
If [2], then (Not (Either [6] or [7].).). [SC2-2]
Therefore, Not [2]..
[SC2-2]
Disjunction Elimination:
Either [9] or [10].
If [9], then (If [2], then (Not (Either [6] or [7].).).).
If [10], then (If [2], then (Not (Either [6] or [7].).).).
Therefore, If [2], then (Not (Either [6] or [7].).)..
|
{0: 'Residual risk is the risk that remains given current levels of environmental regulation and control.', 1: 'Countries create opportunity.', 2: 'Statutes are laws which have been enacted by a vote of the legislature.', 3: 'Most government agencies run private businesses in order to raise funds.', 4: 'Regeneration is a gradual process taking many years, involving effort, love, good works.', 5: 'A khan is a ruler.', 6: 'Reflective tape increases nighttime visibility.', 7: 'Occasional storms move waves and sand with such great force that beaches and shorelines change.', 8: 'True nightmares occur in the non- dream phase of sleep, and have little remembered content.', 9: 'Some soy interferes with protein digestion.', 10: 'Brains actually start developing before birth.'}
| 5 |
4,887 |
['It is rational to believe that either if nicotinic acid is a necessary part of a healthy diet, then most apes feed on vegetation or either fishing is a very challenging sport and is mainly dominated by males or if bats has-part organs, then wind direction is given as the direction the wind is coming from along a compass direction.', "The notion that 'if nicotinic acid is a necessary part of a healthy diet, then most apes feed on vegetation' is untrue.", 'There is good reason to believe that either people have restrictions or bears have (part) faces.', 'Provided that people have restrictions, we know that if fishing is a very challenging sport and is mainly dominated by males, then add boil water wills have results.', 'One may reasonably assume that if if bats has-part organs, then wind direction is given as the direction the wind is coming from along a compass direction, then tourism is a growth industry - a leading creator of jobs.', 'When tourism is a growth industry - a leading creator of jobs is true, it follows that marinades soften or denature tissue with their acid ingredients.', 'Once we know root rot fungal pathogens are found in almost all soils, we also know that if bears have (part) faces, then if fishing is a very challenging sport and is mainly dominated by males, then add boil water wills have results.', 'root rot fungal pathogens are found in almost all soils.']
|
It is rational to believe that either if nicotinic acid is a necessary part of a healthy diet, then most apes feed on vegetation or either fishing is a very challenging sport and is mainly dominated by males or if bats has-part organs, then wind direction is given as the direction the wind is coming from along a compass direction. The notion that 'if nicotinic acid is a necessary part of a healthy diet, then most apes feed on vegetation' is untrue. There is good reason to believe that either people have restrictions or bears have (part) faces. Provided that people have restrictions, we know that if fishing is a very challenging sport and is mainly dominated by males, then add boil water wills have results. One may reasonably assume that if if bats has-part organs, then wind direction is given as the direction the wind is coming from along a compass direction, then tourism is a growth industry - a leading creator of jobs. When tourism is a growth industry - a leading creator of jobs is true, it follows that marinades soften or denature tissue with their acid ingredients. Once we know root rot fungal pathogens are found in almost all soils, we also know that if bears have (part) faces, then if fishing is a very challenging sport and is mainly dominated by males, then add boil water wills have results. root rot fungal pathogens are found in almost all soils.
|
There is good reason to believe that either add boil water wills have results or marinades soften or denature tissue with their acid ingredients.
|
The statement that 'either add boil water wills have results or marinades soften or denature tissue with their acid ingredients' is incorrect.
|
FALSE
|
Constructive Dilemma:
Either [2] or (If [3], then [4].). [SC1-1]
If [2], then [0]. [SC2-1]
If (If [3], then [4].), then [1]. [SC3-1]
Therefore, Either [0] or [1]..
[SC1-1]
Disjunctive Syllogism:
Either (If [5], then [6].) or (Either [2] or (If [3], then [4].).).
Not (If [5], then [6].).
Therefore, Either [2] or (If [3], then [4].)..
[SC2-1]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If [2], then [0].).
If [8], then (If [2], then [0].). [SC3-2]
Therefore, If [2], then [0]..
[SC3-2]
Modus Ponens:
If [10], then (If [8], then (If [2], then [0].).).
