id
int64 0
7k
| premises
stringlengths 118
4.1k
| paragraph
stringlengths 111
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| conclusion
stringlengths 15
240
| question
stringlengths 14
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stringlengths 54
2.02k
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stringlengths 51
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int64 1
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3,631 |
['There is good reason to believe that either either smokers develop same respiratory problems or tarsiers have (part) cell membranes or reproduction involves alternation.', 'It is a fact that either viral infections can produce warts or small growths called molluscum contagiosum or barn owls form monogamous, long-lasting pair bonds.', 'Provided that barn owls form monogamous, long-lasting pair bonds, we know that the statement, either smokers develop same respiratory problems or tarsiers have (part) cell membranes, does not hold.', 'When it is a common misconception that if viral infections can produce warts or small growths called molluscum contagiosum, then the statement, either smokers develop same respiratory problems or tarsiers have (part) cell membranes, does not hold is true, it follows that nitrous oxide is a drug.', "Either if some inventors start new companies to develop and market their patented inventions, then people desire fulls or the statement 'nitrous oxide is a drug' can be considered false.", 'Those that suggest if some inventors start new companies to develop and market their patented inventions, then people desire fulls are wrong.']
|
There is good reason to believe that either either smokers develop same respiratory problems or tarsiers have (part) cell membranes or reproduction involves alternation. It is a fact that either viral infections can produce warts or small growths called molluscum contagiosum or barn owls form monogamous, long-lasting pair bonds. Provided that barn owls form monogamous, long-lasting pair bonds, we know that the statement, either smokers develop same respiratory problems or tarsiers have (part) cell membranes, does not hold. When it is a common misconception that if viral infections can produce warts or small growths called molluscum contagiosum, then the statement, either smokers develop same respiratory problems or tarsiers have (part) cell membranes, does not hold is true, it follows that nitrous oxide is a drug. Either if some inventors start new companies to develop and market their patented inventions, then people desire fulls or the statement 'nitrous oxide is a drug' can be considered false. Those that suggest if some inventors start new companies to develop and market their patented inventions, then people desire fulls are wrong.
|
It is a simple truth that reproduction involves alternation.
|
The claim that reproduction involves alternation is false.
|
FALSE
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or [0].
Not (Either [1] or [2].). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not (Either [1] or [2].).). [SC2-2]
If [4], then (Not (Either [1] or [2].).).
Therefore, Not (Either [1] or [2].)..
[SC2-2]
Modus Tonens:
If (Not (If [3], then (Not (Either [1] or [2].).).).), then [5].
Not [5]. [SC2-3]
Therefore, If [3], then (Not (Either [1] or [2].).)..
[SC2-3]
Disjunctive Syllogism:
Either (If [6], then [7].) or (Not [5].).
Not (If [6], then [7].).
Therefore, Not [5]..
|
{0: 'Reproduction involves alternation.', 1: 'Smokers develop same respiratory problems.', 2: 'Tarsiers have (part) cell membranes.', 3: 'Viral infections can produce warts or small growths called molluscum contagiosum.', 4: 'Barn owls form monogamous, long-lasting pair bonds.', 5: 'Nitrous oxide is a drug.', 6: 'Some inventors start new companies to develop and market their patented inventions.', 7: 'People desire fulls.'}
| 4 |
3,185 |
["The notion that 'chinese culture is acknowledged by many scholars to be the oldest living culture in existence' is untrue.", 'If rubber severely affects silver, then if most sports provide built-in mats in the form of athletic shoes, then develop embryos touch membranes.', 'It is not the case that if most sports provide built-in mats in the form of athletic shoes, then develop embryos touch membranes.', 'It is a fact that either neutering is a safe and relatively painless operation when done by a licenssed veterinarian or if animals consume bugs, then many grocery stores carry an assortment of frozen products.', 'One may reasonably assume that if neutering is a safe and relatively painless operation when done by a licenssed veterinarian, then chinese culture is acknowledged by many scholars to be the oldest living culture in existence.', 'Should it be the case that if animals consume bugs, then many grocery stores carry an assortment of frozen products, it follows that if the claim that agriculture remains the base of the national economy is false, then rubber severely affects silver.']
|
The notion that 'chinese culture is acknowledged by many scholars to be the oldest living culture in existence' is untrue. If rubber severely affects silver, then if most sports provide built-in mats in the form of athletic shoes, then develop embryos touch membranes. It is not the case that if most sports provide built-in mats in the form of athletic shoes, then develop embryos touch membranes. It is a fact that either neutering is a safe and relatively painless operation when done by a licenssed veterinarian or if animals consume bugs, then many grocery stores carry an assortment of frozen products. One may reasonably assume that if neutering is a safe and relatively painless operation when done by a licenssed veterinarian, then chinese culture is acknowledged by many scholars to be the oldest living culture in existence. Should it be the case that if animals consume bugs, then many grocery stores carry an assortment of frozen products, it follows that if the claim that agriculture remains the base of the national economy is false, then rubber severely affects silver.
|
It is fair to say that agriculture remains the base of the national economy.
|
The claim that agriculture remains the base of the national economy does not reflect reality.
|
FALSE
|
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]
Constructive Dilemma:
Either [5] or (If [6], then [7].).
If [5], then [2].
If (If [6], then [7].), then (If (Not [0].), then [1].).
Therefore, Either [2] or (If (Not [0].), then [1].)..
[SC2-1]
Modus Tonens:
If [1], then (If [3], then [4].).
Not (If [3], then [4].).
Therefore, Not [1]..
|
{0: 'Agriculture remains the base of the national economy.', 1: 'Rubber severely affects silver.', 2: 'Chinese culture is acknowledged by many scholars to be the oldest living culture in existence.', 3: 'Most sports provide built-in mats in the form of athletic shoes.', 4: 'Develop embryos touch membranes.', 5: 'Neutering is a safe and relatively painless operation when done by a licenssed veterinarian.', 6: 'Animals consume bugs.', 7: 'Many grocery stores carry an assortment of frozen products.'}
| 4 |
3,732 |
['It is rational to believe that either some anemones piggyback on the shells of hermit crabs or carbon dioxide is a primary factor in global warming.', 'It is a fact that either some animals eat carnivores or if history teaches that wars begin when governments believe the price of aggression is cheap, then the statement, some anemones piggyback on the shells of hermit crabs, does not hold.', 'The claim that some animals eat carnivores does not reflect reality.', 'On the condition that either flamingos are pink or red or atlantic cod are apex predators and adults are generally free from the concerns of predation , it is definitely the case that history teaches that wars begin when governments believe the price of aggression is cheap.', 'We know that at least one of two things is true: flamingos are pink or red, or atlantic cod are apex predators and adults are generally free from the concerns of predation .']
|
It is rational to believe that either some anemones piggyback on the shells of hermit crabs or carbon dioxide is a primary factor in global warming. It is a fact that either some animals eat carnivores or if history teaches that wars begin when governments believe the price of aggression is cheap, then the statement, some anemones piggyback on the shells of hermit crabs, does not hold. The claim that some animals eat carnivores does not reflect reality. On the condition that either flamingos are pink or red or atlantic cod are apex predators and adults are generally free from the concerns of predation , it is definitely the case that history teaches that wars begin when governments believe the price of aggression is cheap. We know that at least one of two things is true: flamingos are pink or red, or atlantic cod are apex predators and adults are generally free from the concerns of predation .
|
The statement 'carbon dioxide is a primary factor in global warming' can be considered true.
|
The statement 'carbon dioxide is a primary factor in global warming' can be considered true.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [2], then (Not [1].). [SC1-2]
[2] [SC2-2]
Therefore, Not [1]..
[SC1-2]
Disjunctive Syllogism:
Either [5] or (If [2], then (Not [1].).).
Not [5].
Therefore, If [2], then (Not [1].)..
[SC2-2]
Modus Ponens:
If (Either [3] or [4].), then [2].
Either [3] or [4].
Therefore, [2].
|
{0: 'Carbon dioxide is a primary factor in global warming.', 1: 'Some anemones piggyback on the shells of hermit crabs.', 2: 'History teaches that wars begin when governments believe the price of aggression is cheap.', 3: 'Flamingos are pink or red.', 4: 'Atlantic cod are apex predators and adults are generally free from the concerns of predation .', 5: 'Some animals eat carnivores.'}
| 4 |
3,404 |
['Either solids hold their shape at room temperature or football is a game played with passion.', 'If solids hold their shape at room temperature, then the claim that a crook is principal is false.', "Whenever it is true that risk managers can turn data into information by relating it to their environment, 'if the claim that if football is a game played with passion, then the claim that a crook is principal is false does not correspond with reality, then laptops are usually as useful for homework as they are for schoolwork' is true.", 'It is true that risk managers can turn data into information by relating it to their environment.', 'Provided that laptops are usually as useful for homework as they are for schoolwork, we know that cape gooseberries contain less calories and a kind of soluble fiber.', 'Provided that laptops are usually as useful for homework as they are for schoolwork, we know that the claim that cape gooseberries contain less calories and a kind of soluble fiber does not correspond with reality.']
|
Either solids hold their shape at room temperature or football is a game played with passion. If solids hold their shape at room temperature, then the claim that a crook is principal is false. Whenever it is true that risk managers can turn data into information by relating it to their environment, 'if the claim that if football is a game played with passion, then the claim that a crook is principal is false does not correspond with reality, then laptops are usually as useful for homework as they are for schoolwork' is true. It is true that risk managers can turn data into information by relating it to their environment. Provided that laptops are usually as useful for homework as they are for schoolwork, we know that cape gooseberries contain less calories and a kind of soluble fiber. Provided that laptops are usually as useful for homework as they are for schoolwork, we know that the claim that cape gooseberries contain less calories and a kind of soluble fiber does not correspond with reality.
|
The claim that a crook is principal is false.
|
A crook is principal.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then (Not [0].).
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC3-1]
Modus Tonens:
If (Not (If [2], then (Not [0].).).), then [3]. [SC1-2]
Not [3]. [SC2-2]
Therefore, If [2], then (Not [0].)..
[SC1-2]
Modus Ponens:
If [5], then (If (Not (If [2], then (Not [0].).).), then [3].).
[5]
Therefore, If (Not (If [2], then (Not [0].).).), then [3]..
[SC2-2]
Reductio Ad Absurdum:
If [3], then [4].
If [3], then (Not [4].).
Therefore, Not [3]..
|
{0: 'A crook is principal.', 1: 'Solids hold their shape at room temperature.', 2: 'Football is a game played with passion.', 3: 'Laptops are usually as useful for homework as they are for schoolwork.', 4: 'Cape gooseberries contain less calories and a kind of soluble fiber.', 5: 'Risk managers can turn data into information by relating it to their environment.'}
| 4 |
3,194 |
['Provided that the claim that if either people of color are less likely to have health insurance or homozygous mutants die of respiratory failure shortly after birth, then if carabiners are the duct tape of rock climbers, then kinesiology is the fastest growing, and most comprehensive holistic therapy in the world today has no merit, we know that the statement that states most nebulas have mass is false.', 'Once we know most insects also have two antennae and two sets of wings, we also know that either people of color are less likely to have health insurance or homozygous mutants die of respiratory failure shortly after birth.', 'It is fair to say that most insects also have two antennae and two sets of wings.', 'It is rational to believe that either observatories have (part) doorsteps or plant cells fix atmospheric carbon using energy from sunlight in a process called photosynthesis.', 'Should it be the case that observatories have (part) doorsteps, it follows that if the claim that if either people of color are less likely to have health insurance or homozygous mutants die of respiratory failure shortly after birth, then if carabiners are the duct tape of rock climbers, then kinesiology is the fastest growing, and most comprehensive holistic therapy in the world today has no merit, then most nebulas have mass.', 'Provided that plant cells fix atmospheric carbon using energy from sunlight in a process called photosynthesis, we know that if the claim that if either people of color are less likely to have health insurance or homozygous mutants die of respiratory failure shortly after birth, then if carabiners are the duct tape of rock climbers, then kinesiology is the fastest growing, and most comprehensive holistic therapy in the world today has no merit, then most nebulas have mass.']
|
Provided that the claim that if either people of color are less likely to have health insurance or homozygous mutants die of respiratory failure shortly after birth, then if carabiners are the duct tape of rock climbers, then kinesiology is the fastest growing, and most comprehensive holistic therapy in the world today has no merit, we know that the statement that states most nebulas have mass is false. Once we know most insects also have two antennae and two sets of wings, we also know that either people of color are less likely to have health insurance or homozygous mutants die of respiratory failure shortly after birth. It is fair to say that most insects also have two antennae and two sets of wings. It is rational to believe that either observatories have (part) doorsteps or plant cells fix atmospheric carbon using energy from sunlight in a process called photosynthesis. Should it be the case that observatories have (part) doorsteps, it follows that if the claim that if either people of color are less likely to have health insurance or homozygous mutants die of respiratory failure shortly after birth, then if carabiners are the duct tape of rock climbers, then kinesiology is the fastest growing, and most comprehensive holistic therapy in the world today has no merit, then most nebulas have mass. Provided that plant cells fix atmospheric carbon using energy from sunlight in a process called photosynthesis, we know that if the claim that if either people of color are less likely to have health insurance or homozygous mutants die of respiratory failure shortly after birth, then if carabiners are the duct tape of rock climbers, then kinesiology is the fastest growing, and most comprehensive holistic therapy in the world today has no merit, then most nebulas have mass.
|
Assuming carabiners are the duct tape of rock climbers, we know that kinesiology is the fastest growing, and most comprehensive holistic therapy in the world today.
|
When carabiners are hoops is true, it follows that kinesiology is the fastest growing, and most comprehensive holistic therapy in the world today.
|
Uncertain
|
Modus Ponens:
If (Either [2] or [3].), then (If [0], then [1].). [SC1-1]
Either [2] or [3]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Either [2] or [3].), then (If [0], then [1].).).), then [4]. [SC1-2]
If (Not (If (Either [2] or [3].), then (If [0], then [1].).).), then (Not [4].).
Therefore, If (Either [2] or [3].), then (If [0], then [1].)..
[SC1-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If (Not (If (Either [2] or [3].), then (If [0], then [1].).).), then [4].).
If [7], then (If (Not (If (Either [2] or [3].), then (If [0], then [1].).).), then [4].).
Therefore, If (Not (If (Either [2] or [3].), then (If [0], then [1].).).), then [4]..
[SC2-1]
Modus Ponens:
If [5], then (Either [2] or [3].).
[5]
Therefore, Either [2] or [3]..
|
{0: 'Carabiners are the duct tape of rock climbers.', 1: 'Kinesiology is the fastest growing, and most comprehensive holistic therapy in the world today.', 2: 'People of color are less likely to have health insurance.', 3: 'Homozygous mutants die of respiratory failure shortly after birth.', 4: 'Most nebulas have mass.', 5: 'Most insects also have two antennae and two sets of wings.', 6: 'Observatories have (part) doorsteps.', 7: 'Plant cells fix atmospheric carbon using energy from sunlight in a process called photosynthesis.'}
| 4 |
3,564 |
['Given that polluted water causes diarrhoea, which kills five million children per year, it can be inferred that most people know that a lack of fibre is related to constipation.', "Whenever it is true that the notion that 'polluted water causes diarrhoea, which kills five million children per year' is untrue, 'skewness measures the lack of symmetry of a probability distribution' is true.", 'On the condition that skewness measures the lack of symmetry of a probability distribution, it is definitely the case that either cages have bottoms or alcohol can make the effects of other drugs much worse.', 'It is a fact that either either some injuries heal on their own with rest, ice, compression, and elevation of the leg or some diseases are caused by motile bacteria or the claim that either cages have bottoms or alcohol can make the effects of other drugs much worse is false.', 'The statement that states either some injuries heal on their own with rest, ice, compression, and elevation of the leg or some diseases are caused by motile bacteria is false.']
|
Given that polluted water causes diarrhoea, which kills five million children per year, it can be inferred that most people know that a lack of fibre is related to constipation. Whenever it is true that the notion that 'polluted water causes diarrhoea, which kills five million children per year' is untrue, 'skewness measures the lack of symmetry of a probability distribution' is true. On the condition that skewness measures the lack of symmetry of a probability distribution, it is definitely the case that either cages have bottoms or alcohol can make the effects of other drugs much worse. It is a fact that either either some injuries heal on their own with rest, ice, compression, and elevation of the leg or some diseases are caused by motile bacteria or the claim that either cages have bottoms or alcohol can make the effects of other drugs much worse is false. The statement that states either some injuries heal on their own with rest, ice, compression, and elevation of the leg or some diseases are caused by motile bacteria is false.
|
The statement that states most people know that a lack of fibre is related to constipation is right.
|
The statement that states most people know that a lack of fibre is related to constipation is right.
|
TRUE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not [1].), then (Either [2] or [3].). [SC1-2]
Not (Either [2] or [3].). [SC2-2]
Therefore, [1].
[SC1-2]
Hypothetical Syllogism:
If (Not [1].), then [4].
If [4], then (Either [2] or [3].).
Therefore, If (Not [1].), then (Either [2] or [3].)..
[SC2-2]
Disjunctive Syllogism:
Either (Either [5] or [6].) or (Not (Either [2] or [3].).).
Not (Either [5] or [6].).
Therefore, Not (Either [2] or [3].)..
|
{0: 'Most people know that a lack of fibre is related to constipation.', 1: 'Polluted water causes diarrhoea, which kills five million children per year.', 2: 'Cages have bottoms.', 3: 'Alcohol can make the effects of other drugs much worse.', 4: 'Skewness measures the lack of symmetry of a probability distribution.', 5: 'Some injuries heal on their own with rest, ice, compression, and elevation of the leg.', 6: 'Some diseases are caused by motile bacteria.'}
| 4 |
3,401 |
['When the statement, if different species prefer different host plants, then faith overcomes the illusion of the darkness, of evil, does not hold is true, it follows that slides are located in parks.', 'One may reasonably assume that if those that suggest if faith overcomes the illusion of the darkness, of evil, then cyclic temperatures are more natural but their effects on dipteran larval growth are ambiguous are wrong, then biology encompasses the study of all living organisms, including microbes, plants, and animals.', "The statement 'biology encompasses the study of all living organisms, including microbes, plants, and animals' can be considered false.", "One may reasonably assume that if the statement, if the statement, if different species prefer different host plants, then faith overcomes the illusion of the darkness, of evil, does not hold, then the notion that 'slides are located in parks' is untrue, does not hold, then ink film is tough and resistant to abrasion.", "Whenever it is true that the statement, if the statement, if different species prefer different host plants, then faith overcomes the illusion of the darkness, of evil, does not hold, then the notion that 'slides are located in parks' is untrue, does not hold, 'it is a common misconception that ink film is tough and resistant to abrasion' is true."]
|
When the statement, if different species prefer different host plants, then faith overcomes the illusion of the darkness, of evil, does not hold is true, it follows that slides are located in parks. One may reasonably assume that if those that suggest if faith overcomes the illusion of the darkness, of evil, then cyclic temperatures are more natural but their effects on dipteran larval growth are ambiguous are wrong, then biology encompasses the study of all living organisms, including microbes, plants, and animals. The statement 'biology encompasses the study of all living organisms, including microbes, plants, and animals' can be considered false. One may reasonably assume that if the statement, if the statement, if different species prefer different host plants, then faith overcomes the illusion of the darkness, of evil, does not hold, then the notion that 'slides are located in parks' is untrue, does not hold, then ink film is tough and resistant to abrasion. Whenever it is true that the statement, if the statement, if different species prefer different host plants, then faith overcomes the illusion of the darkness, of evil, does not hold, then the notion that 'slides are located in parks' is untrue, does not hold, 'it is a common misconception that ink film is tough and resistant to abrasion' is true.
|
Should it be the case that different species prefer different host plants, it follows that cyclic temperatures are more natural but their effects on dipteran larval growth are ambiguous.
|
Should it be the case that different species prefer different host plants, it follows that cyclic temperatures are more natural but their effects on dipteran larval growth are ambiguous.
|
TRUE
|
Hypothetical Syllogism:
If [0], then [2]. [SC1-1]
If [2], then [1]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [0], then [2].).), then [3].