[10]
Therefore, If [8], then (If [2], then [0].)..
[SC3-1]
Hypothetical Syllogism:
If (If [3], then [4].), then [9].
If [9], then [1].
Therefore, If (If [3], then [4].), then [1]..
|
{0: 'Add boil water wills have results.', 1: 'Marinades soften or denature tissue with their acid ingredients.', 2: 'Fishing is a very challenging sport and is mainly dominated by males.', 3: 'Bats has-part organs.', 4: 'Wind direction is given as the direction the wind is coming from along a compass direction.', 5: 'Nicotinic acid is a necessary part of a healthy diet.', 6: 'Most apes feed on vegetation.', 7: 'People have restrictions.', 8: 'Bears have (part) faces.', 9: 'Tourism is a growth industry - a leading creator of jobs.', 10: 'Root rot fungal pathogens are found in almost all soils.'}
| 5 |
4,997 |
['We know that at least one of two things is true: sexual assault is a very serious form of sexual harassment, or insects live in habitats.', "One may reasonably assume that if sexual assault is a very serious form of sexual harassment, then the statement 'longitude is comparable to the y-axis on a graph' can be considered false.", 'Given that the statement that states if sexual assault is a very serious form of sexual harassment, then longitude is comparable to the y-axis on a graph is false, it can be inferred that it is a common misconception that a sloth is hesitation.', 'On the condition that most insects occur in environments, it is definitely the case that a sloth is hesitation.', 'One may reasonably assume that if the statement that states if sexual assault is a very serious form of sexual harassment, then longitude is comparable to the y-axis on a graph is false, then most marigolds belong to particular genus.', 'When most marigolds belong to particular genus is true, it follows that most insects occur in environments.']
|
We know that at least one of two things is true: sexual assault is a very serious form of sexual harassment, or insects live in habitats. One may reasonably assume that if sexual assault is a very serious form of sexual harassment, then the statement 'longitude is comparable to the y-axis on a graph' can be considered false. Given that the statement that states if sexual assault is a very serious form of sexual harassment, then longitude is comparable to the y-axis on a graph is false, it can be inferred that it is a common misconception that a sloth is hesitation. On the condition that most insects occur in environments, it is definitely the case that a sloth is hesitation. One may reasonably assume that if the statement that states if sexual assault is a very serious form of sexual harassment, then longitude is comparable to the y-axis on a graph is false, then most marigolds belong to particular genus. When most marigolds belong to particular genus is true, it follows that most insects occur in environments.
|
It is rational to agree that insects live in habitats.
|
It is rational to agree that insects live in habitats.
|
TRUE
|
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]
Reductio Ad Absurdum:
If (Not (If [1], then [2].).), then [3]. [SC1-3]
If (Not (If [1], then [2].).), then (Not [3].).
Therefore, If [1], then [2]..
[SC1-3]
Hypothetical Syllogism:
If (Not (If [1], then [2].).), then [4]. [SC1-4]
If [4], then [3].
Therefore, If (Not (If [1], then [2].).), then [3]..
[SC1-4]
Hypothetical Syllogism:
If (Not (If [1], then [2].).), then [5].
If [5], then [4].
Therefore, If (Not (If [1], then [2].).), then [4]..
|
{0: 'Insects live in habitats.', 1: 'Sexual assault is a very serious form of sexual harassment.', 2: 'Longitude is comparable to the y-axis on a graph.', 3: 'A sloth is hesitation.', 4: 'Most insects occur in environments.', 5: 'Most marigolds belong to particular genus.'}
| 5 |
4,825 |
['Should it be the case that some plants are annuals, it follows that broad conclusions draw from comparison.', 'Those that suggest aldosterone increases blood pressure are wrong.', 'It is a common misconception that if love is used for giving, then good music comes to be associated with the entire span of time during which it is played.', "So long as if rape creates a specific trauma and is a life-altering event, then cultivation is growth, 'either if love is used for giving, then good music comes to be associated with the entire span of time during which it is played or if broad conclusions draw from comparison, then aldosterone increases blood pressure' is true.", 'Provided that some people mistakenly believe that if rape creates a specific trauma and is a life-altering event, then cultivation is growth, we know that either foots are bottoms or activism mobilizes people to act as a united group to increase their power to affect change.', 'Given that some people mistakenly believe that if rape creates a specific trauma and is a life-altering event, then cultivation is growth, it can be inferred that we know that the claim that either foots are bottoms or activism mobilizes people to act as a united group to increase their power to affect change is false.']