If (Not (If [0], then [2].).), then (Not [3].). [SC2-2]
Therefore, If [0], then [2]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (If [0], then [2].).), then (Not [3].).).), then [5].
If (Not (If (Not (If [0], then [2].).), then (Not [3].).).), then (Not [5].).
Therefore, If (Not (If [0], then [2].).), then (Not [3].)..
[SC2-1]
Modus Tonens:
If (Not (If [2], then [1].).), then [4].
Not [4].
Therefore, If [2], then [1]..
|
{0: 'Different species prefer different host plants.', 1: 'Cyclic temperatures are more natural but their effects on dipteran larval growth are ambiguous.', 2: 'Faith overcomes the illusion of the darkness, of evil.', 3: 'Slides are located in parks.', 4: 'Biology encompasses the study of all living organisms, including microbes, plants, and animals.', 5: 'Ink film is tough and resistant to abrasion.'}
| 4 |
3,530 |
['It is a fact that either either charge cycle begins when battery is connected to the charger or joint strength develops as the cement dries or machines have benefits.', 'Should it be the case that toads reach sexual maturity, it follows that the claim that either charge cycle begins when battery is connected to the charger or joint strength develops as the cement dries does not correspond with reality.', "Whenever it is true that it is not the case that either either most desert plants have reproductive biology or a ptosis is disability or toads reach sexual maturity, 'rabbits are a preferred prey animal' is true.", "The statement that 'rabbits are a preferred prey animal' is incorrect.", 'Should it be the case that some people mistakenly believe that if either most desert plants have reproductive biology or a ptosis is disability, then the claim that either charge cycle begins when battery is connected to the charger or joint strength develops as the cement dries does not correspond with reality, it follows that if some domains show homology, then rice is pasta.', 'It is not the case that if some domains show homology, then rice is pasta.']
|
It is a fact that either either charge cycle begins when battery is connected to the charger or joint strength develops as the cement dries or machines have benefits. Should it be the case that toads reach sexual maturity, it follows that the claim that either charge cycle begins when battery is connected to the charger or joint strength develops as the cement dries does not correspond with reality. Whenever it is true that it is not the case that either either most desert plants have reproductive biology or a ptosis is disability or toads reach sexual maturity, 'rabbits are a preferred prey animal' is true. The statement that 'rabbits are a preferred prey animal' is incorrect. Should it be the case that some people mistakenly believe that if either most desert plants have reproductive biology or a ptosis is disability, then the claim that either charge cycle begins when battery is connected to the charger or joint strength develops as the cement dries does not correspond with reality, it follows that if some domains show homology, then rice is pasta. It is not the case that if some domains show homology, then rice is pasta.
|
Those that suggest machines have benefits are right.
|
Machines are apparatus.
|
Uncertain
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or [0].
Not (Either [1] or [2].). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either (Either [3] or [4].) or [5]. [SC1-2]
If (Either [3] or [4].), then (Not (Either [1] or [2].).). [SC2-2]
If [5], then (Not (Either [1] or [2].).).
Therefore, Not (Either [1] or [2].)..
[SC1-2]
Modus Tonens:
If (Not (Either (Either [3] or [4].) or [5].).), then [8].
Not [8].
Therefore, Either (Either [3] or [4].) or [5]..
[SC2-2]
Modus Tonens:
If (Not (If (Either [3] or [4].), then (Not (Either [1] or [2].).).).), then (If [6], then [7].).
Not (If [6], then [7].).
Therefore, If (Either [3] or [4].), then (Not (Either [1] or [2].).)..
|
{0: 'Machines have benefits.', 1: 'Charge cycle begins when battery is connected to the charger.', 2: 'Joint strength develops as the cement dries.', 3: 'Most desert plants have reproductive biology.', 4: 'A ptosis is disability.', 5: 'Toads reach sexual maturity.', 6: 'Some domains show homology.', 7: 'Rice is pasta.', 8: 'Rabbits are a preferred prey animal.'}
| 4 |
3,656 |
['There is good reason to believe that either any language develops as a spoken language or float seaweed finds in blue water.', 'On the condition that float seaweed finds in blue water, it is definitely the case that hindquarters are cuts.', "It is a fact that either oblates are monasticism's gift to the world or attention is related to expressed saccade.", "Once we know oblates are monasticism's gift to the world , we also know that if any language develops as a spoken language, then grandmas have (part) personality.", 'If attention is related to expressed saccade, then if any language develops as a spoken language, then grandmas have (part) personality.', 'Provided that it is not the case that if grandmas have (part) personality, then hindquarters are cuts, we know that bone fractures are a major cause of morbidity and mortality associated with osteoporosis.', 'The statement, bone fractures are a major cause of morbidity and mortality associated with osteoporosis, does not hold.']
|
There is good reason to believe that either any language develops as a spoken language or float seaweed finds in blue water. On the condition that float seaweed finds in blue water, it is definitely the case that hindquarters are cuts. It is a fact that either oblates are monasticism's gift to the world or attention is related to expressed saccade. Once we know oblates are monasticism's gift to the world , we also know that if any language develops as a spoken language, then grandmas have (part) personality. If attention is related to expressed saccade, then if any language develops as a spoken language, then grandmas have (part) personality. Provided that it is not the case that if grandmas have (part) personality, then hindquarters are cuts, we know that bone fractures are a major cause of morbidity and mortality associated with osteoporosis. The statement, bone fractures are a major cause of morbidity and mortality associated with osteoporosis, does not hold.
|
It is a simple truth that hindquarters are cuts.
|
Some people mistakenly believe that hindquarters are cuts.
|
FALSE
|
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]. [SC2-2]
Therefore, If [1], then [0]..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [1], then [3].).
If [5], then (If [1], then [3].).
Therefore, If [1], then [3]..
[SC2-2]
Modus Tonens:
If (Not (If [3], then [0].).), then [6].
Not [6].
Therefore, If [3], then [0]..
|
{0: 'Hindquarters are cuts.', 1: 'Any language develops as a spoken language.', 2: 'Float seaweed finds in blue water.', 3: 'Grandmas have (part) personality.', 4: "Oblates are monasticism's gift to the world .", 5: 'Attention is related to expressed saccade.', 6: 'Bone fractures are a major cause of morbidity and mortality associated with osteoporosis.'}
| 4 |
3,441 |
['Once we know sun is located in universes, we also know that a nought is a figure.', "So long as if polysyllables tend to have all syllables equally stressed, then sustainable forests are also essential to a robust and profitable forest-products industry, 'if chiggers feed on a wide variety of snakes, turtles, birds, and small mammals as well as humans, then sun is located in universes' is true.", "So long as vegetation helps keep streams flowing during dry periods, 'if chiggers feed on a wide variety of snakes, turtles, birds, and small mammals as well as humans, then sun is located in universes' is true.", "So long as it is a common misconception that either if polysyllables tend to have all syllables equally stressed, then sustainable forests are also essential to a robust and profitable forest-products industry or vegetation helps keep streams flowing during dry periods, 'it is not the case that radiation can be of several types' is true.", "Whenever it is true that the claim that if it is a common misconception that either if polysyllables tend to have all syllables equally stressed, then sustainable forests are also essential to a robust and profitable forest-products industry or vegetation helps keep streams flowing during dry periods, then radiation can be of several types is false, 'departments begin services' is true.", "The notion that 'departments begin services' is untrue."]
|
Once we know sun is located in universes, we also know that a nought is a figure. So long as if polysyllables tend to have all syllables equally stressed, then sustainable forests are also essential to a robust and profitable forest-products industry, 'if chiggers feed on a wide variety of snakes, turtles, birds, and small mammals as well as humans, then sun is located in universes' is true. So long as vegetation helps keep streams flowing during dry periods, 'if chiggers feed on a wide variety of snakes, turtles, birds, and small mammals as well as humans, then sun is located in universes' is true. So long as it is a common misconception that either if polysyllables tend to have all syllables equally stressed, then sustainable forests are also essential to a robust and profitable forest-products industry or vegetation helps keep streams flowing during dry periods, 'it is not the case that radiation can be of several types' is true. Whenever it is true that the claim that if it is a common misconception that either if polysyllables tend to have all syllables equally stressed, then sustainable forests are also essential to a robust and profitable forest-products industry or vegetation helps keep streams flowing during dry periods, then radiation can be of several types is false, 'departments begin services' is true. The notion that 'departments begin services' is untrue.
|
If chiggers feed on a wide variety of snakes, turtles, birds, and small mammals as well as humans, then a nought is a figure.
|
If chiggers feed on a wide variety of snakes, turtles, birds, and small mammals as well as humans, then a nought is a figure.
|
TRUE
|
Hypothetical Syllogism:
If [0], then [2]. [SC1-1]
If [2], then [1].
Therefore, If [0], then [1]..
[SC1-1]
Disjunction Elimination:
Either (If [3], then [4].) or [5]. [SC1-2]
If (If [3], then [4].), then (If [0], then [2].).
If [5], then (If [0], then [2].).
Therefore, If [0], then [2]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either (If [3], then [4].) or [5].).), then [6]. [SC1-3]
If (Not (Either (If [3], then [4].) or [5].).), then (Not [6].).
Therefore, Either (If [3], then [4].) or [5]..
[SC1-3]
Modus Tonens:
If (Not (If (Not (Either (If [3], then [4].) or [5].).), then [6].).), then [7].
Not [7].
Therefore, If (Not (Either (If [3], then [4].) or [5].).), then [6]..
|
{0: 'Chiggers feed on a wide variety of snakes, turtles, birds, and small mammals as well as humans.', 1: 'A nought is a figure.', 2: 'Sun is located in universes.', 3: 'Polysyllables tend to have all syllables equally stressed.', 4: 'Sustainable forests are also essential to a robust and profitable forest-products industry.', 5: 'Vegetation helps keep streams flowing during dry periods.', 6: 'Radiation can be of several types.', 7: 'Departments begin services.'}
| 4 |
3,132 |
["So long as the statement, either most children naturally stop between the ages of two and four or dietary management is crucial for long term management in the affected dogs, does not hold, 'probability is the ratio of the favorable cases to all the cases' is true.", "The notion that 'probability is the ratio of the favorable cases to all the cases' is untrue.", 'Given that most children naturally stop between the ages of two and four, it can be inferred that we know that the claim that human vision is very poor in relation to some animals is false.', 'We know that either most absorption causes chemical reaction or if most children naturally stop between the ages of two and four, then human vision is very poor in relation to some animals.', 'It is not the case that most absorption causes chemical reaction.']
|
So long as the statement, either most children naturally stop between the ages of two and four or dietary management is crucial for long term management in the affected dogs, does not hold, 'probability is the ratio of the favorable cases to all the cases' is true. The notion that 'probability is the ratio of the favorable cases to all the cases' is untrue. Given that most children naturally stop between the ages of two and four, it can be inferred that we know that the claim that human vision is very poor in relation to some animals is false. We know that either most absorption causes chemical reaction or if most children naturally stop between the ages of two and four, then human vision is very poor in relation to some animals. It is not the case that most absorption causes chemical reaction.
|
dietary management is crucial for long term management in the affected dogs.
|
Dietary management is crucial for long term management in the affected dogs.
|
TRUE
|
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].
Therefore, Either [1] or [0]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2]. [SC1-2]
If [1], then (Not [2].).
Therefore, Not [1]..
[SC1-2]
Disjunctive Syllogism:
Either [4] or (If [1], then [2].).
Not [4].
Therefore, If [1], then [2]..
|
{0: 'Dietary management is crucial for long term management in the affected dogs.', 1: 'Most children naturally stop between the ages of two and four.', 2: 'Human vision is very poor in relation to some animals.', 3: 'Probability is the ratio of the favorable cases to all the cases.', 4: 'Most absorption causes chemical reaction.'}
| 4 |
3,233 |
["Whenever it is true that some people mistakenly believe that if the claim that casinos are corporations does not correspond with reality, then salt can accumulate and cause kidney disease in old age, 'if college football is still popular today among students, alumni, and other fans of the sport, then few things harbor as many human taboos as the anal and genital organs' is true.", 'Either selenium is solids or if most evolutionary development takes years, then some meat induces inflammation.', "Provided that selenium is solids, we know that if the claim that casinos are corporations does not correspond with reality, then the notion that 'salt can accumulate and cause kidney disease in old age' is untrue.", "Once we know if most evolutionary development takes years, then some meat induces inflammation, we also know that if the claim that casinos are corporations does not correspond with reality, then the notion that 'salt can accumulate and cause kidney disease in old age' is untrue.", 'Given that if college football is still popular today among students, alumni, and other fans of the sport, then few things harbor as many human taboos as the anal and genital organs, it can be inferred that retractable claws remain sharp.', 'On the condition that if college football is still popular today among students, alumni, and other fans of the sport, then few things harbor as many human taboos as the anal and genital organs, it is definitely the case that it is not the case that retractable claws remain sharp.']
|
Whenever it is true that some people mistakenly believe that if the claim that casinos are corporations does not correspond with reality, then salt can accumulate and cause kidney disease in old age, 'if college football is still popular today among students, alumni, and other fans of the sport, then few things harbor as many human taboos as the anal and genital organs' is true. Either selenium is solids or if most evolutionary development takes years, then some meat induces inflammation. Provided that selenium is solids, we know that if the claim that casinos are corporations does not correspond with reality, then the notion that 'salt can accumulate and cause kidney disease in old age' is untrue. Once we know if most evolutionary development takes years, then some meat induces inflammation, we also know that if the claim that casinos are corporations does not correspond with reality, then the notion that 'salt can accumulate and cause kidney disease in old age' is untrue. Given that if college football is still popular today among students, alumni, and other fans of the sport, then few things harbor as many human taboos as the anal and genital organs, it can be inferred that retractable claws remain sharp. On the condition that if college football is still popular today among students, alumni, and other fans of the sport, then few things harbor as many human taboos as the anal and genital organs, it is definitely the case that it is not the case that retractable claws remain sharp.
|
The statement 'casinos are corporations' can be considered true.
|
Most casinos have slot machines.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
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]
Reductio Ad Absurdum:
If (If [2], then [3].), then [7].
If (If [2], then [3].), then (Not [7].).
Therefore, Not (If [2], then [3].)..
[SC2-1]
Disjunction Elimination:
Either [4] or (If [5], then [6].).
If [4], then (If (Not [0].), then (Not [1].).).
If (If [5], then [6].), then (If (Not [0].), then (Not [1].).).
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Casinos are corporations.', 1: 'Salt can accumulate and cause kidney disease in old age.', 2: 'College football is still popular today among students, alumni, and other fans of the sport.', 3: 'Few things harbor as many human taboos as the anal and genital organs.', 4: 'Selenium is solids.', 5: 'Most evolutionary development takes years.', 6: 'Some meat induces inflammation.', 7: 'Retractable claws remain sharp.'}
| 4 |
3,173 |
['Should it be the case that berries grow in areas, it follows that beets are also good as are lycium berries, little berries that can be eaten instead of raisins.', 'There is good reason to believe that either a desalination is a chemical action or least weasels have own territory.', 'When least weasels have own territory is true, it follows that berries grow in areas.', 'Should it be the case that some cancers are hereditary, it follows that if a desalination is a chemical action, then berries grow in areas.', 'If if statute is a noun that refers to a law or rule, then tortoises occasionally eliminate a gray to whitish, chalky substance, then if a desalination is a chemical action, then berries grow in areas.', 'If canoes are located in water, then either some cancers are hereditary or if statute is a noun that refers to a law or rule, then tortoises occasionally eliminate a gray to whitish, chalky substance.', 'Those that suggest canoes are located in water are right.']
|
Should it be the case that berries grow in areas, it follows that beets are also good as are lycium berries, little berries that can be eaten instead of raisins. There is good reason to believe that either a desalination is a chemical action or least weasels have own territory. When least weasels have own territory is true, it follows that berries grow in areas. Should it be the case that some cancers are hereditary, it follows that if a desalination is a chemical action, then berries grow in areas. If if statute is a noun that refers to a law or rule, then tortoises occasionally eliminate a gray to whitish, chalky substance, then if a desalination is a chemical action, then berries grow in areas. If canoes are located in water, then either some cancers are hereditary or if statute is a noun that refers to a law or rule, then tortoises occasionally eliminate a gray to whitish, chalky substance. Those that suggest canoes are located in water are right.
|
The statement 'beets are also good as are lycium berries, little berries that can be eaten instead of raisins' can be considered true.
|
The claim that beets are also good as are lycium berries, little berries that can be eaten instead of raisins is false.
|
FALSE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then [1]. [SC2-2]
If [3], then [1].
Therefore, [1].
[SC2-2]
Disjunction Elimination:
Either [4] or (If [5], then [6].). [SC1-3]
If [4], then (If [2], then [1].).
If (If [5], then [6].), then (If [2], then [1].).
Therefore, If [2], then [1]..
[SC1-3]
Modus Ponens:
If [7], then (Either [4] or (If [5], then [6].).).