|
Should it be the case that some plants are annuals, it follows that broad conclusions draw from comparison. Those that suggest aldosterone increases blood pressure are wrong. It is a common misconception that if love is used for giving, then good music comes to be associated with the entire span of time during which it is played. So long as if rape creates a specific trauma and is a life-altering event, then cultivation is growth, 'either if love is used for giving, then good music comes to be associated with the entire span of time during which it is played or if broad conclusions draw from comparison, then aldosterone increases blood pressure' is true. Provided that some people mistakenly believe that if rape creates a specific trauma and is a life-altering event, then cultivation is growth, we know that either foots are bottoms or activism mobilizes people to act as a united group to increase their power to affect change. Given that some people mistakenly believe that if rape creates a specific trauma and is a life-altering event, then cultivation is growth, it can be inferred that we know that the claim that either foots are bottoms or activism mobilizes people to act as a united group to increase their power to affect change is false.
|
Those that suggest some plants are annuals are wrong.
|
It is rational to agree that some plants are annuals.
|
FALSE
|
Modus Tonens:
If [0], then [1].
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC2-1]
Modus Tonens:
If [1], then [2]. [SC1-2]
Not [2].
Therefore, Not [1]..
[SC1-2]
Disjunctive Syllogism:
Either (If [3], then [4].) or (If [1], then [2].). [SC1-3]
Not (If [3], then [4].).
Therefore, If [1], then [2]..
[SC1-3]
Modus Ponens:
If (If [5], then [6].), then (Either (If [3], then [4].) or (If [1], then [2].).).
If [5], then [6]. [SC2-4]
Therefore, Either (If [3], then [4].) or (If [1], then [2].)..
[SC2-4]
Reductio Ad Absurdum:
If (Not (If [5], then [6].).), then (Either [7] or [8].).
If (Not (If [5], then [6].).), then (Not (Either [7] or [8].).).
Therefore, If [5], then [6]..
|
{0: 'Some plants are annuals.', 1: 'Broad conclusions draw from comparison.', 2: 'Aldosterone increases blood pressure.', 3: 'Love is used for giving.', 4: 'Good music comes to be associated with the entire span of time during which it is played.', 5: 'Rape creates a specific trauma and is a life-altering event.', 6: 'Cultivation is growth.', 7: 'Foots are bottoms.', 8: 'Activism mobilizes people to act as a united group to increase their power to affect change.'}
| 5 |
4,056 |
['The statement that states prostate cancer is the second most common cancer affecting Canadian men is right.', "The statement 'bodies have (part) shinbones' can be considered false.", 'We know that at least one of two things is true: most natural gas is produced from the Devonian black shale in Eastern Kentucky, or if it is not true that if prostate cancer is the second most common cancer affecting Canadian men, then rap is just to make money, then the claim that mice appear to be more resistant than rats to the effects of orally administered furfural is false.', 'It is not true that most natural gas is produced from the Devonian black shale in Eastern Kentucky.', 'If it is not the case that either bodies have (part) shinbones or if it is not true that if prostate cancer is the second most common cancer affecting Canadian men, then rap is just to make money, then mice appear to be more resistant than rats to the effects of orally administered furfural, then avocado trees come from Central America and Mexico .', 'Some people mistakenly believe that avocado trees come from Central America and Mexico .']
|
The statement that states prostate cancer is the second most common cancer affecting Canadian men is right. The statement 'bodies have (part) shinbones' can be considered false. We know that at least one of two things is true: most natural gas is produced from the Devonian black shale in Eastern Kentucky, or if it is not true that if prostate cancer is the second most common cancer affecting Canadian men, then rap is just to make money, then the claim that mice appear to be more resistant than rats to the effects of orally administered furfural is false. It is not true that most natural gas is produced from the Devonian black shale in Eastern Kentucky. If it is not the case that either bodies have (part) shinbones or if it is not true that if prostate cancer is the second most common cancer affecting Canadian men, then rap is just to make money, then mice appear to be more resistant than rats to the effects of orally administered furfural, then avocado trees come from Central America and Mexico . Some people mistakenly believe that avocado trees come from Central America and Mexico .
|
It is true that rap is just to make money.
|
Rap is now the second most popular form of music behind rock.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [1], then [0].).), then [2]. [SC1-2]
If (Not (If [1], then [0].).), then (Not [2].). [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Disjunctive Syllogism:
Either [4] or (If (Not (If [1], then [0].).), then [2].). [SC1-3]
Not [4].
Therefore, If (Not (If [1], then [0].).), then [2]..
[SC1-3]
Modus Tonens:
If (Not (Either [4] or (If (Not (If [1], then [0].).), then [2].).).), then [5].
Not [5].
Therefore, Either [4] or (If (Not (If [1], then [0].).), then [2].)..
[SC2-2]
Disjunctive Syllogism:
Either [3] or (If (Not (If [1], then [0].).), then (Not [2].).).
Not [3].
Therefore, If (Not (If [1], then [0].).), then (Not [2].)..
|
{0: 'Rap is just to make money.', 1: 'Prostate cancer is the second most common cancer affecting Canadian men.', 2: 'Mice appear to be more resistant than rats to the effects of orally administered furfural.', 3: 'Most natural gas is produced from the Devonian black shale in Eastern Kentucky.', 4: 'Bodies have (part) shinbones.', 5: 'Avocado trees come from Central America and Mexico .'}
| 5 |
4,400 |
['Either all identical twins are clones or adults have types.', 'It is not the case that if a rock wallaby is a kangaroo, then most arthropods have tough exoskeletons.', "When diversity is of vital importance in the engineering profession as it fuels creativity is true, it follows that either if a rock wallaby is a kangaroo, then most arthropods have tough exoskeletons or the statement that 'all identical twins are clones' is incorrect.", 'Many people rightly believe that diamonds are a mineral form of carbon but are very different from graphite.', "Whenever it is true that diamonds are a mineral form of carbon but are very different from graphite, 'either children are aware of racial differences by the time they're preschoolers or scientists believe that turtles live longer than any other back boned animal' is true.", "Given that either children are aware of racial differences by the time they're preschoolers or scientists believe that turtles live longer than any other back boned animal, it can be inferred that diversity is of vital importance in the engineering profession as it fuels creativity."]
|
Either all identical twins are clones or adults have types. It is not the case that if a rock wallaby is a kangaroo, then most arthropods have tough exoskeletons. When diversity is of vital importance in the engineering profession as it fuels creativity is true, it follows that either if a rock wallaby is a kangaroo, then most arthropods have tough exoskeletons or the statement that 'all identical twins are clones' is incorrect. Many people rightly believe that diamonds are a mineral form of carbon but are very different from graphite. Whenever it is true that diamonds are a mineral form of carbon but are very different from graphite, 'either children are aware of racial differences by the time they're preschoolers or scientists believe that turtles live longer than any other back boned animal' is true. Given that either children are aware of racial differences by the time they're preschoolers or scientists believe that turtles live longer than any other back boned animal, it can be inferred that diversity is of vital importance in the engineering profession as it fuels creativity.
|
It is the case that adults have types.
|
Most adults eat animals.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either (If [2], then [3].) or (Not [1].). [SC1-2]
Not (If [2], then [3].).
Therefore, Not [1]..
[SC1-2]
Modus Ponens:
If [4], then (Either (If [2], then [3].) or (Not [1].).).
[4] [SC2-3]
Therefore, Either (If [2], then [3].) or (Not [1].)..
[SC2-3]
Modus Ponens:
If [5], then [4]. [SC1-4]
[5]
Therefore, [4].
[SC1-4]
Hypothetical Syllogism:
If [5], then (Either [6] or [7].).
If (Either [6] or [7].), then [4].