[7]
Therefore, Either [4] or (If [5], then [6].)..
|
{0: 'Beets are also good as are lycium berries, little berries that can be eaten instead of raisins.', 1: 'Berries grow in areas.', 2: 'A desalination is a chemical action.', 3: 'Least weasels have own territory.', 4: 'Some cancers are hereditary.', 5: 'Statute is a noun that refers to a law or rule.', 6: 'Tortoises occasionally eliminate a gray to whitish, chalky substance.', 7: 'Canoes are located in water.'}
| 4 |
3,428 |
['If underdeveloped lungs is one of the major problems of prematurity, then signs are responsible for establishing ambience and frame of mind.', 'Given that the claim that if it is not true that if signs are responsible for establishing ambience and frame of mind, then uterine prolapse affects females only, then caffeine desensitizes some individuals does not reflect reality, it can be inferred that birds love to dine on all sorts of bugs, big and small.', 'The claim that birds love to dine on all sorts of bugs, big and small is false.', 'When it is not true that if signs are responsible for establishing ambience and frame of mind, then uterine prolapse affects females only is true, it follows that horses are herd animals and do better with company.', "So long as horses are herd animals and do better with company, 'the claim that caffeine desensitizes some individuals is false' is true."]
|
If underdeveloped lungs is one of the major problems of prematurity, then signs are responsible for establishing ambience and frame of mind. Given that the claim that if it is not true that if signs are responsible for establishing ambience and frame of mind, then uterine prolapse affects females only, then caffeine desensitizes some individuals does not reflect reality, it can be inferred that birds love to dine on all sorts of bugs, big and small. The claim that birds love to dine on all sorts of bugs, big and small is false. When it is not true that if signs are responsible for establishing ambience and frame of mind, then uterine prolapse affects females only is true, it follows that horses are herd animals and do better with company. So long as horses are herd animals and do better with company, 'the claim that caffeine desensitizes some individuals is false' is true.
|
On the condition that underdeveloped lungs is one of the major problems of prematurity, it is definitely the case that uterine prolapse affects females only.
|
It is not the case that if underdeveloped lungs is one of the major problems of prematurity, then uterine prolapse affects females only.
|
FALSE
|
Hypothetical Syllogism:
If [0], then [2].
If [2], then [1]. [SC2-1]
Therefore, If [0], then [1]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [2], then [1].).), then [3]. [SC1-2]
If (Not (If [2], then [1].).), then (Not [3].). [SC2-2]
Therefore, If [2], then [1]..
[SC1-2]
Modus Tonens:
If (Not (If (Not (If [2], then [1].).), then [3].).), then [4].
Not [4].
Therefore, If (Not (If [2], then [1].).), then [3]..
[SC2-2]
Hypothetical Syllogism:
If (Not (If [2], then [1].).), then [5].
If [5], then (Not [3].).
Therefore, If (Not (If [2], then [1].).), then (Not [3].)..
|
{0: 'Underdeveloped lungs is one of the major problems of prematurity.', 1: 'Uterine prolapse affects females only.', 2: 'Signs are responsible for establishing ambience and frame of mind.', 3: 'Caffeine desensitizes some individuals.', 4: 'Birds love to dine on all sorts of bugs, big and small.', 5: 'Horses are herd animals and do better with company.'}
| 4 |
3,567 |
["So long as rabbit ears serve purposes, 'vectors have a direction and a magnitude' is true.", 'If industrialism combined with advanced technology influences the size and complexity of our society, then either rabbit ears serve purposes or ponies are located in fairs.', 'Either myths are about the gods or if ponies are located in fairs, then vectors have a direction and a magnitude.', "The notion that 'myths are about the gods' is untrue.", 'It is rational to believe that either some blood types have peanuts or industrialism combined with advanced technology influences the size and complexity of our society.', 'Those that suggest some blood types have peanuts are wrong.']
|
So long as rabbit ears serve purposes, 'vectors have a direction and a magnitude' is true. If industrialism combined with advanced technology influences the size and complexity of our society, then either rabbit ears serve purposes or ponies are located in fairs. Either myths are about the gods or if ponies are located in fairs, then vectors have a direction and a magnitude. The notion that 'myths are about the gods' is untrue. It is rational to believe that either some blood types have peanuts or industrialism combined with advanced technology influences the size and complexity of our society. Those that suggest some blood types have peanuts are wrong.
|
The claim that vectors have a direction and a magnitude holds true.
|
Vectors are agents.
|
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 [3], then (Either [1] or [2].).
[3] [SC2-2]
Therefore, Either [1] or [2]..
[SC2-2]
Disjunctive Syllogism:
Either [5] or [3].
Not [5].
Therefore, [3].
[SC3-1]
Disjunctive Syllogism:
Either [4] or (If [2], then [0].).
Not [4].
Therefore, If [2], then [0]..
|
{0: 'Vectors have a direction and a magnitude.', 1: 'Rabbit ears serve purposes.', 2: 'Ponies are located in fairs.', 3: 'Industrialism combined with advanced technology influences the size and complexity of our society.', 4: 'Myths are about the gods.', 5: 'Some blood types have peanuts.'}
| 4 |
3,967 |
['Should it be the case that some people mistakenly believe that if the claim that if professors gain teach experience, then art also can offer a visceral kind of healing, something every person and every society needs does not reflect reality, then councils are organizations, it follows that mosquito bites can be more than just annoying and itchy.', 'One may reasonably assume that if some people mistakenly believe that if the claim that if professors gain teach experience, then art also can offer a visceral kind of healing, something every person and every society needs does not reflect reality, then councils are organizations, then some people mistakenly believe that mosquito bites can be more than just annoying and itchy.', 'The claim that wind generators give off a low frequency sound which shakes objects in near by homes does not correspond with reality.', 'When we know that the claim that if it is not true that if the claim that if professors gain teach experience, then art also can offer a visceral kind of healing, something every person and every society needs does not reflect reality, then the claim that councils are organizations has no merit, then wind generators give off a low frequency sound which shakes objects in near by homes is false is true, it follows that either multiculturalism helps to legitimize whole new areas of consumerism or some traffic circles are part of causeways.', 'Those that suggest either multiculturalism helps to legitimize whole new areas of consumerism or some traffic circles are part of causeways are wrong.']
|
Should it be the case that some people mistakenly believe that if the claim that if professors gain teach experience, then art also can offer a visceral kind of healing, something every person and every society needs does not reflect reality, then councils are organizations, it follows that mosquito bites can be more than just annoying and itchy. One may reasonably assume that if some people mistakenly believe that if the claim that if professors gain teach experience, then art also can offer a visceral kind of healing, something every person and every society needs does not reflect reality, then councils are organizations, then some people mistakenly believe that mosquito bites can be more than just annoying and itchy. The claim that wind generators give off a low frequency sound which shakes objects in near by homes does not correspond with reality. When we know that the claim that if it is not true that if the claim that if professors gain teach experience, then art also can offer a visceral kind of healing, something every person and every society needs does not reflect reality, then the claim that councils are organizations has no merit, then wind generators give off a low frequency sound which shakes objects in near by homes is false is true, it follows that either multiculturalism helps to legitimize whole new areas of consumerism or some traffic circles are part of causeways. Those that suggest either multiculturalism helps to legitimize whole new areas of consumerism or some traffic circles are part of causeways are wrong.
|
Once we know professors gain teach experience, we also know that art also can offer a visceral kind of healing, something every person and every society needs.
|
Once we know professors gain teach experience, we also know that art also can offer a visceral kind of healing, something every person and every society needs.
|
TRUE
|
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then [2]. [SC1-1]
If (Not (If [0], then [1].).), then (Not [2].). [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not (If [0], then [1].).), then [2].).), then [4].
If (Not (If (Not (If [0], then [1].).), then [2].).), then (Not [4].).
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC2-1]
Modus Tonens:
If (Not (If (Not (If [0], then [1].).), then (Not [2].).).), then [3]. [SC1-2]
Not [3].
Therefore, If (Not (If [0], then [1].).), then (Not [2].)..
[SC1-2]
Modus Tonens:
If (Not (If (Not (If (Not (If [0], then [1].).), then (Not [2].).).), then [3].).), then (Either [5] or [6].).
Not (Either [5] or [6].).
Therefore, If (Not (If (Not (If [0], then [1].).), then (Not [2].).).), then [3]..
|
{0: 'Professors gain teach experience.', 1: 'Art also can offer a visceral kind of healing, something every person and every society needs.', 2: 'Councils are organizations.', 3: 'Wind generators give off a low frequency sound which shakes objects in near by homes.', 4: 'Mosquito bites can be more than just annoying and itchy.', 5: 'Multiculturalism helps to legitimize whole new areas of consumerism.', 6: 'Some traffic circles are part of causeways.'}
| 4 |
3,758 |
['Assuming those that suggest either breast imaging is a specialized field in radiology that studies the breast or it is not the case that many women swear by natural progesterone creams are wrong, we know that volcanoes play a role by sending up particles that block sunlight and cool the atmosphere.', "There is good reason to believe that either salinity is determined by observing where the line intersects with the gradient or the statement 'breast imaging is a specialized field in radiology that studies the breast' can be considered false.", 'The claim that salinity is determined by observing where the line intersects with the gradient does not correspond with reality.', 'Given that the statement that states if those that suggest either breast imaging is a specialized field in radiology that studies the breast or it is not the case that many women swear by natural progesterone creams are wrong, then it is not true that volcanoes play a role by sending up particles that block sunlight and cool the atmosphere is false, it can be inferred that nausea is controlled by a part of the nervous system that controls involuntary bodily functions.', "If the statement that states if those that suggest either breast imaging is a specialized field in radiology that studies the breast or it is not the case that many women swear by natural progesterone creams are wrong, then it is not true that volcanoes play a role by sending up particles that block sunlight and cool the atmosphere is false, then the statement that 'nausea is controlled by a part of the nervous system that controls involuntary bodily functions' is incorrect."]
|
Assuming those that suggest either breast imaging is a specialized field in radiology that studies the breast or it is not the case that many women swear by natural progesterone creams are wrong, we know that volcanoes play a role by sending up particles that block sunlight and cool the atmosphere. There is good reason to believe that either salinity is determined by observing where the line intersects with the gradient or the statement 'breast imaging is a specialized field in radiology that studies the breast' can be considered false. The claim that salinity is determined by observing where the line intersects with the gradient does not correspond with reality. Given that the statement that states if those that suggest either breast imaging is a specialized field in radiology that studies the breast or it is not the case that many women swear by natural progesterone creams are wrong, then it is not true that volcanoes play a role by sending up particles that block sunlight and cool the atmosphere is false, it can be inferred that nausea is controlled by a part of the nervous system that controls involuntary bodily functions. If the statement that states if those that suggest either breast imaging is a specialized field in radiology that studies the breast or it is not the case that many women swear by natural progesterone creams are wrong, then it is not true that volcanoes play a role by sending up particles that block sunlight and cool the atmosphere is false, then the statement that 'nausea is controlled by a part of the nervous system that controls involuntary bodily functions' is incorrect.
|
It is not the case that many women swear by natural progesterone creams.
|
It is not the case that many women swear by natural progesterone creams.
|
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 [3].
If (Not (Either [1] or (Not [0].).).), then (Not [3].). [SC2-2]
Therefore, Either [1] or (Not [0].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (Either [1] or (Not [0].).).), then (Not [3].).).), then [4].
If (Not (If (Not (Either [1] or (Not [0].).).), then (Not [3].).).), then (Not [4].).
Therefore, If (Not (Either [1] or (Not [0].).).), then (Not [3].)..
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].).
Not [2].
Therefore, Not [1]..
|
{0: 'Many women swear by natural progesterone creams.', 1: 'Breast imaging is a specialized field in radiology that studies the breast.', 2: 'Salinity is determined by observing where the line intersects with the gradient.', 3: 'Volcanoes play a role by sending up particles that block sunlight and cool the atmosphere.', 4: 'Nausea is controlled by a part of the nervous system that controls involuntary bodily functions.'}
| 4 |
3,626 |
['Should it be the case that either habitat management is the science and art of changing habitat or girls are also concerned about the shape of their legs, breasts, waist and about their eyes, it follows that if neoplastic lesions containing both an adenomatous component and a carcinoid component are rare, then bilbies are omnivores and eat small lizards, mice, spiders, insects, roots and seeds.', 'Should it be the case that if neoplastic lesions containing both an adenomatous component and a carcinoid component are rare, then bilbies are omnivores and eat small lizards, mice, spiders, insects, roots and seeds, it follows that rhythmicity is a property.', "Should it be the case that the statement 'if either habitat management is the science and art of changing habitat or girls are also concerned about the shape of their legs, breasts, waist and about their eyes, then it is not true that rhythmicity is a property' can be considered false, it follows that warm foods have more aroma than cold.", 'Should it be the case that most little girls develop ear infection, it follows that it is not the case that warm foods have more aroma than cold.', 'It is true that most little girls develop ear infection.']
|
Should it be the case that either habitat management is the science and art of changing habitat or girls are also concerned about the shape of their legs, breasts, waist and about their eyes, it follows that if neoplastic lesions containing both an adenomatous component and a carcinoid component are rare, then bilbies are omnivores and eat small lizards, mice, spiders, insects, roots and seeds. Should it be the case that if neoplastic lesions containing both an adenomatous component and a carcinoid component are rare, then bilbies are omnivores and eat small lizards, mice, spiders, insects, roots and seeds, it follows that rhythmicity is a property. Should it be the case that the statement 'if either habitat management is the science and art of changing habitat or girls are also concerned about the shape of their legs, breasts, waist and about their eyes, then it is not true that rhythmicity is a property' can be considered false, it follows that warm foods have more aroma than cold. Should it be the case that most little girls develop ear infection, it follows that it is not the case that warm foods have more aroma than cold. It is true that most little girls develop ear infection.
|
It is a common misconception that either habitat management is the science and art of changing habitat or girls are also concerned about the shape of their legs, breasts, waist and about their eyes.
|
At least one of two things is true: habitat management is the science and art of changing habitat, or girls are also concerned about the shape of their legs, breasts, waist and about their eyes.
|
FALSE
|
Reductio Ad Absurdum:
If (Either [0] or [1].), then [2]. [SC1-1]
If (Either [0] or [1].), then (Not [2].). [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Hypothetical Syllogism:
If (Either [0] or [1].), then (If [4], then [5].).
If (If [4], then [5].), then [2].
Therefore, If (Either [0] or [1].), then [2]..
[SC2-1]
Modus Tonens:
If (Not (If (Either [0] or [1].), then (Not [2].).).), then [3].
Not [3]. [SC2-2]
Therefore, If (Either [0] or [1].), then (Not [2].)..
[SC2-2]
Modus Ponens:
If [6], then (Not [3].).
[6]
Therefore, Not [3]..
|
{0: 'Habitat management is the science and art of changing habitat.', 1: 'Girls are also concerned about the shape of their legs, breasts, waist and about their eyes.', 2: 'Rhythmicity is a property.', 3: 'Warm foods have more aroma than cold.', 4: 'Neoplastic lesions containing both an adenomatous component and a carcinoid component are rare.', 5: 'Bilbies are omnivores and eat small lizards, mice, spiders, insects, roots and seeds.', 6: 'Most little girls develop ear infection.'}
| 4 |
3,096 |
["Should it be the case that we know that the claim that copper is required for the function of angiogenesis is false, it follows that the statement that 'either dreams are our own brain's attempt to solve and resolve real-life problems or silence is a form of speech' is incorrect.", "Provided that advertising attempts to affect attitudes, we know that if we know that the claim that copper is required for the function of angiogenesis is false, then either dreams are our own brain's attempt to solve and resolve real-life problems or silence is a form of speech.", 'Either one or both of these statements are true: some individuals choose to become pregnant and parent on their own, or either smoking reduces the levels of antioxidants and impairs blood circulation or advertising attempts to affect attitudes.', 'The statement, some individuals choose to become pregnant and parent on their own, does not hold.', "Either writing is a mindset, a psychological view of life or if smoking reduces the levels of antioxidants and impairs blood circulation, then if we know that the claim that copper is required for the function of angiogenesis is false, then either dreams are our own brain's attempt to solve and resolve real-life problems or silence is a form of speech.", 'The statement, writing is a mindset, a psychological view of life, does not hold.']
|
Should it be the case that we know that the claim that copper is required for the function of angiogenesis is false, it follows that the statement that 'either dreams are our own brain's attempt to solve and resolve real-life problems or silence is a form of speech' is incorrect. Provided that advertising attempts to affect attitudes, we know that if we know that the claim that copper is required for the function of angiogenesis is false, then either dreams are our own brain's attempt to solve and resolve real-life problems or silence is a form of speech. Either one or both of these statements are true: some individuals choose to become pregnant and parent on their own, or either smoking reduces the levels of antioxidants and impairs blood circulation or advertising attempts to affect attitudes. The statement, some individuals choose to become pregnant and parent on their own, does not hold. Either writing is a mindset, a psychological view of life or if smoking reduces the levels of antioxidants and impairs blood circulation, then if we know that the claim that copper is required for the function of angiogenesis is false, then either dreams are our own brain's attempt to solve and resolve real-life problems or silence is a form of speech. The statement, writing is a mindset, a psychological view of life, does not hold.
|
It is the case that copper is required for the function of angiogenesis.
|
Copper causes the blue colour.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then (Either [1] or [2].). [SC1-1]
If (Not [0].), then (Not (Either [1] or [2].).).
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (If (Not [0].), then (Either [1] or [2].).). [SC2-2]
If [4], then (If (Not [0].), then (Either [1] or [2].).).
Therefore, If (Not [0].), then (Either [1] or [2].)..
[SC1-2]
Disjunctive Syllogism:
Either [5] or (Either [3] or [4].).
Not [5].
Therefore, Either [3] or [4]..
[SC2-2]
Disjunctive Syllogism:
Either [6] or (If [3], then (If (Not [0].), then (Either [1] or [2].).).).
Not [6].
Therefore, If [3], then (If (Not [0].), then (Either [1] or [2].).)..
|
{0: 'Copper is required for the function of angiogenesis.', 1: "Dreams are our own brain's attempt to solve and resolve real-life problems.", 2: 'Silence is a form of speech.', 3: 'Smoking reduces the levels of antioxidants and impairs blood circulation.', 4: 'Advertising attempts to affect attitudes.', 5: 'Some individuals choose to become pregnant and parent on their own.', 6: 'Writing is a mindset, a psychological view of life.'}
| 4 |
3,781 |
['It is a fact that either if elk are a herding species but the extent of herding can vary by sex and time of year, then beetles have compound eyes or soil drainage is a major factor controlling nitrate concentrations in streams.', "Whenever it is true that if elk are a herding species but the extent of herding can vary by sex and time of year, then beetles have compound eyes, 'either muscles respond to overload by growing bigger and stronger or stone birch belongs also to high density broadleaved species' is true.", "Either one or both of these statements are true: sulfur dioxide affects respiratory systems and aggravates cardiovascular disease, or the statement that 'either muscles respond to overload by growing bigger and stronger or stone birch belongs also to high density broadleaved species' is incorrect.", "If either eastern gorillas have vary diets or mahogany is one of Honduras' primary lumber exports, then the claim that sulfur dioxide affects respiratory systems and aggravates cardiovascular disease does not correspond with reality.", "It is a fact that either eastern gorillas have vary diets or mahogany is one of Honduras' primary lumber exports."]
|
It is a fact that either if elk are a herding species but the extent of herding can vary by sex and time of year, then beetles have compound eyes or soil drainage is a major factor controlling nitrate concentrations in streams. Whenever it is true that if elk are a herding species but the extent of herding can vary by sex and time of year, then beetles have compound eyes, 'either muscles respond to overload by growing bigger and stronger or stone birch belongs also to high density broadleaved species' is true. Either one or both of these statements are true: sulfur dioxide affects respiratory systems and aggravates cardiovascular disease, or the statement that 'either muscles respond to overload by growing bigger and stronger or stone birch belongs also to high density broadleaved species' is incorrect. If either eastern gorillas have vary diets or mahogany is one of Honduras' primary lumber exports, then the claim that sulfur dioxide affects respiratory systems and aggravates cardiovascular disease does not correspond with reality. It is a fact that either eastern gorillas have vary diets or mahogany is one of Honduras' primary lumber exports.
|
It is true that soil drainage is a major factor controlling nitrate concentrations in streams.
|
Soil drainage is another problem for vegetation or flowers.
|
Uncertain
|
Disjunctive Syllogism:
Either (If [1], then [2].) or [0].
Not (If [1], then [2].). [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (If [1], then [2].), then (Either [3] or [4].).
Not (Either [3] or [4].). [SC2-2]
Therefore, Not (If [1], then [2].)..
[SC2-2]
Disjunctive Syllogism:
Either [5] or (Not (Either [3] or [4].).).
Not [5]. [SC2-3]
Therefore, Not (Either [3] or [4].)..
[SC2-3]
Modus Ponens:
If (Either [6] or [7].), then (Not [5].).
Either [6] or [7].
Therefore, Not [5]..
|
{0: 'Soil drainage is a major factor controlling nitrate concentrations in streams.', 1: 'Elk are a herding species but the extent of herding can vary by sex and time of year.', 2: 'Beetles have compound eyes.', 3: 'Muscles respond to overload by growing bigger and stronger.', 4: 'Stone birch belongs also to high density broadleaved species.', 5: 'Sulfur dioxide affects respiratory systems and aggravates cardiovascular disease.', 6: 'Eastern gorillas have vary diets.', 7: "Mahogany is one of Honduras' primary lumber exports."}
| 4 |
3,499 |
['Assuming some homes have three or even four computers from which they can access the Internet, we know that behavior affects strategies.', "When the notion that 'if behavior affects strategies, then physics also seeks to construct models which can be used to explain or predict complex interactions' is untrue is true, it follows that steam vegetables to lock in nutrients.", "Whenever it is true that the notion that 'if behavior affects strategies, then physics also seeks to construct models which can be used to explain or predict complex interactions' is untrue, 'the statement that states steam vegetables to lock in nutrients is false' is true.", "At least one of two things is true: either mates have (part) brains or helium balloons are located in birthday parties, or the statement that 'physics also seeks to construct models which can be used to explain or predict complex interactions' is incorrect.", "The statement that 'either mates have (part) brains or helium balloons are located in birthday parties' is incorrect."]
|
Assuming some homes have three or even four computers from which they can access the Internet, we know that behavior affects strategies. When the notion that 'if behavior affects strategies, then physics also seeks to construct models which can be used to explain or predict complex interactions' is untrue is true, it follows that steam vegetables to lock in nutrients. Whenever it is true that the notion that 'if behavior affects strategies, then physics also seeks to construct models which can be used to explain or predict complex interactions' is untrue, 'the statement that states steam vegetables to lock in nutrients is false' is true. At least one of two things is true: either mates have (part) brains or helium balloons are located in birthday parties, or the statement that 'physics also seeks to construct models which can be used to explain or predict complex interactions' is incorrect. The statement that 'either mates have (part) brains or helium balloons are located in birthday parties' is incorrect.
|
Those that suggest some homes have three or even four computers from which they can access the Internet are wrong.
|
The claim that home is a surrogate for, and extension of, the self and the body is false.
|
Uncertain
|
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]. [SC2-2]
Therefore, Not [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [1], then [2].).), then [5].
If (Not (If [1], then [2].).), then (Not [5].).
Therefore, If [1], then [2]..
[SC2-2]
Disjunctive Syllogism:
Either (Either [3] or [4].) or (Not [2].).
Not (Either [3] or [4].).
Therefore, Not [2]..
|
{0: 'Some homes have three or even four computers from which they can access the Internet.', 1: 'Behavior affects strategies.', 2: 'Physics also seeks to construct models which can be used to explain or predict complex interactions.', 3: 'Mates have (part) brains.', 4: 'Helium balloons are located in birthday parties.', 5: 'Steam vegetables to lock in nutrients.'}
| 4 |
3,074 |
['Those that suggest fish wastes that enter irrigation canals become a supplementary fertilizer for crops are right.', 'We know that either if high rises are located in residential areas, then tails are organs or if we know that the claim that if fish wastes that enter irrigation canals become a supplementary fertilizer for crops, then the statement, either sables are rare almost everywhere or pagans believe that making distinctions is sin, does not hold is false, then either shrimp has hard shells or pasterns are strong, springy and almost perpendicular to the ground.', 'The claim that if high rises are located in residential areas, then tails are organs does not correspond with reality.', 'Should it be the case that the statement, if we know that the claim that if fish wastes that enter irrigation canals become a supplementary fertilizer for crops, then the statement, either sables are rare almost everywhere or pagans believe that making distinctions is sin, does not hold is false, then it is not the case that either shrimp has hard shells or pasterns are strong, springy and almost perpendicular to the ground, does not hold, it follows that life requires food.', 'When the statement, if we know that the claim that if fish wastes that enter irrigation canals become a supplementary fertilizer for crops, then the statement, either sables are rare almost everywhere or pagans believe that making distinctions is sin, does not hold is false, then it is not the case that either shrimp has hard shells or pasterns are strong, springy and almost perpendicular to the ground, does not hold is true, it follows that it is a common misconception that life requires food.']
|
Those that suggest fish wastes that enter irrigation canals become a supplementary fertilizer for crops are right. We know that either if high rises are located in residential areas, then tails are organs or if we know that the claim that if fish wastes that enter irrigation canals become a supplementary fertilizer for crops, then the statement, either sables are rare almost everywhere or pagans believe that making distinctions is sin, does not hold is false, then either shrimp has hard shells or pasterns are strong, springy and almost perpendicular to the ground. The claim that if high rises are located in residential areas, then tails are organs does not correspond with reality. Should it be the case that the statement, if we know that the claim that if fish wastes that enter irrigation canals become a supplementary fertilizer for crops, then the statement, either sables are rare almost everywhere or pagans believe that making distinctions is sin, does not hold is false, then it is not the case that either shrimp has hard shells or pasterns are strong, springy and almost perpendicular to the ground, does not hold, it follows that life requires food. When the statement, if we know that the claim that if fish wastes that enter irrigation canals become a supplementary fertilizer for crops, then the statement, either sables are rare almost everywhere or pagans believe that making distinctions is sin, does not hold is false, then it is not the case that either shrimp has hard shells or pasterns are strong, springy and almost perpendicular to the ground, does not hold is true, it follows that it is a common misconception that life requires food.
|
The statement, either sables are rare almost everywhere or pagans believe that making distinctions is sin, does not hold.
|
We know that at least one of two things is true: sables are rare almost everywhere, or pagans believe that making distinctions is sin.
|
FALSE
|
Modus Ponens:
If [2], then (Not (Either [0] or [1].).). [SC1-1]
[2]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [2], then (Not (Either [0] or [1].).).).), then (Either [3] or [4].). [SC1-2]
If (Not (If [2], then (Not (Either [0] or [1].).).).), then (Not (Either [3] or [4].).). [SC2-2]
Therefore, If [2], then (Not (Either [0] or [1].).)..
[SC1-2]
Disjunctive Syllogism:
Either (If [6], then [7].) or (If (Not (If [2], then (Not (Either [0] or [1].).).).), then (Either [3] or [4].).).
Not (If [6], then [7].).
Therefore, If (Not (If [2], then (Not (Either [0] or [1].).).).), then (Either [3] or [4].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Not (If [2], then (Not (Either [0] or [1].).).).), then (Not (Either [3] or [4].).).).), then [5].
If (Not (If (Not (If [2], then (Not (Either [0] or [1].).).).), then (Not (Either [3] or [4].).).).), then (Not [5].).
Therefore, If (Not (If [2], then (Not (Either [0] or [1].).).).), then (Not (Either [3] or [4].).)..
|
{0: 'Sables are rare almost everywhere.', 1: 'Pagans believe that making distinctions is sin.', 2: 'Fish wastes that enter irrigation canals become a supplementary fertilizer for crops.', 3: 'Shrimp has hard shells.', 4: 'Pasterns are strong, springy and almost perpendicular to the ground.', 5: 'Life requires food.', 6: 'High rises are located in residential areas.', 7: 'Tails are organs.'}
| 4 |
3,089 |
["So long as either weed control depends on good cultural practices and herbicides or lions have a wide habitat tolerance ranging from desert conditions to fairly dense bush, 'maine is the only state with just one syllable' is true.", 'Either one or both of these statements are true: a bohemian is a recusant, or either mouths have lips or either weed control depends on good cultural practices and herbicides or lions have a wide habitat tolerance ranging from desert conditions to fairly dense bush.', 'One may reasonably assume that if mouths have lips, then capital leases are essentially installment purchases of property.', 'When capital leases are essentially installment purchases of property is true, it follows that maine is the only state with just one syllable.', 'We know that either some distinctive rings surround eyes or it is a common misconception that a bohemian is a recusant.', 'Those that suggest some distinctive rings surround eyes are wrong.']
|
So long as either weed control depends on good cultural practices and herbicides or lions have a wide habitat tolerance ranging from desert conditions to fairly dense bush, 'maine is the only state with just one syllable' is true. Either one or both of these statements are true: a bohemian is a recusant, or either mouths have lips or either weed control depends on good cultural practices and herbicides or lions have a wide habitat tolerance ranging from desert conditions to fairly dense bush. One may reasonably assume that if mouths have lips, then capital leases are essentially installment purchases of property. When capital leases are essentially installment purchases of property is true, it follows that maine is the only state with just one syllable. We know that either some distinctive rings surround eyes or it is a common misconception that a bohemian is a recusant. Those that suggest some distinctive rings surround eyes are wrong.
|
The idea that maine is the only state with just one syllable is true.
|
Maine has the largest black bear population east of the Mississippi.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].). [SC1-1]
If [1], then [0]. [SC2-1]
If (Either [2] or [3].), then [0].
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [5] or (Either [1] or (Either [2] or [3].).).
Not [5]. [SC2-2]
Therefore, Either [1] or (Either [2] or [3].)..
[SC2-2]
Disjunctive Syllogism:
Either [6] or (Not [5].).
Not [6].
Therefore, Not [5]..
[SC2-1]
Hypothetical Syllogism:
If [1], then [4].
If [4], then [0].
Therefore, If [1], then [0]..
|
{0: 'Maine is the only state with just one syllable.', 1: 'Mouths have lips.', 2: 'Weed control depends on good cultural practices and herbicides.', 3: 'Lions have a wide habitat tolerance ranging from desert conditions to fairly dense bush.', 4: 'Capital leases are essentially installment purchases of property.', 5: 'A bohemian is a recusant.', 6: 'Some distinctive rings surround eyes.'}
| 4 |
3,609 |
['We know that either cholesterol is a fat-like substance that is needed to build cells and manufacture hormones or hammers are basic tools in many trades .', 'At least one of two things is true: truth is Love and Light, or if cholesterol is a fat-like substance that is needed to build cells and manufacture hormones, then museums are ideal settings to study children s socialization into science.', "The statement that 'truth is Love and Light' is incorrect.", 'When either diffusion only works in a very small organism or circus is disturbances is true, it follows that if hammers are basic tools in many trades , then museums are ideal settings to study children s socialization into science.', 'When light rain can last for days is true, it follows that if hammers are basic tools in many trades , then museums are ideal settings to study children s socialization into science.', 'It is rational to believe that either cloning is the artificial reproduction of an organism that is an exact duplicate of the original or royal fern likes a moist, somewhat water retentive soil.', 'Provided that cloning is the artificial reproduction of an organism that is an exact duplicate of the original, we know that either either diffusion only works in a very small organism or circus is disturbances or light rain can last for days.', "So long as royal fern likes a moist, somewhat water retentive soil, 'either either diffusion only works in a very small organism or circus is disturbances or light rain can last for days' is true."]
|
We know that either cholesterol is a fat-like substance that is needed to build cells and manufacture hormones or hammers are basic tools in many trades . At least one of two things is true: truth is Love and Light, or if cholesterol is a fat-like substance that is needed to build cells and manufacture hormones, then museums are ideal settings to study children s socialization into science. The statement that 'truth is Love and Light' is incorrect. When either diffusion only works in a very small organism or circus is disturbances is true, it follows that if hammers are basic tools in many trades , then museums are ideal settings to study children s socialization into science. When light rain can last for days is true, it follows that if hammers are basic tools in many trades , then museums are ideal settings to study children s socialization into science. It is rational to believe that either cloning is the artificial reproduction of an organism that is an exact duplicate of the original or royal fern likes a moist, somewhat water retentive soil. Provided that cloning is the artificial reproduction of an organism that is an exact duplicate of the original, we know that either either diffusion only works in a very small organism or circus is disturbances or light rain can last for days. So long as royal fern likes a moist, somewhat water retentive soil, 'either either diffusion only works in a very small organism or circus is disturbances or light rain can last for days' is true.
|
It is the case that museums are ideal settings to study children s socialization into science.
|
It is the case that museums are ideal settings to study children s socialization into science.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [6] or (If [1], then [0].).
Not [6].
Therefore, If [1], then [0]..
[SC3-1]
Disjunction Elimination:
Either (Either [3] or [4].) or [5]. [SC1-2]
If (Either [3] or [4].), then (If [2], then [0].).
If [5], then (If [2], then [0].).
Therefore, If [2], then [0]..
[SC1-2]
Disjunction Elimination:
Either [7] or [8].
If [7], then (Either (Either [3] or [4].) or [5].).
If [8], then (Either (Either [3] or [4].) or [5].).
Therefore, Either (Either [3] or [4].) or [5]..
|
{0: 'Museums are ideal settings to study children s socialization into science.', 1: 'Cholesterol is a fat-like substance that is needed to build cells and manufacture hormones.', 2: 'Hammers are basic tools in many trades .', 3: 'Diffusion only works in a very small organism.', 4: 'Circus is disturbances.', 5: 'Light rain can last for days.', 6: 'Truth is Love and Light.', 7: 'Cloning is the artificial reproduction of an organism that is an exact duplicate of the original.', 8: 'Royal fern likes a moist, somewhat water retentive soil.'}
| 4 |
3,000 |
['The statement, rashes are also common at time of onset, does not hold.', 'On the condition that those that suggest if it is a common misconception that if the statement, invasion isa penetration, does not hold, then rashes are also common at time of onset, then if a synopsis is a summary, then cognitive models try to represent the robot, the world, and how they interact are wrong, it is definitely the case that anchovies are fish.', "If those that suggest if it is a common misconception that if the statement, invasion isa penetration, does not hold, then rashes are also common at time of onset, then if a synopsis is a summary, then cognitive models try to represent the robot, the world, and how they interact are wrong, then the statement that 'anchovies are fish' is incorrect.", "One may reasonably assume that if some people mistakenly believe that if it is a common misconception that if the statement, invasion isa penetration, does not hold, then rashes are also common at time of onset, then the statement that 'if a synopsis is a summary, then cognitive models try to represent the robot, the world, and how they interact' is incorrect, then animals take in energy by eating food.", 'The statement, animals take in energy by eating food, does not hold.']
|
The statement, rashes are also common at time of onset, does not hold. On the condition that those that suggest if it is a common misconception that if the statement, invasion isa penetration, does not hold, then rashes are also common at time of onset, then if a synopsis is a summary, then cognitive models try to represent the robot, the world, and how they interact are wrong, it is definitely the case that anchovies are fish. If those that suggest if it is a common misconception that if the statement, invasion isa penetration, does not hold, then rashes are also common at time of onset, then if a synopsis is a summary, then cognitive models try to represent the robot, the world, and how they interact are wrong, then the statement that 'anchovies are fish' is incorrect. One may reasonably assume that if some people mistakenly believe that if it is a common misconception that if the statement, invasion isa penetration, does not hold, then rashes are also common at time of onset, then the statement that 'if a synopsis is a summary, then cognitive models try to represent the robot, the world, and how they interact' is incorrect, then animals take in energy by eating food. The statement, animals take in energy by eating food, does not hold.
|
The claim that invasion isa penetration is true.
|
The claim that invasion isa penetration is true.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then [1].).), then (If [2], then [3].). [SC1-2]
If (Not (If (Not [0].), then [1].).), then (Not (If [2], then [3].).). [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not [0].), then [1].).), then (If [2], then [3].).).), then [4].
If (Not (If (Not (If (Not [0].), then [1].).), then (If [2], then [3].).).), then (Not [4].).
Therefore, If (Not (If (Not [0].), then [1].).), then (If [2], then [3].)..
[SC2-2]
Modus Tonens:
If (Not (If (Not (If (Not [0].), then [1].).), then (Not (If [2], then [3].).).).), then [5].
Not [5].
Therefore, If (Not (If (Not [0].), then [1].).), then (Not (If [2], then [3].).)..
|
{0: 'Invasion isa penetration.', 1: 'Rashes are also common at time of onset.', 2: 'A synopsis is a summary.', 3: 'Cognitive models try to represent the robot, the world, and how they interact.', 4: 'Anchovies are fish.', 5: 'Animals take in energy by eating food.'}
| 4 |
3,392 |
['At least one of two things is true: some people kill bats, or either accounting is the process of measuring the resources a user has consumed or some african parrots have years.', "Given that some people kill bats, it can be inferred that if the statement 'phenomena cause displacement' can be considered false, then curly coats have abundant, fine hair that is, thick, dense, of uniform length, forming even curls.", "On the condition that either accounting is the process of measuring the resources a user has consumed or some african parrots have years, it is definitely the case that if the statement 'phenomena cause displacement' can be considered false, then curly coats have abundant, fine hair that is, thick, dense, of uniform length, forming even curls.", 'We can assume that hanumans have (part) sections.', 'Either one or both of these statements are true: sunflower seeds sprout overnight and alfalfa sprouts take only a few days, or if some alligators eat snakes, then some plants just take longer to wake up from their naps.', "When sunflower seeds sprout overnight and alfalfa sprouts take only a few days is true, it follows that if hanumans have (part) sections, then if the statement 'phenomena cause displacement' can be considered false, then the claim that curly coats have abundant, fine hair that is, thick, dense, of uniform length, forming even curls does not correspond with reality.", "Assuming if some alligators eat snakes, then some plants just take longer to wake up from their naps, we know that if hanumans have (part) sections, then if the statement 'phenomena cause displacement' can be considered false, then the claim that curly coats have abundant, fine hair that is, thick, dense, of uniform length, forming even curls does not correspond with reality."]
|
At least one of two things is true: some people kill bats, or either accounting is the process of measuring the resources a user has consumed or some african parrots have years. Given that some people kill bats, it can be inferred that if the statement 'phenomena cause displacement' can be considered false, then curly coats have abundant, fine hair that is, thick, dense, of uniform length, forming even curls. On the condition that either accounting is the process of measuring the resources a user has consumed or some african parrots have years, it is definitely the case that if the statement 'phenomena cause displacement' can be considered false, then curly coats have abundant, fine hair that is, thick, dense, of uniform length, forming even curls. We can assume that hanumans have (part) sections. Either one or both of these statements are true: sunflower seeds sprout overnight and alfalfa sprouts take only a few days, or if some alligators eat snakes, then some plants just take longer to wake up from their naps. When sunflower seeds sprout overnight and alfalfa sprouts take only a few days is true, it follows that if hanumans have (part) sections, then if the statement 'phenomena cause displacement' can be considered false, then the claim that curly coats have abundant, fine hair that is, thick, dense, of uniform length, forming even curls does not correspond with reality. Assuming if some alligators eat snakes, then some plants just take longer to wake up from their naps, we know that if hanumans have (part) sections, then if the statement 'phenomena cause displacement' can be considered false, then the claim that curly coats have abundant, fine hair that is, thick, dense, of uniform length, forming even curls does not correspond with reality.
|
The claim that phenomena cause displacement holds true.
|
The claim that phenomena cause displacement has no merit.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [2] or (Either [3] or [4].).