Therefore, If [5], then [4]..
|
{0: 'Adults have types.', 1: 'All identical twins are clones.', 2: 'A rock wallaby is a kangaroo.', 3: 'Most arthropods have tough exoskeletons.', 4: 'Diversity is of vital importance in the engineering profession as it fuels creativity.', 5: 'Diamonds are a mineral form of carbon but are very different from graphite.', 6: "Children are aware of racial differences by the time they're preschoolers.", 7: 'Scientists believe that turtles live longer than any other back boned animal.'}
| 5 |
4,572 |
["Given that search engines search the Web using programs called spiders or robots, it can be inferred that the statement that 'either stents support the vessel walls and are believed to help prevent blockages or prostate cancer is also the most common form of cancer in American men' is incorrect.", "The statement 'teams have sighting' can be considered true.", 'Either one or both of these statements are true: kilometre isa unit, or seals have black eyes.', "So long as kilometre isa unit, 'either either benzodiazepines are addictive or teenage vegans have nutritional needs that are the same as any other teenager or if teams have sighting, then search engines search the Web using programs called spiders or robots' is true.", 'Should it be the case that seals have black eyes, it follows that either either benzodiazepines are addictive or teenage vegans have nutritional needs that are the same as any other teenager or if teams have sighting, then search engines search the Web using programs called spiders or robots.', 'It is a fact that either vegetable soup contains chicken broths or the claim that either benzodiazepines are addictive or teenage vegans have nutritional needs that are the same as any other teenager is false.', 'The statement that states vegetable soup contains chicken broths is false.']
|
Given that search engines search the Web using programs called spiders or robots, it can be inferred that the statement that 'either stents support the vessel walls and are believed to help prevent blockages or prostate cancer is also the most common form of cancer in American men' is incorrect. The statement 'teams have sighting' can be considered true. Either one or both of these statements are true: kilometre isa unit, or seals have black eyes. So long as kilometre isa unit, 'either either benzodiazepines are addictive or teenage vegans have nutritional needs that are the same as any other teenager or if teams have sighting, then search engines search the Web using programs called spiders or robots' is true. Should it be the case that seals have black eyes, it follows that either either benzodiazepines are addictive or teenage vegans have nutritional needs that are the same as any other teenager or if teams have sighting, then search engines search the Web using programs called spiders or robots. It is a fact that either vegetable soup contains chicken broths or the claim that either benzodiazepines are addictive or teenage vegans have nutritional needs that are the same as any other teenager is false. The statement that states vegetable soup contains chicken broths is false.
|
The statement that 'either stents support the vessel walls and are believed to help prevent blockages or prostate cancer is also the most common form of cancer in American men' is incorrect.
|
The statement that 'either stents support the vessel walls and are believed to help prevent blockages or prostate cancer is also the most common form of cancer in American men' is incorrect.
|
TRUE
|
Modus Ponens:
If [2], then (Not (Either [0] or [1].).).
[2] [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC2-1]
Modus Ponens:
If [3], then [2]. [SC1-2]
[3]
Therefore, [2].
[SC1-2]
Disjunctive Syllogism:
Either (Either [4] or [5].) or (If [3], then [2].). [SC1-3]
Not (Either [4] or [5].). [SC2-3]
Therefore, If [3], then [2]..
[SC1-3]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Either (Either [4] or [5].) or (If [3], then [2].).).
If [7], then (Either (Either [4] or [5].) or (If [3], then [2].).).
Therefore, Either (Either [4] or [5].) or (If [3], then [2].)..
[SC2-3]
Disjunctive Syllogism:
Either [8] or (Not (Either [4] or [5].).).
Not [8].
Therefore, Not (Either [4] or [5].)..