If [2], then (If (Not [0].), then [1].).
If (Either [3] or [4].), then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Modus Ponens:
If [5], then (If (Not [0].), then (Not [1].).). [SC1-2]
[5]
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Disjunction Elimination:
Either [6] or (If [7], then [8].).
If [6], then (If [5], then (If (Not [0].), then (Not [1].).).).
If (If [7], then [8].), then (If [5], then (If (Not [0].), then (Not [1].).).).
Therefore, If [5], then (If (Not [0].), then (Not [1].).)..
|
{0: 'Phenomena cause displacement.', 1: 'Curly coats have abundant, fine hair that is, thick, dense, of uniform length, forming even curls.', 2: 'Some people kill bats.', 3: 'Accounting is the process of measuring the resources a user has consumed.', 4: 'Some african parrots have years.', 5: 'Hanumans have (part) sections.', 6: 'Sunflower seeds sprout overnight and alfalfa sprouts take only a few days.', 7: 'Some alligators eat snakes.', 8: 'Some plants just take longer to wake up from their naps.'}
| 4 |
3,476 |
['It is a fact that either sunscreen chemicals protect the skin against ultraviolet radiation or laptops are particularly vulnerable to information theft because of their mobility.', "Whenever it is true that sunscreen chemicals protect the skin against ultraviolet radiation, 'either if potatoes are more prone to common scab when grown in high pH soils, then colds are upper respiratory viral infections or most camels have skin' is true.", 'Provided that laptops are particularly vulnerable to information theft because of their mobility, we know that either if potatoes are more prone to common scab when grown in high pH soils, then colds are upper respiratory viral infections or most camels have skin.', 'It is a fact that either experiments reflect differences or if if potatoes are more prone to common scab when grown in high pH soils, then colds are upper respiratory viral infections, then tin tellurides are potentially a useful class of compound for which reactivity studies are rare.', 'Those that suggest experiments reflect differences are wrong.', 'It is rational to believe that either highs are air mass or if most camels have skin, then tin tellurides are potentially a useful class of compound for which reactivity studies are rare.', 'The claim that highs are air mass is false.']
|
It is a fact that either sunscreen chemicals protect the skin against ultraviolet radiation or laptops are particularly vulnerable to information theft because of their mobility. Whenever it is true that sunscreen chemicals protect the skin against ultraviolet radiation, 'either if potatoes are more prone to common scab when grown in high pH soils, then colds are upper respiratory viral infections or most camels have skin' is true. Provided that laptops are particularly vulnerable to information theft because of their mobility, we know that either if potatoes are more prone to common scab when grown in high pH soils, then colds are upper respiratory viral infections or most camels have skin. It is a fact that either experiments reflect differences or if if potatoes are more prone to common scab when grown in high pH soils, then colds are upper respiratory viral infections, then tin tellurides are potentially a useful class of compound for which reactivity studies are rare. Those that suggest experiments reflect differences are wrong. It is rational to believe that either highs are air mass or if most camels have skin, then tin tellurides are potentially a useful class of compound for which reactivity studies are rare. The claim that highs are air mass is false.
|
It is fair to say that tin tellurides are potentially a useful class of compound for which reactivity studies are rare.
|
It is a common misconception that tin tellurides are potentially a useful class of compound for which reactivity studies are rare.
|
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]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [5] or [6].
If [5], then (Either (If [1], then [2].) or [3].).
If [6], then (Either (If [1], then [2].) or [3].).
Therefore, Either (If [1], then [2].) or [3]..
[SC2-1]
Disjunctive Syllogism:
Either [7] or (If (If [1], then [2].), then [0].).
Not [7].
Therefore, If (If [1], then [2].), then [0]..
[SC3-1]
Disjunctive Syllogism:
Either [4] or (If [3], then [0].).
Not [4].
Therefore, If [3], then [0]..
|
{0: 'Tin tellurides are potentially a useful class of compound for which reactivity studies are rare.', 1: 'Potatoes are more prone to common scab when grown in high pH soils.', 2: 'Colds are upper respiratory viral infections.', 3: 'Most camels have skin.', 4: 'Highs are air mass.', 5: 'Sunscreen chemicals protect the skin against ultraviolet radiation.', 6: 'Laptops are particularly vulnerable to information theft because of their mobility.', 7: 'Experiments reflect differences.'}
| 4 |
3,799 |
['There is good reason to believe that either normal moles develop in childhood and early adulthood or some ornamental grasses get extremely tall.', "Either social mammals recognize each other as individuals, appreciating each other's feelings or the statement, normal moles develop in childhood and early adulthood, does not hold.", "Given that either pupae look like little balls in the water or a leash is a constraint, it can be inferred that it is not the case that social mammals recognize each other as individuals, appreciating each other's feelings.", "One may reasonably assume that if some salmon migrate hundreds of miles up river, then it is not the case that social mammals recognize each other as individuals, appreciating each other's feelings.", 'One may reasonably assume that if the statement that states either either pupae look like little balls in the water or a leash is a constraint or some salmon migrate hundreds of miles up river is false, then blubber has (part) chemical chain.', 'Assuming the statement that states either either pupae look like little balls in the water or a leash is a constraint or some salmon migrate hundreds of miles up river is false, we know that the claim that blubber has (part) chemical chain is false.']
|
There is good reason to believe that either normal moles develop in childhood and early adulthood or some ornamental grasses get extremely tall. Either social mammals recognize each other as individuals, appreciating each other's feelings or the statement, normal moles develop in childhood and early adulthood, does not hold. Given that either pupae look like little balls in the water or a leash is a constraint, it can be inferred that it is not the case that social mammals recognize each other as individuals, appreciating each other's feelings. One may reasonably assume that if some salmon migrate hundreds of miles up river, then it is not the case that social mammals recognize each other as individuals, appreciating each other's feelings. One may reasonably assume that if the statement that states either either pupae look like little balls in the water or a leash is a constraint or some salmon migrate hundreds of miles up river is false, then blubber has (part) chemical chain. Assuming the statement that states either either pupae look like little balls in the water or a leash is a constraint or some salmon migrate hundreds of miles up river is false, we know that the claim that blubber has (part) chemical chain is false.
|
The statement that states some ornamental grasses get extremely tall is right.
|
The claim that some ornamental grasses get extremely tall 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].).
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Disjunction Elimination:
Either (Either [3] or [4].) or [5]. [SC1-3]
If (Either [3] or [4].), then (Not [2].).
If [5], then (Not [2].).
Therefore, Not [2]..
[SC1-3]
Reductio Ad Absurdum:
If (Not (Either (Either [3] or [4].) or [5].).), then [6].
If (Not (Either (Either [3] or [4].) or [5].).), then (Not [6].).
Therefore, Either (Either [3] or [4].) or [5]..
|
{0: 'Some ornamental grasses get extremely tall.', 1: 'Normal moles develop in childhood and early adulthood.', 2: "Social mammals recognize each other as individuals, appreciating each other's feelings.", 3: 'Pupae look like little balls in the water.', 4: 'A leash is a constraint.', 5: 'Some salmon migrate hundreds of miles up river.', 6: 'Blubber has (part) chemical chain.'}
| 4 |
3,519 |
["The statement 'if air is passed through the molten metal, then jewelry is the preferred currency of most pawn brokers' can be considered false.", "If the notion that 'either if air is passed through the molten metal, then jewelry is the preferred currency of most pawn brokers or horses can withstand cold weather rather well if dry, in good body condition and adequately fed' is untrue, then prayer is the greatest spiritual asset in the world.", 'We know that at least one of two things is true: education is an ornament in prosperity and a refuge in adversity, or pools are excavation.', "Should it be the case that pools are excavation, it follows that if the notion that 'either if air is passed through the molten metal, then jewelry is the preferred currency of most pawn brokers or horses can withstand cold weather rather well if dry, in good body condition and adequately fed' is untrue, then some people mistakenly believe that prayer is the greatest spiritual asset in the world.", 'Should it be the case that education is an ornament in prosperity and a refuge in adversity, it follows that grubs feed on grass roots, adults feed on a variety of plants.', "If grubs feed on grass roots, adults feed on a variety of plants, then if the notion that 'either if air is passed through the molten metal, then jewelry is the preferred currency of most pawn brokers or horses can withstand cold weather rather well if dry, in good body condition and adequately fed' is untrue, then some people mistakenly believe that prayer is the greatest spiritual asset in the world."]
|
The statement 'if air is passed through the molten metal, then jewelry is the preferred currency of most pawn brokers' can be considered false. If the notion that 'either if air is passed through the molten metal, then jewelry is the preferred currency of most pawn brokers or horses can withstand cold weather rather well if dry, in good body condition and adequately fed' is untrue, then prayer is the greatest spiritual asset in the world. We know that at least one of two things is true: education is an ornament in prosperity and a refuge in adversity, or pools are excavation. Should it be the case that pools are excavation, it follows that if the notion that 'either if air is passed through the molten metal, then jewelry is the preferred currency of most pawn brokers or horses can withstand cold weather rather well if dry, in good body condition and adequately fed' is untrue, then some people mistakenly believe that prayer is the greatest spiritual asset in the world. Should it be the case that education is an ornament in prosperity and a refuge in adversity, it follows that grubs feed on grass roots, adults feed on a variety of plants. If grubs feed on grass roots, adults feed on a variety of plants, then if the notion that 'either if air is passed through the molten metal, then jewelry is the preferred currency of most pawn brokers or horses can withstand cold weather rather well if dry, in good body condition and adequately fed' is untrue, then some people mistakenly believe that prayer is the greatest spiritual asset in the world.
|
It is rational to agree that horses can withstand cold weather rather well if dry, in good body condition and adequately fed.
|
It is rational to agree that horses can withstand cold weather rather well if dry, in good body condition and adequately fed.
|
TRUE
|
Disjunctive Syllogism:
Either (If [1], then [2].) or [0]. [SC1-1]
Not (If [1], then [2].).
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either (If [1], then [2].) or [0].).), then [3].
If (Not (Either (If [1], then [2].) or [0].).), then (Not [3].). [SC2-2]
Therefore, Either (If [1], then [2].) or [0]..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not (Either (If [1], then [2].) or [0].).), then (Not [3].).). [SC2-3]
If [5], then (If (Not (Either (If [1], then [2].) or [0].).), then (Not [3].).).
Therefore, If (Not (Either (If [1], then [2].) or [0].).), then (Not [3].)..
[SC2-3]
Hypothetical Syllogism:
If [4], then [6].
If [6], then (If (Not (Either (If [1], then [2].) or [0].).), then (Not [3].).).
Therefore, If [4], then (If (Not (Either (If [1], then [2].) or [0].).), then (Not [3].).)..
|
{0: 'Horses can withstand cold weather rather well if dry, in good body condition and adequately fed.', 1: 'Air is passed through the molten metal.', 2: 'Jewelry is the preferred currency of most pawn brokers.', 3: 'Prayer is the greatest spiritual asset in the world.', 4: 'Education is an ornament in prosperity and a refuge in adversity.', 5: 'Pools are excavation.', 6: 'Grubs feed on grass roots, adults feed on a variety of plants.'}
| 4 |
3,107 |
['Either one or both of these statements are true: if most allergies require attention, then nitrate concentration is highest in young plants and decreases as the plant matures, or either juniper has (part) plasma membranes or accumulation is net incomes.', 'One may reasonably assume that if if most allergies require attention, then nitrate concentration is highest in young plants and decreases as the plant matures, then chromosomes are the structures that hold our genes.', "One may reasonably assume that if either juniper has (part) plasma membranes or accumulation is net incomes, then temperate grasslands are the most threatened of the world's ecosystems.", 'Provided that wood ducks have a phenomenal ability to return to the same breeding area year after year, we know that if chromosomes are the structures that hold our genes, then the claim that if whales have lungs and breathe air, then a floater is insurance has no merit.', 'Many people rightly believe that wood ducks have a phenomenal ability to return to the same breeding area year after year.', "When food is crushed between hard spines on the tongue and the roof of the mouth is true, it follows that if temperate grasslands are the most threatened of the world's ecosystems, then the claim that if whales have lungs and breathe air, then a floater is insurance has no merit.", 'It is rational to agree that food is crushed between hard spines on the tongue and the roof of the mouth.']
|
Either one or both of these statements are true: if most allergies require attention, then nitrate concentration is highest in young plants and decreases as the plant matures, or either juniper has (part) plasma membranes or accumulation is net incomes. One may reasonably assume that if if most allergies require attention, then nitrate concentration is highest in young plants and decreases as the plant matures, then chromosomes are the structures that hold our genes. One may reasonably assume that if either juniper has (part) plasma membranes or accumulation is net incomes, then temperate grasslands are the most threatened of the world's ecosystems. Provided that wood ducks have a phenomenal ability to return to the same breeding area year after year, we know that if chromosomes are the structures that hold our genes, then the claim that if whales have lungs and breathe air, then a floater is insurance has no merit. Many people rightly believe that wood ducks have a phenomenal ability to return to the same breeding area year after year. When food is crushed between hard spines on the tongue and the roof of the mouth is true, it follows that if temperate grasslands are the most threatened of the world's ecosystems, then the claim that if whales have lungs and breathe air, then a floater is insurance has no merit. It is rational to agree that food is crushed between hard spines on the tongue and the roof of the mouth.
|
The claim that if whales have lungs and breathe air, then a floater is insurance has no merit.
|
It is a common misconception that whales are still most densely concentrated on the southern half of the bank.
|
Uncertain
|
Disjunction Elimination:
Either [2] or [3]. [SC1-1]
If [2], then (Not (If [0], then [1].).). [SC2-1]
If [3], then (Not (If [0], then [1].).). [SC3-1]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Constructive Dilemma:
Either (If [5], then [6].) or (Either [7] or [8].).
If (If [5], then [6].), then [2].
If (Either [7] or [8].), then [3].
Therefore, Either [2] or [3]..
[SC2-1]
Modus Ponens:
If [9], then (If [2], then (Not (If [0], then [1].).).).
[9]
Therefore, If [2], then (Not (If [0], then [1].).)..
[SC3-1]
Modus Ponens:
If [4], then (If [3], then (Not (If [0], then [1].).).).
[4]
Therefore, If [3], then (Not (If [0], then [1].).)..
|
{0: 'Whales have lungs and breathe air.', 1: 'A floater is insurance.', 2: 'Chromosomes are the structures that hold our genes.', 3: "Temperate grasslands are the most threatened of the world's ecosystems.", 4: 'Food is crushed between hard spines on the tongue and the roof of the mouth.', 5: 'Most allergies require attention.', 6: 'Nitrate concentration is highest in young plants and decreases as the plant matures.', 7: 'Juniper has (part) plasma membranes.', 8: 'Accumulation is net incomes.', 9: 'Wood ducks have a phenomenal ability to return to the same breeding area year after year.'}
| 4 |
3,708 |
['Assuming money is usually the magnet that draws people into criminal activity, we know that eyes sense light.', 'When religion has an important role to play in human rights education is true, it follows that if we know that the claim that crude oil produces many byproducts important to our lives is false, then it is not true that eyes sense light.', "The statement 'religion has an important role to play in human rights education' is true.", "So long as either friends reveal identities or orchid isa angiosperm, 'if we know that the claim that crude oil produces many byproducts important to our lives is false, then money is usually the magnet that draws people into criminal activity' is true.", 'We know that at least one of two things is true: friends reveal identities, or orchid isa angiosperm.']
|
Assuming money is usually the magnet that draws people into criminal activity, we know that eyes sense light. When religion has an important role to play in human rights education is true, it follows that if we know that the claim that crude oil produces many byproducts important to our lives is false, then it is not true that eyes sense light. The statement 'religion has an important role to play in human rights education' is true. So long as either friends reveal identities or orchid isa angiosperm, 'if we know that the claim that crude oil produces many byproducts important to our lives is false, then money is usually the magnet that draws people into criminal activity' is true. We know that at least one of two things is true: friends reveal identities, or orchid isa angiosperm.
|
The claim that crude oil produces many byproducts important to our lives is true.
|
We know that the claim that crude oil produces many byproducts important to our lives is false.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Hypothetical Syllogism:
If (Not [0].), then [2]. [SC1-2]
If [2], then [1].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Modus Ponens:
If (Either [4] or [5].), then (If (Not [0].), then [2].).
Either [4] or [5].
Therefore, If (Not [0].), then [2]..
[SC2-1]
Modus Ponens:
If [3], then (If (Not [0].), then (Not [1].).).
[3]
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Crude oil produces many byproducts important to our lives.', 1: 'Eyes sense light.', 2: 'Money is usually the magnet that draws people into criminal activity.', 3: 'Religion has an important role to play in human rights education.', 4: 'Friends reveal identities.', 5: 'Orchid isa angiosperm.'}
| 4 |
3,634 |
['There is good reason to believe that either language is a social act or if the claim that vermin have (part) corpi does not correspond with reality, then ozone is extremely reactive chemically and is very poisonous.', "The statement that 'language is a social act' is incorrect.", 'If cats has-part muscles, then if the claim that vermin have (part) corpi does not correspond with reality, then the statement that states ozone is extremely reactive chemically and is very poisonous is false.', "Whenever it is true that the statement that states cats has-part muscles is false, 'all protists do, they are all eukaryotic' is true.", 'Given that the statement that states cats has-part muscles is false, it can be inferred that the statement that states all protists do, they are all eukaryotic is false.']
|
There is good reason to believe that either language is a social act or if the claim that vermin have (part) corpi does not correspond with reality, then ozone is extremely reactive chemically and is very poisonous. The statement that 'language is a social act' is incorrect. If cats has-part muscles, then if the claim that vermin have (part) corpi does not correspond with reality, then the statement that states ozone is extremely reactive chemically and is very poisonous is false. Whenever it is true that the statement that states cats has-part muscles is false, 'all protists do, they are all eukaryotic' is true. Given that the statement that states cats has-part muscles is false, it can be inferred that the statement that states all protists do, they are all eukaryotic is false.
|
It is reasonable to believe that vermin have (part) corpi.
|
It is reasonable to believe that vermin have (part) corpi.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If (Not [0].), then [1].).
Not [3].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Modus Ponens:
If [2], then (If (Not [0].), then (Not [1].).).
[2] [SC2-2]
Therefore, If (Not [0].), then (Not [1].)..
[SC2-2]
Reductio Ad Absurdum:
If (Not [2].), then [4].
If (Not [2].), then (Not [4].).
Therefore, [2].
|
{0: 'Vermin have (part) corpi.', 1: 'Ozone is extremely reactive chemically and is very poisonous.', 2: 'Cats has-part muscles.', 3: 'Language is a social act.', 4: 'All protists do, they are all eukaryotic.'}
| 4 |
3,223 |
['Given that hearts are games, it can be inferred that some people mistakenly believe that greens are one of the most regular nesters, nesting every other year.', 'Once we know vicious viruses emerge when they remain latent for a long period of time, we also know that if hearts are games, then greens are one of the most regular nesters, nesting every other year.', 'Either either magnetic materials are attracted to magnets or official isa worker or pressure solution is also an important way to form cleavage .', 'Given that either magnetic materials are attracted to magnets or official isa worker, it can be inferred that vicious viruses emerge when they remain latent for a long period of time.', 'On the condition that some people mistakenly believe that if pressure solution is also an important way to form cleavage , then vicious viruses emerge when they remain latent for a long period of time, it is definitely the case that some voltage powers small electrical devices.', 'If some people mistakenly believe that if pressure solution is also an important way to form cleavage , then vicious viruses emerge when they remain latent for a long period of time, then the claim that some voltage powers small electrical devices is false.']
|
Given that hearts are games, it can be inferred that some people mistakenly believe that greens are one of the most regular nesters, nesting every other year. Once we know vicious viruses emerge when they remain latent for a long period of time, we also know that if hearts are games, then greens are one of the most regular nesters, nesting every other year. Either either magnetic materials are attracted to magnets or official isa worker or pressure solution is also an important way to form cleavage . Given that either magnetic materials are attracted to magnets or official isa worker, it can be inferred that vicious viruses emerge when they remain latent for a long period of time. On the condition that some people mistakenly believe that if pressure solution is also an important way to form cleavage , then vicious viruses emerge when they remain latent for a long period of time, it is definitely the case that some voltage powers small electrical devices. If some people mistakenly believe that if pressure solution is also an important way to form cleavage , then vicious viruses emerge when they remain latent for a long period of time, then the claim that some voltage powers small electrical devices is false.
|
The claim that hearts are games is false.
|
The statement, most hearts have chambers, does not hold.
|
Uncertain
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].).
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [2], then (If [0], then [1].).
[2] [SC2-2]
Therefore, If [0], then [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]
Reductio Ad Absurdum:
If (Not (If [5], then [2].).), then [6].
If (Not (If [5], then [2].).), then (Not [6].).
Therefore, If [5], then [2]..
|
{0: 'Hearts are games.', 1: 'Greens are one of the most regular nesters, nesting every other year.', 2: 'Vicious viruses emerge when they remain latent for a long period of time.', 3: 'Magnetic materials are attracted to magnets.', 4: 'Official isa worker.', 5: 'Pressure solution is also an important way to form cleavage .', 6: 'Some voltage powers small electrical devices.'}
| 4 |
3,327 |
["If the statement 'if some people mistakenly believe that spontaneous rips appear in the skin, and hemorrhagic blood pours from the rips, then air flows through the lung in the same direction on inspiration and expiration' can be considered false, then calories are the same at any hour of the day.", 'The claim that calories are the same at any hour of the day is false.', 'Assuming air flows through the lung in the same direction on inspiration and expiration, we know that escalators are located in motion.', 'When escalators are located in motion is true, it follows that strategic planning is, of course, a form of planning.', "The statement 'strategic planning is, of course, a form of planning' can be considered false."]
|
If the statement 'if some people mistakenly believe that spontaneous rips appear in the skin, and hemorrhagic blood pours from the rips, then air flows through the lung in the same direction on inspiration and expiration' can be considered false, then calories are the same at any hour of the day. The claim that calories are the same at any hour of the day is false. Assuming air flows through the lung in the same direction on inspiration and expiration, we know that escalators are located in motion. When escalators are located in motion is true, it follows that strategic planning is, of course, a form of planning. The statement 'strategic planning is, of course, a form of planning' can be considered false.
|
It is the case that spontaneous rips appear in the skin, and hemorrhagic blood pours from the rips.
|
Retention refers to the number of students returning from the previous year.
|
Uncertain
|
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]
Modus Tonens:
If [1], then [2].
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Modus Tonens:
If [2], then [4].
Not [4].
Therefore, Not [2]..
|
{0: 'Spontaneous rips appear in the skin, and hemorrhagic blood pours from the rips.', 1: 'Air flows through the lung in the same direction on inspiration and expiration.', 2: 'Escalators are located in motion.', 3: 'Calories are the same at any hour of the day.', 4: 'Strategic planning is, of course, a form of planning.'}
| 4 |
3,102 |
['Either one or both of these statements are true: if stains are often times specific to bind with only certain structures of the cell, then some dust contains fiber, or caterpillars spend the day in shelters of rolled or tied leaves and feed on leaves at night.', 'When if stains are often times specific to bind with only certain structures of the cell, then some dust contains fiber is true, it follows that if platypuses construct burrows, then skeletal calcium is comprised mainly of calcium phosphate with some calcium carbonate.', 'One may reasonably assume that if constitutionalists traditionally shun the use of violence and terror as a tactic to further a cause, then if platypuses construct burrows, then it is not the case that skeletal calcium is comprised mainly of calcium phosphate with some calcium carbonate.', 'The statement that states constitutionalists traditionally shun the use of violence and terror as a tactic to further a cause is right.', 'It is a fact that either some fish incorporate plants into the nest and some are all bubbles or patterns are data values that can be combined in various ways to form other patterns.', 'Should it be the case that some fish incorporate plants into the nest and some are all bubbles, it follows that if caterpillars spend the day in shelters of rolled or tied leaves and feed on leaves at night, then if platypuses construct burrows, then skeletal calcium is comprised mainly of calcium phosphate with some calcium carbonate.', 'On the condition that patterns are data values that can be combined in various ways to form other patterns, it is definitely the case that if caterpillars spend the day in shelters of rolled or tied leaves and feed on leaves at night, then if platypuses construct burrows, then skeletal calcium is comprised mainly of calcium phosphate with some calcium carbonate.']
|
Either one or both of these statements are true: if stains are often times specific to bind with only certain structures of the cell, then some dust contains fiber, or caterpillars spend the day in shelters of rolled or tied leaves and feed on leaves at night. When if stains are often times specific to bind with only certain structures of the cell, then some dust contains fiber is true, it follows that if platypuses construct burrows, then skeletal calcium is comprised mainly of calcium phosphate with some calcium carbonate. One may reasonably assume that if constitutionalists traditionally shun the use of violence and terror as a tactic to further a cause, then if platypuses construct burrows, then it is not the case that skeletal calcium is comprised mainly of calcium phosphate with some calcium carbonate. The statement that states constitutionalists traditionally shun the use of violence and terror as a tactic to further a cause is right. It is a fact that either some fish incorporate plants into the nest and some are all bubbles or patterns are data values that can be combined in various ways to form other patterns. Should it be the case that some fish incorporate plants into the nest and some are all bubbles, it follows that if caterpillars spend the day in shelters of rolled or tied leaves and feed on leaves at night, then if platypuses construct burrows, then skeletal calcium is comprised mainly of calcium phosphate with some calcium carbonate. On the condition that patterns are data values that can be combined in various ways to form other patterns, it is definitely the case that if caterpillars spend the day in shelters of rolled or tied leaves and feed on leaves at night, then if platypuses construct burrows, then skeletal calcium is comprised mainly of calcium phosphate with some calcium carbonate.
|
The statement that 'platypuses construct burrows' is incorrect.
|
It is true that platypuses construct burrows.
|
FALSE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either (If [2], then [3].) or [4].
If (If [2], then [3].), then (If [0], then [1].).
If [4], then (If [0], then [1].). [SC3-2]
Therefore, If [0], then [1]..
[SC3-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If [4], then (If [0], then [1].).).
If [7], then (If [4], then (If [0], then [1].).).
Therefore, If [4], then (If [0], then [1].)..
[SC2-1]
Modus Ponens:
If [5], then (If [0], then (Not [1].).).
[5]
Therefore, If [0], then (Not [1].)..
|
{0: 'Platypuses construct burrows.', 1: 'Skeletal calcium is comprised mainly of calcium phosphate with some calcium carbonate.', 2: 'Stains are often times specific to bind with only certain structures of the cell.', 3: 'Some dust contains fiber.', 4: 'Caterpillars spend the day in shelters of rolled or tied leaves and feed on leaves at night.', 5: 'Constitutionalists traditionally shun the use of violence and terror as a tactic to further a cause.', 6: 'Some fish incorporate plants into the nest and some are all bubbles.', 7: 'Patterns are data values that can be combined in various ways to form other patterns.'}
| 4 |
3,704 |
['If experts say one third of all women face weight loss, for the first time, after the birth of a child, then some surgical procedures involve uteruses.', 'The statement that states wars produce crises which can lead to socialist revolution is false.', 'Once we know it is not true that if we know that the claim that if if experts say one third of all women face weight loss, for the first time, after the birth of a child, then some surgical procedures involve uteruses, then boas have (part) corpi is false, then wars produce crises which can lead to socialist revolution, we also know that intolerance is the death knell for a culturally pluralistic society.', 'It is a fact that either neurologic complications can occur in achondroplasia or if it is not true that if we know that the claim that if if experts say one third of all women face weight loss, for the first time, after the birth of a child, then some surgical procedures involve uteruses, then boas have (part) corpi is false, then wars produce crises which can lead to socialist revolution, then we know that the claim that intolerance is the death knell for a culturally pluralistic society is false.', 'It is not the case that neurologic complications can occur in achondroplasia.']
|
If experts say one third of all women face weight loss, for the first time, after the birth of a child, then some surgical procedures involve uteruses. The statement that states wars produce crises which can lead to socialist revolution is false. Once we know it is not true that if we know that the claim that if if experts say one third of all women face weight loss, for the first time, after the birth of a child, then some surgical procedures involve uteruses, then boas have (part) corpi is false, then wars produce crises which can lead to socialist revolution, we also know that intolerance is the death knell for a culturally pluralistic society. It is a fact that either neurologic complications can occur in achondroplasia or if it is not true that if we know that the claim that if if experts say one third of all women face weight loss, for the first time, after the birth of a child, then some surgical procedures involve uteruses, then boas have (part) corpi is false, then wars produce crises which can lead to socialist revolution, then we know that the claim that intolerance is the death knell for a culturally pluralistic society is false. It is not the case that neurologic complications can occur in achondroplasia.
|
It is rational to agree that boas have (part) corpi.
|
The claim that boas have (part) corpi is false.
|
FALSE
|
Modus Ponens:
If (If [1], then [2].), then [0]. [SC1-1]
If [1], then [2].
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (If [1], then [2].), then [0].).), then [3]. [SC1-2]
Not [3].
Therefore, If (If [1], then [2].), then [0]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (If (If [1], then [2].), then [0].).), then [3].).), then [4].
If (Not (If (Not (If (If [1], then [2].), then [0].).), then [3].).), then (Not [4].). [SC2-3]
Therefore, If (Not (If (If [1], then [2].), then [0].).), then [3]..
[SC2-3]
Disjunctive Syllogism:
Either [5] or (If (Not (If (Not (If (If [1], then [2].), then [0].).), then [3].).), then (Not [4].).).
Not [5].
Therefore, If (Not (If (Not (If (If [1], then [2].), then [0].).), then [3].).), then (Not [4].)..
|
{0: 'Boas have (part) corpi.', 1: 'Experts say one third of all women face weight loss, for the first time, after the birth of a child.', 2: 'Some surgical procedures involve uteruses.', 3: 'Wars produce crises which can lead to socialist revolution.', 4: 'Intolerance is the death knell for a culturally pluralistic society.', 5: 'Neurologic complications can occur in achondroplasia.'}
| 4 |
3,475 |
["The statement that 'religion caste the fear of dreaming into so many people' is incorrect.", "The statement 'limestone is a sedimentary rock' is true.", 'Once we know bacterial ooze splashed by rain also can spread the pathogen, we also know that if limestone is a sedimentary rock, then if inhalant use refers to the intentional breathing of a gas or vapor with of purpose of getting high, then religion caste the fear of dreaming into so many people.', 'When some centipedes care for their young is true, it follows that bacterial ooze splashed by rain also can spread the pathogen.', 'It is fair to say that some centipedes care for their young.']
|
The statement that 'religion caste the fear of dreaming into so many people' is incorrect. The statement 'limestone is a sedimentary rock' is true. Once we know bacterial ooze splashed by rain also can spread the pathogen, we also know that if limestone is a sedimentary rock, then if inhalant use refers to the intentional breathing of a gas or vapor with of purpose of getting high, then religion caste the fear of dreaming into so many people. When some centipedes care for their young is true, it follows that bacterial ooze splashed by rain also can spread the pathogen. It is fair to say that some centipedes care for their young.
|
The notion that 'inhalant use refers to the intentional breathing of a gas or vapor with of purpose of getting high' is untrue.
|
The claim that inhalant use refers to the intentional breathing of a gas or vapor with of purpose of getting high holds true.
|
FALSE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [2], then (If [0], then [1].). [SC1-2]
[2]
Therefore, If [0], then [1]..
[SC1-2]
Modus Ponens:
If [3], then (If [2], then (If [0], then [1].).).
[3] [SC2-3]
Therefore, If [2], then (If [0], then [1].)..
[SC2-3]
Modus Ponens:
If [4], then [3].
[4]
Therefore, [3].
|
{0: 'Inhalant use refers to the intentional breathing of a gas or vapor with of purpose of getting high.', 1: 'Religion caste the fear of dreaming into so many people.', 2: 'Limestone is a sedimentary rock.', 3: 'Bacterial ooze splashed by rain also can spread the pathogen.', 4: 'Some centipedes care for their young.'}
| 4 |
3,213 |
['One may reasonably assume that if gravity fills the universe, then either water is a very important nutrient or vervain is an essence that can help dogs relax.', 'Given that water is a very important nutrient, it can be inferred that most fire salamanders adapt to habitats.', 'Once we know water is a very important nutrient, we also know that the claim that most fire salamanders adapt to habitats is false.', 'When nummular eczema is a chronic condition that frequently worsens in times of emotional stress is true, it follows that gravity fills the universe.', "The statement 'nummular eczema is a chronic condition that frequently worsens in times of emotional stress' is true."]
|
One may reasonably assume that if gravity fills the universe, then either water is a very important nutrient or vervain is an essence that can help dogs relax. Given that water is a very important nutrient, it can be inferred that most fire salamanders adapt to habitats. Once we know water is a very important nutrient, we also know that the claim that most fire salamanders adapt to habitats is false. When nummular eczema is a chronic condition that frequently worsens in times of emotional stress is true, it follows that gravity fills the universe. The statement 'nummular eczema is a chronic condition that frequently worsens in times of emotional stress' is true.
|
It is a simple truth that vervain is an essence that can help dogs relax.
|
It is a simple truth that vervain is an essence that can help dogs relax.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (Either [1] or [0].).
[3] [SC2-2]
Therefore, Either [1] or [0]..
[SC2-2]
Modus Ponens:
If [4], then [3].
[4]
Therefore, [3].
[SC2-1]
Reductio Ad Absurdum:
If [1], then [2].
If [1], then (Not [2].).
Therefore, Not [1]..
|
{0: 'Vervain is an essence that can help dogs relax.', 1: 'Water is a very important nutrient.', 2: 'Most fire salamanders adapt to habitats.', 3: 'Gravity fills the universe.', 4: 'Nummular eczema is a chronic condition that frequently worsens in times of emotional stress.'}
| 4 |
3,135 |
['There is good reason to believe that either if some predators feed on small insects, then alders grow well in moist soil near ponds and other wet ground or wisdom is the ultimate aim of learning.', "Whenever it is true that if some predators feed on small insects, then alders grow well in moist soil near ponds and other wet ground, 'if concurrences are simultaneity, then language helps shape a people's identity' is true.", "One may reasonably assume that if wisdom is the ultimate aim of learning, then if concurrences are simultaneity, then language helps shape a people's identity.", "Whenever it is true that those that suggest concurrences are simultaneity are wrong, 'the claim that desertification involves the depletion of vegetation and soils does not reflect reality' is true.", 'On the condition that wings are the lift- producing part of the aircraft, it is definitely the case that if those that suggest concurrences are simultaneity are wrong, then desertification involves the depletion of vegetation and soils.', 'Many people rightly believe that wings are the lift- producing part of the aircraft.']
|
There is good reason to believe that either if some predators feed on small insects, then alders grow well in moist soil near ponds and other wet ground or wisdom is the ultimate aim of learning. Whenever it is true that if some predators feed on small insects, then alders grow well in moist soil near ponds and other wet ground, 'if concurrences are simultaneity, then language helps shape a people's identity' is true. One may reasonably assume that if wisdom is the ultimate aim of learning, then if concurrences are simultaneity, then language helps shape a people's identity. Whenever it is true that those that suggest concurrences are simultaneity are wrong, 'the claim that desertification involves the depletion of vegetation and soils does not reflect reality' is true. On the condition that wings are the lift- producing part of the aircraft, it is definitely the case that if those that suggest concurrences are simultaneity are wrong, then desertification involves the depletion of vegetation and soils. Many people rightly believe that wings are the lift- producing part of the aircraft.
|
language helps shape a people's identity.
|
Many languages are spoken in Liberia.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (If [3], then [4].) or [5].
If (If [3], then [4].), then (If [1], then [0].).
If [5], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then [2]. [SC1-2]
If (Not [1].), then (Not [2].).
Therefore, [1].
[SC1-2]
Modus Ponens:
If [6], then (If (Not [1].), then [2].).
[6]
Therefore, If (Not [1].), then [2]..
|
{0: "Language helps shape a people's identity.", 1: 'Concurrences are simultaneity.', 2: 'Desertification involves the depletion of vegetation and soils.', 3: 'Some predators feed on small insects.', 4: 'Alders grow well in moist soil near ponds and other wet ground.', 5: 'Wisdom is the ultimate aim of learning.', 6: 'Wings are the lift- producing part of the aircraft.'}
| 4 |
3,246 |
['Assuming we know that the claim that some dugongs have bones is false, we know that feathers act as insulation and allow for flight.', 'Once we know the claim that if feathers act as insulation and allow for flight, then some digital cameras use multiple CCDs to capture red, green and blue values does not reflect reality, we also know that vitamin E is comprised of a group of compounds called tocopherols.', "The statement 'vitamin E is comprised of a group of compounds called tocopherols' can be considered false.", "So long as evidence identifies culprits, 'the claim that some digital cameras use multiple CCDs to capture red, green and blue values has no merit' is true.", 'It is rational to agree that evidence identifies culprits.']
|
Assuming we know that the claim that some dugongs have bones is false, we know that feathers act as insulation and allow for flight. Once we know the claim that if feathers act as insulation and allow for flight, then some digital cameras use multiple CCDs to capture red, green and blue values does not reflect reality, we also know that vitamin E is comprised of a group of compounds called tocopherols. The statement 'vitamin E is comprised of a group of compounds called tocopherols' can be considered false. So long as evidence identifies culprits, 'the claim that some digital cameras use multiple CCDs to capture red, green and blue values has no merit' is true. It is rational to agree that evidence identifies culprits.
|
The idea that some dugongs have bones is true.
|
The statement that 'some dugongs have bones' is incorrect.
|
FALSE
|
Modus Tonens:
If (Not [0].), then [1].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If [1], then [2]. [SC1-2]
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC1-2]
Modus Tonens:
If (Not (If [1], then [2].).), then [4].