|
{0: 'Stents support the vessel walls and are believed to help prevent blockages.', 1: 'Prostate cancer is also the most common form of cancer in American men.', 2: 'Search engines search the Web using programs called spiders or robots.', 3: 'Teams have sighting.', 4: 'Benzodiazepines are addictive.', 5: 'Teenage vegans have nutritional needs that are the same as any other teenager.', 6: 'Kilometre isa unit.', 7: 'Seals have black eyes.', 8: 'Vegetable soup contains chicken broths.'}
| 5 |
4,473 |
['Some people mistakenly believe that either homeowners work all day, then they have kids to feed at night or moral impurity is a dangerous virus in marriage.', "Whenever it is true that it is not true that if the statement, soil erosion is a naturally occurring process that affects all landforms, does not hold, then either homeowners work all day, then they have kids to feed at night or moral impurity is a dangerous virus in marriage, 'the claim that summers are warm, cooled by the sea breezes, with excessive heat a rarity does not correspond with reality' is true.", "Whenever it is true that the statement that 'if it is not true that if the statement, soil erosion is a naturally occurring process that affects all landforms, does not hold, then either homeowners work all day, then they have kids to feed at night or moral impurity is a dangerous virus in marriage, then summers are warm, cooled by the sea breezes, with excessive heat a rarity' is incorrect, 'the statement 'smoking is the greatest risk for bladder cancer' can be considered false' is true.", "Provided that the claim that if the statement that 'if it is not true that if the statement, soil erosion is a naturally occurring process that affects all landforms, does not hold, then either homeowners work all day, then they have kids to feed at night or moral impurity is a dangerous virus in marriage, then summers are warm, cooled by the sea breezes, with excessive heat a rarity' is incorrect, then smoking is the greatest risk for bladder cancer is false, we know that alcoholism is also a disease that can be acquired over a long period of time.", 'It is rational to believe that either risk Management is simply the management of risks or wild lupine grows in open sandy areas that can contain some trees.', 'Given that risk Management is simply the management of risks, it can be inferred that the claim that alcoholism is also a disease that can be acquired over a long period of time does not reflect reality.', 'Once we know wild lupine grows in open sandy areas that can contain some trees, we also know that the claim that alcoholism is also a disease that can be acquired over a long period of time does not reflect reality.']
|
Some people mistakenly believe that either homeowners work all day, then they have kids to feed at night or moral impurity is a dangerous virus in marriage. Whenever it is true that it is not true that if the statement, soil erosion is a naturally occurring process that affects all landforms, does not hold, then either homeowners work all day, then they have kids to feed at night or moral impurity is a dangerous virus in marriage, 'the claim that summers are warm, cooled by the sea breezes, with excessive heat a rarity does not correspond with reality' is true. Whenever it is true that the statement that 'if it is not true that if the statement, soil erosion is a naturally occurring process that affects all landforms, does not hold, then either homeowners work all day, then they have kids to feed at night or moral impurity is a dangerous virus in marriage, then summers are warm, cooled by the sea breezes, with excessive heat a rarity' is incorrect, 'the statement 'smoking is the greatest risk for bladder cancer' can be considered false' is true. Provided that the claim that if the statement that 'if it is not true that if the statement, soil erosion is a naturally occurring process that affects all landforms, does not hold, then either homeowners work all day, then they have kids to feed at night or moral impurity is a dangerous virus in marriage, then summers are warm, cooled by the sea breezes, with excessive heat a rarity' is incorrect, then smoking is the greatest risk for bladder cancer is false, we know that alcoholism is also a disease that can be acquired over a long period of time. It is rational to believe that either risk Management is simply the management of risks or wild lupine grows in open sandy areas that can contain some trees. Given that risk Management is simply the management of risks, it can be inferred that the claim that alcoholism is also a disease that can be acquired over a long period of time does not reflect reality. Once we know wild lupine grows in open sandy areas that can contain some trees, we also know that the claim that alcoholism is also a disease that can be acquired over a long period of time does not reflect reality.
|
The claim that soil erosion is a naturally occurring process that affects all landforms holds true.
|
Soil erosion causes more damage than floods.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then (Either [1] or [2].). [SC1-1]
Not (Either [1] or [2].).
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3]. [SC1-2]
If (Not (If (Not [0].), then (Either [1] or [2].).).), then (Not [3].).
Therefore, If (Not [0].), then (Either [1] or [2].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3].).), then [4]. [SC1-3]
If (Not (If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3].).), then (Not [4].).
Therefore, If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3]..
[SC1-3]
Modus Tonens:
If (Not (If (Not (If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3].).), then [4].).), then [5].
Not [5]. [SC2-4]
Therefore, If (Not (If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3].).), then [4]..
[SC2-4]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Not [5].).
If [7], then (Not [5].).
Therefore, Not [5]..
|
{0: 'Soil erosion is a naturally occurring process that affects all landforms.', 1: 'Homeowners work all day, then they have kids to feed at night.', 2: 'Moral impurity is a dangerous virus in marriage.', 3: 'Summers are warm, cooled by the sea breezes, with excessive heat a rarity.', 4: 'Smoking is the greatest risk for bladder cancer.', 5: 'Alcoholism is also a disease that can be acquired over a long period of time.', 6: 'Risk Management is simply the management of risks.', 7: 'Wild lupine grows in open sandy areas that can contain some trees.'}
| 5 |
4,468 |
['The claim that either meningococcal disease is a serious illness caused by bacterial infection or social policy is policy does not reflect reality.', 'Provided that the statement that states if it is a common misconception that volatility is the variance in price or return of the underlying stock, then either meningococcal disease is a serious illness caused by bacterial infection or social policy is policy is false, we know that the statement that states birds can see their reflection in a window is false.', 'We know that either snails range greatly in size or integral proteins have domains that extend into the hydrocarbon core of the membrane.', 'Given that snails range greatly in size, it can be inferred that if the statement that states if it is a common misconception that volatility is the variance in price or return of the underlying stock, then either meningococcal disease is a serious illness caused by bacterial infection or social policy is policy is false, then birds can see their reflection in a window.', 'Given that some geckos drop tails, it can be inferred that if the statement that states if it is a common misconception that volatility is the variance in price or return of the underlying stock, then either meningococcal disease is a serious illness caused by bacterial infection or social policy is policy is false, then birds can see their reflection in a window.', 'It is rational to believe that either bulls are slain for men just to watch the sport of bull fighting or if integral proteins have domains that extend into the hydrocarbon core of the membrane, then some geckos drop tails.', 'The claim that bulls are slain for men just to watch the sport of bull fighting does not correspond with reality.']
|
The claim that either meningococcal disease is a serious illness caused by bacterial infection or social policy is policy does not reflect reality. Provided that the statement that states if it is a common misconception that volatility is the variance in price or return of the underlying stock, then either meningococcal disease is a serious illness caused by bacterial infection or social policy is policy is false, we know that the statement that states birds can see their reflection in a window is false. We know that either snails range greatly in size or integral proteins have domains that extend into the hydrocarbon core of the membrane. Given that snails range greatly in size, it can be inferred that if the statement that states if it is a common misconception that volatility is the variance in price or return of the underlying stock, then either meningococcal disease is a serious illness caused by bacterial infection or social policy is policy is false, then birds can see their reflection in a window. Given that some geckos drop tails, it can be inferred that if the statement that states if it is a common misconception that volatility is the variance in price or return of the underlying stock, then either meningococcal disease is a serious illness caused by bacterial infection or social policy is policy is false, then birds can see their reflection in a window. It is rational to believe that either bulls are slain for men just to watch the sport of bull fighting or if integral proteins have domains that extend into the hydrocarbon core of the membrane, then some geckos drop tails. The claim that bulls are slain for men just to watch the sport of bull fighting does not correspond with reality.
|
The idea that volatility is the variance in price or return of the underlying stock is true.
|
Volatility is a form of risk.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then (Either [1] or [2].). [SC1-1]
Not (Either [1] or [2].).
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3]. [SC1-2]
If (Not (If (Not [0].), then (Either [1] or [2].).).), then (Not [3].).
Therefore, If (Not [0].), then (Either [1] or [2].)..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3].).
If [5], then (If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3].). [SC3-3]
Therefore, If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3]..
[SC3-3]
Hypothetical Syllogism:
If [5], then [6]. [SC1-4]
If [6], then (If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3].).
Therefore, If [5], then (If (Not (If (Not [0].), then (Either [1] or [2].).).), then [3].)..
[SC1-4]
Disjunctive Syllogism:
Either [7] or (If [5], then [6].).
Not [7].
Therefore, If [5], then [6]..
|
{0: 'Volatility is the variance in price or return of the underlying stock.', 1: 'Meningococcal disease is a serious illness caused by bacterial infection.', 2: 'Social policy is policy.', 3: 'Birds can see their reflection in a window.', 4: 'Snails range greatly in size.', 5: 'Integral proteins have domains that extend into the hydrocarbon core of the membrane.', 6: 'Some geckos drop tails.', 7: 'Bulls are slain for men just to watch the sport of bull fighting.'}
| 5 |
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