Not [4].
Therefore, If [1], then [2]..
[SC2-2]
Modus Ponens:
If [3], then (Not [2].).
[3]
Therefore, Not [2]..
|
{0: 'Some dugongs have bones.', 1: 'Feathers act as insulation and allow for flight.', 2: 'Some digital cameras use multiple CCDs to capture red, green and blue values.', 3: 'Evidence identifies culprits.', 4: 'Vitamin E is comprised of a group of compounds called tocopherols.'}
| 4 |
3,970 |
['Either freedom is the product of religious faith or asian eggplants are milder and more delicate in flavor than other types.', "Provided that freedom is the product of religious faith, we know that if it is not the case that capital structure refers to a company's sources of financing, then methods involve observations.", "When it is not the case that capital structure refers to a company's sources of financing is true, it follows that buffalo has far less fat than beef.", "Should it be the case that buffalo has far less fat than beef, it follows that the statement 'methods involve observations' can be considered false.", "Assuming the claim that if asian eggplants are milder and more delicate in flavor than other types, then if it is not the case that capital structure refers to a company's sources of financing, then methods involve observations does not correspond with reality, we know that cosmology is the study of the origin, evolution and fate of the universe.", 'The claim that cosmology is the study of the origin, evolution and fate of the universe is false.']
|
Either freedom is the product of religious faith or asian eggplants are milder and more delicate in flavor than other types. Provided that freedom is the product of religious faith, we know that if it is not the case that capital structure refers to a company's sources of financing, then methods involve observations. When it is not the case that capital structure refers to a company's sources of financing is true, it follows that buffalo has far less fat than beef. Should it be the case that buffalo has far less fat than beef, it follows that the statement 'methods involve observations' can be considered false. Assuming the claim that if asian eggplants are milder and more delicate in flavor than other types, then if it is not the case that capital structure refers to a company's sources of financing, then methods involve observations does not correspond with reality, we know that cosmology is the study of the origin, evolution and fate of the universe. The claim that cosmology is the study of the origin, evolution and fate of the universe is false.
|
The claim that capital structure refers to a company's sources of financing holds true.
|
The claim that capital structure refers to a company's sources of financing holds true.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If (Not [0].), then [1].).
If [4], then (If (Not [0].), then [1].). [SC3-2]
Therefore, If (Not [0].), then [1]..
[SC3-2]
Modus Tonens:
If (Not (If [4], then (If (Not [0].), then [1].).).), then [5].
Not [5].
Therefore, If [4], then (If (Not [0].), then [1].)..
[SC2-1]
Hypothetical Syllogism:
If (Not [0].), then [2].
If [2], then (Not [1].).
Therefore, If (Not [0].), then (Not [1].)..
|
{0: "Capital structure refers to a company's sources of financing.", 1: 'Methods involve observations.', 2: 'Buffalo has far less fat than beef.', 3: 'Freedom is the product of religious faith.', 4: 'Asian eggplants are milder and more delicate in flavor than other types.', 5: 'Cosmology is the study of the origin, evolution and fate of the universe.'}
| 4 |
3,891 |
['There is good reason to believe that either either depression is an illness that involves understanding and support or variation is useful for the survival of species over time or either horses come in many colors but mostly black and brown or most ducks breed near aquatic habitats such as wetlands.', 'The statement, either depression is an illness that involves understanding and support or variation is useful for the survival of species over time, does not hold.', 'If horses come in many colors but mostly black and brown, then if worker termites feed on substances, then plants make considerable growth.', 'Once we know if worker termites feed on substances, then plants make considerable growth, we also know that influenza is a respiratory disease, but it affects the entire body.', 'Provided that the claim that if most ducks breed near aquatic habitats such as wetlands, then influenza is a respiratory disease, but it affects the entire body does not reflect reality, we know that some cats wait for birds.', 'The claim that some cats wait for birds does not correspond with reality.']
|
There is good reason to believe that either either depression is an illness that involves understanding and support or variation is useful for the survival of species over time or either horses come in many colors but mostly black and brown or most ducks breed near aquatic habitats such as wetlands. The statement, either depression is an illness that involves understanding and support or variation is useful for the survival of species over time, does not hold. If horses come in many colors but mostly black and brown, then if worker termites feed on substances, then plants make considerable growth. Once we know if worker termites feed on substances, then plants make considerable growth, we also know that influenza is a respiratory disease, but it affects the entire body. Provided that the claim that if most ducks breed near aquatic habitats such as wetlands, then influenza is a respiratory disease, but it affects the entire body does not reflect reality, we know that some cats wait for birds. The claim that some cats wait for birds does not correspond with reality.
|
The statement 'influenza is a respiratory disease, but it affects the entire body' is true.
|
We know that the claim that influenza is a respiratory disease, but it affects the entire body is false.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either (Either [5] or [6].) or (Either [1] or [2].).
Not (Either [5] or [6].).
Therefore, Either [1] or [2]..
[SC2-1]
Hypothetical Syllogism:
If [1], then (If [3], then [4].).
If (If [3], then [4].), then [0].
Therefore, If [1], then [0]..
[SC3-1]
Modus Tonens:
If (Not (If [2], then [0].).), then [7].
Not [7].
Therefore, If [2], then [0]..
|
{0: 'Influenza is a respiratory disease, but it affects the entire body.', 1: 'Horses come in many colors but mostly black and brown.', 2: 'Most ducks breed near aquatic habitats such as wetlands.', 3: 'Worker termites feed on substances.', 4: 'Plants make considerable growth.', 5: 'Depression is an illness that involves understanding and support.', 6: 'Variation is useful for the survival of species over time.', 7: 'Some cats wait for birds.'}
| 4 |
3,619 |
['Those that suggest words are part of dictionaries are right.', 'On the condition that the claim that if those that suggest traumatic events can cause a state of shock are wrong, then it is a common misconception that mouses have whiskers has no merit, it is definitely the case that many mothers are desperate to wean at different stages of breastfeeding.', "Assuming the claim that if those that suggest traumatic events can cause a state of shock are wrong, then it is a common misconception that mouses have whiskers has no merit, we know that the statement that 'many mothers are desperate to wean at different stages of breastfeeding' is incorrect.", 'It is rational to believe that either martial eagles are powerful hunters, able to kill game birds, hyraxes and small antelope or young people receiving chemotherapy generally have a lower white cell count than normal.', 'Provided that martial eagles are powerful hunters, able to kill game birds, hyraxes and small antelope, we know that if words are part of dictionaries, then if those that suggest traumatic events can cause a state of shock are wrong, then mouses have whiskers.', 'Once we know young people receiving chemotherapy generally have a lower white cell count than normal, we also know that if words are part of dictionaries, then if those that suggest traumatic events can cause a state of shock are wrong, then mouses have whiskers.']
|
Those that suggest words are part of dictionaries are right. On the condition that the claim that if those that suggest traumatic events can cause a state of shock are wrong, then it is a common misconception that mouses have whiskers has no merit, it is definitely the case that many mothers are desperate to wean at different stages of breastfeeding. Assuming the claim that if those that suggest traumatic events can cause a state of shock are wrong, then it is a common misconception that mouses have whiskers has no merit, we know that the statement that 'many mothers are desperate to wean at different stages of breastfeeding' is incorrect. It is rational to believe that either martial eagles are powerful hunters, able to kill game birds, hyraxes and small antelope or young people receiving chemotherapy generally have a lower white cell count than normal. Provided that martial eagles are powerful hunters, able to kill game birds, hyraxes and small antelope, we know that if words are part of dictionaries, then if those that suggest traumatic events can cause a state of shock are wrong, then mouses have whiskers. Once we know young people receiving chemotherapy generally have a lower white cell count than normal, we also know that if words are part of dictionaries, then if those that suggest traumatic events can cause a state of shock are wrong, then mouses have whiskers.
|
Many people rightly believe that traumatic events can cause a state of shock.
|
Traumatic events appear to result in anger and depression.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (If (Not [0].), then [1].). [SC1-2]
[3]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [3], then (If (Not [0].), then [1].).).
If [5], then (If [3], then (If (Not [0].), then [1].).).
Therefore, If [3], then (If (Not [0].), then [1].)..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then (Not [1].).).), then [2].
If (Not (If (Not [0].), then (Not [1].).).), then (Not [2].).
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Traumatic events can cause a state of shock.', 1: 'Mouses have whiskers.', 2: 'Many mothers are desperate to wean at different stages of breastfeeding.', 3: 'Words are part of dictionaries.', 4: 'Martial eagles are powerful hunters, able to kill game birds, hyraxes and small antelope.', 5: 'Young people receiving chemotherapy generally have a lower white cell count than normal.'}
| 4 |
3,815 |
['Assuming it is a common misconception that either leadership affects both foreign relations and internal stability or computers impact almost every aspect of our lives, we know that if agoraphobia also tends to be more difficult to control compared to simple phobias, then complex systems exist at surfaces, interfaces and thin films.', "So long as it is a common misconception that either leadership affects both foreign relations and internal stability or computers impact almost every aspect of our lives, 'the statement, if agoraphobia also tends to be more difficult to control compared to simple phobias, then complex systems exist at surfaces, interfaces and thin films, does not hold' is true.", "So long as leadership affects both foreign relations and internal stability, 'polarization is one way the system preserves balance, but it is an unstable and conflictual balance' is true.", 'Once we know polarization is one way the system preserves balance, but it is an unstable and conflictual balance, we also know that viruses live in the intracellular part of the body and are hard to reach.', 'Provided that computers impact almost every aspect of our lives, we know that fertilization occurs when the nuclei of the sperm and egg meet and join together or fuse.', 'One may reasonably assume that if fertilization occurs when the nuclei of the sperm and egg meet and join together or fuse, then viruses live in the intracellular part of the body and are hard to reach.']
|
Assuming it is a common misconception that either leadership affects both foreign relations and internal stability or computers impact almost every aspect of our lives, we know that if agoraphobia also tends to be more difficult to control compared to simple phobias, then complex systems exist at surfaces, interfaces and thin films. So long as it is a common misconception that either leadership affects both foreign relations and internal stability or computers impact almost every aspect of our lives, 'the statement, if agoraphobia also tends to be more difficult to control compared to simple phobias, then complex systems exist at surfaces, interfaces and thin films, does not hold' is true. So long as leadership affects both foreign relations and internal stability, 'polarization is one way the system preserves balance, but it is an unstable and conflictual balance' is true. Once we know polarization is one way the system preserves balance, but it is an unstable and conflictual balance, we also know that viruses live in the intracellular part of the body and are hard to reach. Provided that computers impact almost every aspect of our lives, we know that fertilization occurs when the nuclei of the sperm and egg meet and join together or fuse. One may reasonably assume that if fertilization occurs when the nuclei of the sperm and egg meet and join together or fuse, then viruses live in the intracellular part of the body and are hard to reach.
|
We can assume that viruses live in the intracellular part of the body and are hard to reach.
|
We can assume that viruses live in the intracellular part of the body and are hard to reach.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or [2].).), then (If [3], then [4].).
If (Not (Either [1] or [2].).), then (Not (If [3], then [4].).).
Therefore, Either [1] or [2]..
[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: 'Viruses live in the intracellular part of the body and are hard to reach.', 1: 'Leadership affects both foreign relations and internal stability.', 2: 'Computers impact almost every aspect of our lives.', 3: 'Agoraphobia also tends to be more difficult to control compared to simple phobias.', 4: 'Complex systems exist at surfaces, interfaces and thin films.', 5: 'Polarization is one way the system preserves balance, but it is an unstable and conflictual balance.', 6: 'Fertilization occurs when the nuclei of the sperm and egg meet and join together or fuse.'}
| 4 |
3,365 |
['It is fair to say that clinical depression is an illness, and it requires specific treatment.', 'If the claim that either most people take vitamin supplements daily to insure against nutritional deficiencies or if clinical depression is an illness, and it requires specific treatment, then the statement that states bears have (part) rib cages is false does not reflect reality, then brain inflammation causes symptoms.', 'Provided that the claim that either most people take vitamin supplements daily to insure against nutritional deficiencies or if clinical depression is an illness, and it requires specific treatment, then the statement that states bears have (part) rib cages is false does not reflect reality, we know that the claim that brain inflammation causes symptoms is false.', "There is good reason to believe that either bone marrow is the 'orchard' within the bones where blood cells form or some clouds make up atoms.", "So long as bone marrow is the 'orchard' within the bones where blood cells form, 'the statement that states most people take vitamin supplements daily to insure against nutritional deficiencies is false' is true.", 'Given that some clouds make up atoms, it can be inferred that the statement that states most people take vitamin supplements daily to insure against nutritional deficiencies is false.']
|
It is fair to say that clinical depression is an illness, and it requires specific treatment. If the claim that either most people take vitamin supplements daily to insure against nutritional deficiencies or if clinical depression is an illness, and it requires specific treatment, then the statement that states bears have (part) rib cages is false does not reflect reality, then brain inflammation causes symptoms. Provided that the claim that either most people take vitamin supplements daily to insure against nutritional deficiencies or if clinical depression is an illness, and it requires specific treatment, then the statement that states bears have (part) rib cages is false does not reflect reality, we know that the claim that brain inflammation causes symptoms is false. There is good reason to believe that either bone marrow is the 'orchard' within the bones where blood cells form or some clouds make up atoms. So long as bone marrow is the 'orchard' within the bones where blood cells form, 'the statement that states most people take vitamin supplements daily to insure against nutritional deficiencies is false' is true. Given that some clouds make up atoms, it can be inferred that the statement that states most people take vitamin supplements daily to insure against nutritional deficiencies is false.
|
The statement that states bears have (part) rib cages is false.
|
The claim that bears have (part) rib cages holds true.
|
FALSE
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [1], then (Not [0].).). [SC1-2]
Not [2]. [SC2-2]
Therefore, If [1], then (Not [0].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [2] or (If [1], then (Not [0].).).).), then [3].
If (Not (Either [2] or (If [1], then (Not [0].).).).), then (Not [3].).
Therefore, Either [2] or (If [1], then (Not [0].).)..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Not [2].).
If [5], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Bears have (part) rib cages.', 1: 'Clinical depression is an illness, and it requires specific treatment.', 2: 'Most people take vitamin supplements daily to insure against nutritional deficiencies.', 3: 'Brain inflammation causes symptoms.', 4: "Bone marrow is the 'orchard' within the bones where blood cells form.", 5: 'Some clouds make up atoms.'}
| 4 |
3,812 |
['It is rational to believe that either some wind helps mosquitoes or water is located in gyms.', 'One may reasonably assume that if some wind helps mosquitoes, then if some antelopes have origins, then moist air meets cold canadian air.', 'Should it be the case that water is located in gyms, it follows that if some antelopes have origins, then moist air meets cold canadian air.', "When the notion that 'some antelopes have origins' is untrue is true, it follows that it is not the case that loudspeakers are actual emitters.", "It is a fact that either computers allow press operators to perform many of their tasks electronically or if the notion that 'some antelopes have origins' is untrue, then loudspeakers are actual emitters.", 'We know that the claim that computers allow press operators to perform many of their tasks electronically is false.']
|
It is rational to believe that either some wind helps mosquitoes or water is located in gyms. One may reasonably assume that if some wind helps mosquitoes, then if some antelopes have origins, then moist air meets cold canadian air. Should it be the case that water is located in gyms, it follows that if some antelopes have origins, then moist air meets cold canadian air. When the notion that 'some antelopes have origins' is untrue is true, it follows that it is not the case that loudspeakers are actual emitters. It is a fact that either computers allow press operators to perform many of their tasks electronically or if the notion that 'some antelopes have origins' is untrue, then loudspeakers are actual emitters. We know that the claim that computers allow press operators to perform many of their tasks electronically is false.
|
The claim that moist air meets cold canadian air holds true.
|
Those that suggest moist air meets cold canadian air are wrong.
|
FALSE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If [1], then [0].).
If [3], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then [4]. [SC1-2]
If (Not [1].), then (Not [4].).
Therefore, [1].
[SC1-2]
Disjunctive Syllogism:
Either [5] or (If (Not [1].), then [4].).
Not [5].
Therefore, If (Not [1].), then [4]..
|
{0: 'Moist air meets cold canadian air.', 1: 'Some antelopes have origins.', 2: 'Some wind helps mosquitoes.', 3: 'Water is located in gyms.', 4: 'Loudspeakers are actual emitters.', 5: 'Computers allow press operators to perform many of their tasks electronically.'}
| 4 |
3,026 |
['Many people rightly believe that silver bromides are electrolytes.', 'If some people mistakenly believe that if silver bromides are electrolytes, then friendships are created by trust, then the claim that japan is probably the only country in the world where a person can write poetry as a paying career is false.', 'When the claim that if some people mistakenly believe that if silver bromides are electrolytes, then friendships are created by trust, then japan is probably the only country in the world where a person can write poetry as a paying career does not reflect reality is true, it follows that some oxide causes acid rain.', 'One may reasonably assume that if most busy people can have periods when they are frustrated, forgetful or have trouble concentrating, then if the claim that if some people mistakenly believe that if silver bromides are electrolytes, then friendships are created by trust, then japan is probably the only country in the world where a person can write poetry as a paying career does not reflect reality, then we know that the claim that some oxide causes acid rain is false.', 'It is reasonable to believe that most busy people can have periods when they are frustrated, forgetful or have trouble concentrating.']
|
Many people rightly believe that silver bromides are electrolytes. If some people mistakenly believe that if silver bromides are electrolytes, then friendships are created by trust, then the claim that japan is probably the only country in the world where a person can write poetry as a paying career is false. When the claim that if some people mistakenly believe that if silver bromides are electrolytes, then friendships are created by trust, then japan is probably the only country in the world where a person can write poetry as a paying career does not reflect reality is true, it follows that some oxide causes acid rain. One may reasonably assume that if most busy people can have periods when they are frustrated, forgetful or have trouble concentrating, then if the claim that if some people mistakenly believe that if silver bromides are electrolytes, then friendships are created by trust, then japan is probably the only country in the world where a person can write poetry as a paying career does not reflect reality, then we know that the claim that some oxide causes acid rain is false. It is reasonable to believe that most busy people can have periods when they are frustrated, forgetful or have trouble concentrating.
|
It is reasonable to believe that friendships are created by trust.
|
It is reasonable to believe that friendships are created by trust.
|
TRUE
|
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]
Reductio Ad Absurdum:
If (Not (If (Not (If [1], then [0].).), then [2].).), then [3].
If (Not (If (Not (If [1], then [0].).), then [2].).), then (Not [3].). [SC2-3]
Therefore, If (Not (If [1], then [0].).), then [2]..
[SC2-3]
Modus Ponens:
If [4], then (If (Not (If (Not (If [1], then [0].).), then [2].).), then (Not [3].).).
[4]
Therefore, If (Not (If (Not (If [1], then [0].).), then [2].).), then (Not [3].)..
|
{0: 'Friendships are created by trust.', 1: 'Silver bromides are electrolytes.', 2: 'Japan is probably the only country in the world where a person can write poetry as a paying career.', 3: 'Some oxide causes acid rain.', 4: 'Most busy people can have periods when they are frustrated, forgetful or have trouble concentrating.'}
| 4 |
3,642 |
['At least one of two things is true: either dialysis is unnecessary as long as the kidney is functioning or some essential oils can cause skin sensitization, or manatees have wide-ranging migratory habits.', 'Provided that manatees have wide-ranging migratory habits, we know that if fire extinguishers are devices, then temperature increases during summer.', 'When the statement that states fire extinguishers are devices is false is true, it follows that scientists observe types.', "The notion that 'scientists observe types' is untrue.", 'Assuming the statement that states if either dialysis is unnecessary as long as the kidney is functioning or some essential oils can cause skin sensitization, then if fire extinguishers are devices, then temperature increases during summer is false, we know that goldfinches have (part) skulls.', "Assuming the statement that states if either dialysis is unnecessary as long as the kidney is functioning or some essential oils can cause skin sensitization, then if fire extinguishers are devices, then temperature increases during summer is false, we know that the notion that 'goldfinches have (part) skulls' is untrue."]
|
At least one of two things is true: either dialysis is unnecessary as long as the kidney is functioning or some essential oils can cause skin sensitization, or manatees have wide-ranging migratory habits. Provided that manatees have wide-ranging migratory habits, we know that if fire extinguishers are devices, then temperature increases during summer. When the statement that states fire extinguishers are devices is false is true, it follows that scientists observe types. The notion that 'scientists observe types' is untrue. Assuming the statement that states if either dialysis is unnecessary as long as the kidney is functioning or some essential oils can cause skin sensitization, then if fire extinguishers are devices, then temperature increases during summer is false, we know that goldfinches have (part) skulls. Assuming the statement that states if either dialysis is unnecessary as long as the kidney is functioning or some essential oils can cause skin sensitization, then if fire extinguishers are devices, then temperature increases during summer is false, we know that the notion that 'goldfinches have (part) skulls' is untrue.
|
Those that suggest temperature increases during summer are right.
|
It is not the case that temperature increases during summer.
|
FALSE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [3] or [4].) or [5].
If (Either [3] or [4].), then (If [1], then [0].). [SC2-2]
If [5], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Either [3] or [4].), then (If [1], then [0].).).), then [6].
If (Not (If (Either [3] or [4].), then (If [1], then [0].).).), then (Not [6].).
Therefore, If (Either [3] or [4].), then (If [1], then [0].)..
[SC2-1]
Modus Tonens:
If (Not [1].), then [2].
Not [2].
Therefore, [1].
|
{0: 'Temperature increases during summer.', 1: 'Fire extinguishers are devices.', 2: 'Scientists observe types.', 3: 'Dialysis is unnecessary as long as the kidney is functioning.', 4: 'Some essential oils can cause skin sensitization.', 5: 'Manatees have wide-ranging migratory habits.', 6: 'Goldfinches have (part) skulls.'}
| 4 |
3,417 |
['It is a fact that either either slaves have (part) legs or viral meningitis occurs more commonly than bacterial meningitis or the claim that either a heavenly body is a natural object or money is anything that is generally acceptable to sellers in exchange for good s and services does not reflect reality.', 'If manure causes increases of microbial predators, while decreasing the abundance of plant parasites, then the claim that either slaves have (part) legs or viral meningitis occurs more commonly than bacterial meningitis does not reflect reality.', 'Assuming some people mistakenly believe that either if naive realism is the belief that people everywhere see the world in the same way, then variation is most important to the breeder and the organism or manure causes increases of microbial predators, while decreasing the abundance of plant parasites, we know that a collect is prayer.', 'The claim that a collect is prayer does not correspond with reality.', 'If it is not the case that if if naive realism is the belief that people everywhere see the world in the same way, then variation is most important to the breeder and the organism, then the claim that either slaves have (part) legs or viral meningitis occurs more commonly than bacterial meningitis does not reflect reality, then pinyons have (part) bark.', 'The statement that states pinyons have (part) bark is false.']
|
It is a fact that either either slaves have (part) legs or viral meningitis occurs more commonly than bacterial meningitis or the claim that either a heavenly body is a natural object or money is anything that is generally acceptable to sellers in exchange for good s and services does not reflect reality. If manure causes increases of microbial predators, while decreasing the abundance of plant parasites, then the claim that either slaves have (part) legs or viral meningitis occurs more commonly than bacterial meningitis does not reflect reality. Assuming some people mistakenly believe that either if naive realism is the belief that people everywhere see the world in the same way, then variation is most important to the breeder and the organism or manure causes increases of microbial predators, while decreasing the abundance of plant parasites, we know that a collect is prayer. The claim that a collect is prayer does not correspond with reality. If it is not the case that if if naive realism is the belief that people everywhere see the world in the same way, then variation is most important to the breeder and the organism, then the claim that either slaves have (part) legs or viral meningitis occurs more commonly than bacterial meningitis does not reflect reality, then pinyons have (part) bark. The statement that states pinyons have (part) bark is false.
|
The claim that either a heavenly body is a natural object or money is anything that is generally acceptable to sellers in exchange for good s and services does not reflect reality.
|
At least one of two things is true: a heavenly body is a natural object, or money is anything that is generally acceptable to sellers in exchange for good s and services.
|
FALSE
|
Disjunctive Syllogism:
Either (Either [2] or [3].) or (Not (Either [0] or [1].).).
Not (Either [2] or [3].). [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC2-1]
Disjunction Elimination:
Either (If [4], then [5].) or [6]. [SC1-2]
If (If [4], then [5].), then (Not (Either [2] or [3].).). [SC2-2]
If [6], then (Not (Either [2] or [3].).).
Therefore, Not (Either [2] or [3].)..
[SC1-2]
Modus Tonens:
If (Not (Either (If [4], then [5].) or [6].).), then [7].
Not [7].
Therefore, Either (If [4], then [5].) or [6]..
[SC2-2]
Modus Tonens:
If (Not (If (If [4], then [5].), then (Not (Either [2] or [3].).).).), then [8].
Not [8].
Therefore, If (If [4], then [5].), then (Not (Either [2] or [3].).)..
|
{0: 'A heavenly body is a natural object.', 1: 'Money is anything that is generally acceptable to sellers in exchange for good s and services.', 2: 'Slaves have (part) legs.', 3: 'Viral meningitis occurs more commonly than bacterial meningitis.', 4: 'Naive realism is the belief that people everywhere see the world in the same way.', 5: 'Variation is most important to the breeder and the organism.', 6: 'Manure causes increases of microbial predators, while decreasing the abundance of plant parasites.', 7: 'A collect is prayer.', 8: 'Pinyons have (part) bark.'}
| 4 |
3,907 |
["If the statement that 'either if some rattlesnakes live in burrows, then teamwork is what gets the job done or nylon brushes can stir-up electricity' is incorrect, then if lightning always produces thunder, then cystic fibrosis is a genetic disease that affects the respiratory and digestive systems.", "So long as the statement that 'either if some rattlesnakes live in burrows, then teamwork is what gets the job done or nylon brushes can stir-up electricity' is incorrect, 'those that suggest if lightning always produces thunder, then cystic fibrosis is a genetic disease that affects the respiratory and digestive systems are wrong' is true.", "So long as people show a wide range of variability in their tolerance for chemical exposure, 'if if some rattlesnakes live in burrows, then teamwork is what gets the job done, then all breeds of horses have calm, quiet horses as well as anxious, dangerous horses' is true.", 'It is rational to agree that people show a wide range of variability in their tolerance for chemical exposure.', "Assuming the notion that 'if nylon brushes can stir-up electricity, then all breeds of horses have calm, quiet horses as well as anxious, dangerous horses' is untrue, we know that some epidermises are part of pachyderms.", "Assuming the notion that 'if nylon brushes can stir-up electricity, then all breeds of horses have calm, quiet horses as well as anxious, dangerous horses' is untrue, we know that the notion that 'some epidermises are part of pachyderms' is untrue."]
|
If the statement that 'either if some rattlesnakes live in burrows, then teamwork is what gets the job done or nylon brushes can stir-up electricity' is incorrect, then if lightning always produces thunder, then cystic fibrosis is a genetic disease that affects the respiratory and digestive systems. So long as the statement that 'either if some rattlesnakes live in burrows, then teamwork is what gets the job done or nylon brushes can stir-up electricity' is incorrect, 'those that suggest if lightning always produces thunder, then cystic fibrosis is a genetic disease that affects the respiratory and digestive systems are wrong' is true. So long as people show a wide range of variability in their tolerance for chemical exposure, 'if if some rattlesnakes live in burrows, then teamwork is what gets the job done, then all breeds of horses have calm, quiet horses as well as anxious, dangerous horses' is true. It is rational to agree that people show a wide range of variability in their tolerance for chemical exposure. Assuming the notion that 'if nylon brushes can stir-up electricity, then all breeds of horses have calm, quiet horses as well as anxious, dangerous horses' is untrue, we know that some epidermises are part of pachyderms. Assuming the notion that 'if nylon brushes can stir-up electricity, then all breeds of horses have calm, quiet horses as well as anxious, dangerous horses' is untrue, we know that the notion that 'some epidermises are part of pachyderms' is untrue.
|
It is true that all breeds of horses have calm, quiet horses as well as anxious, dangerous horses.
|
It is true that all breeds of horses have calm, quiet horses as well as anxious, dangerous horses.
|
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]. [SC3-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either (If [1], then [2].) or [3].).), then (If [5], then [6].).
If (Not (Either (If [1], then [2].) or [3].).), then (Not (If [5], then [6].).).
Therefore, Either (If [1], then [2].) or [3]..
[SC2-1]
Modus Ponens:
If [4], then (If (If [1], then [2].), then [0].).
[4]
Therefore, If (If [1], then [2].), then [0]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [3], then [0].).), then [7].
If (Not (If [3], then [0].).), then (Not [7].).
Therefore, If [3], then [0]..
|
{0: 'All breeds of horses have calm, quiet horses as well as anxious, dangerous horses.', 1: 'Some rattlesnakes live in burrows.', 2: 'Teamwork is what gets the job done.', 3: 'Nylon brushes can stir-up electricity.', 4: 'People show a wide range of variability in their tolerance for chemical exposure.', 5: 'Lightning always produces thunder.', 6: 'Cystic fibrosis is a genetic disease that affects the respiratory and digestive systems.', 7: 'Some epidermises are part of pachyderms.'}
| 4 |
3,921 |
['It is a fact that either if chimpanzees possess friends, then digital image consists of discrete picture elements called pixels or treadmills are, by far, the most popular piece of aerobic equipment.', 'There is good reason to believe that either if skunks kill poultry and eat eggs, then oysters naturally grow in estuarine bodies of brackish water or many types of fish use the huge kelp forests to hide from predators.', 'If many types of fish use the huge kelp forests to hide from predators, then it is a common misconception that if chimpanzees possess friends, then digital image consists of discrete picture elements called pixels.', 'Should it be the case that most cars use a radiator to cool the engine, it follows that if if skunks kill poultry and eat eggs, then oysters naturally grow in estuarine bodies of brackish water , then it is a common misconception that if chimpanzees possess friends, then digital image consists of discrete picture elements called pixels.', 'Should it be the case that affected birds remain quiet because breathing is difficult, it follows that if if skunks kill poultry and eat eggs, then oysters naturally grow in estuarine bodies of brackish water , then it is a common misconception that if chimpanzees possess friends, then digital image consists of discrete picture elements called pixels.', 'It is a fact that either chromatids are part of chromosomes or either most cars use a radiator to cool the engine or affected birds remain quiet because breathing is difficult.', 'Those that suggest chromatids are part of chromosomes are wrong.']
|
It is a fact that either if chimpanzees possess friends, then digital image consists of discrete picture elements called pixels or treadmills are, by far, the most popular piece of aerobic equipment. There is good reason to believe that either if skunks kill poultry and eat eggs, then oysters naturally grow in estuarine bodies of brackish water or many types of fish use the huge kelp forests to hide from predators. If many types of fish use the huge kelp forests to hide from predators, then it is a common misconception that if chimpanzees possess friends, then digital image consists of discrete picture elements called pixels. Should it be the case that most cars use a radiator to cool the engine, it follows that if if skunks kill poultry and eat eggs, then oysters naturally grow in estuarine bodies of brackish water , then it is a common misconception that if chimpanzees possess friends, then digital image consists of discrete picture elements called pixels. Should it be the case that affected birds remain quiet because breathing is difficult, it follows that if if skunks kill poultry and eat eggs, then oysters naturally grow in estuarine bodies of brackish water , then it is a common misconception that if chimpanzees possess friends, then digital image consists of discrete picture elements called pixels. It is a fact that either chromatids are part of chromosomes or either most cars use a radiator to cool the engine or affected birds remain quiet because breathing is difficult. Those that suggest chromatids are part of chromosomes are wrong.
|
The claim that treadmills are, by far, the most popular piece of aerobic equipment is true.
|
The claim that treadmills are, by far, the most popular piece of aerobic equipment has no merit.
|
FALSE
|
Disjunctive Syllogism:
Either (If [1], then [2].) or [0].
Not (If [1], then [2].). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either (If [3], then [4].) or [5].
If (If [3], then [4].), then (Not (If [1], then [2].).). [SC2-2]
If [5], then (Not (If [1], then [2].).).
Therefore, Not (If [1], then [2].)..
[SC2-2]
Disjunction Elimination:
Either [6] or [7]. [SC1-3]
If [6], then (If (If [3], then [4].), then (Not (If [1], then [2].).).).
If [7], then (If (If [3], then [4].), then (Not (If [1], then [2].).).).
Therefore, If (If [3], then [4].), then (Not (If [1], then [2].).)..
[SC1-3]
Disjunctive Syllogism:
Either [8] or (Either [6] or [7].).
Not [8].
Therefore, Either [6] or [7]..
|
{0: 'Treadmills are, by far, the most popular piece of aerobic equipment.', 1: 'Chimpanzees possess friends.', 2: 'Digital image consists of discrete picture elements called pixels.', 3: 'Skunks kill poultry and eat eggs.', 4: 'Oysters naturally grow in estuarine bodies of brackish water .', 5: 'Many types of fish use the huge kelp forests to hide from predators.', 6: 'Most cars use a radiator to cool the engine.', 7: 'Affected birds remain quiet because breathing is difficult.', 8: 'Chromatids are part of chromosomes.'}
| 4 |
3,003 |
['Should it be the case that the claim that either survival drives population growth or drinking water is very important to moth survival and reproduction is false, it follows that some dandelions have health benefits.', "Given that the notion that 'if the claim that either survival drives population growth or drinking water is very important to moth survival and reproduction is false, then the statement 'colleoid cephalopods have complex organs which they use to change colour rapidly' can be considered false' is untrue, it can be inferred that either millions starve when governments spend on weapons or some spiders reproduce during periods.", "Once we know the notion that 'if the claim that either survival drives population growth or drinking water is very important to moth survival and reproduction is false, then the statement 'colleoid cephalopods have complex organs which they use to change colour rapidly' can be considered false' is untrue, we also know that some people mistakenly believe that either millions starve when governments spend on weapons or some spiders reproduce during periods.", 'One may reasonably assume that if the claim that if some dandelions have health benefits, then colleoid cephalopods have complex organs which they use to change colour rapidly has no merit, then monochromatic light is shone on the electrode surface at a succession of wavelengths.', 'It is not true that monochromatic light is shone on the electrode surface at a succession of wavelengths.']
|
Should it be the case that the claim that either survival drives population growth or drinking water is very important to moth survival and reproduction is false, it follows that some dandelions have health benefits. Given that the notion that 'if the claim that either survival drives population growth or drinking water is very important to moth survival and reproduction is false, then the statement 'colleoid cephalopods have complex organs which they use to change colour rapidly' can be considered false' is untrue, it can be inferred that either millions starve when governments spend on weapons or some spiders reproduce during periods. Once we know the notion that 'if the claim that either survival drives population growth or drinking water is very important to moth survival and reproduction is false, then the statement 'colleoid cephalopods have complex organs which they use to change colour rapidly' can be considered false' is untrue, we also know that some people mistakenly believe that either millions starve when governments spend on weapons or some spiders reproduce during periods. One may reasonably assume that if the claim that if some dandelions have health benefits, then colleoid cephalopods have complex organs which they use to change colour rapidly has no merit, then monochromatic light is shone on the electrode surface at a succession of wavelengths. It is not true that monochromatic light is shone on the electrode surface at a succession of wavelengths.
|
It is a fact that either survival drives population growth or drinking water is very important to moth survival and reproduction.
|
It is a fact that either survival drives population growth or drinking water is very important to moth survival and reproduction.
|
TRUE
|
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]
Hypothetical Syllogism:
If (Not (Either [0] or [1].).), then [3].
If [3], then [2]. [SC2-2]
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC2-2]
Modus Tonens:
If (Not (If [3], then [2].).), then [6].
Not [6].
Therefore, If [3], then [2]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (Either [4] or [5].).
If (Not (If (Not (Either [0] or [1].).), then (Not [2].).).), then (Not (Either [4] or [5].).).
Therefore, If (Not (Either [0] or [1].).), then (Not [2].)..
|
{0: 'Survival drives population growth.', 1: 'Drinking water is very important to moth survival and reproduction.', 2: 'Colleoid cephalopods have complex organs which they use to change colour rapidly.', 3: 'Some dandelions have health benefits.', 4: 'Millions starve when governments spend on weapons.', 5: 'Some spiders reproduce during periods.', 6: 'Monochromatic light is shone on the electrode surface at a succession of wavelengths.'}
| 4 |
3,134 |
['Provided that the claim that anger can also bind a child to a parent well into adulthood does not correspond with reality, we know that cholesterol is a soft, waxy-like substance found in each cell of the body.', 'If the claim that if those that suggest if the claim that anger can also bind a child to a parent well into adulthood does not correspond with reality, then some people mistakenly believe that cholesterol is a soft, waxy-like substance found in each cell of the body are wrong, then contrails are clouds does not reflect reality, then some ancestors leave water.', 'Once we know the claim that if those that suggest if the claim that anger can also bind a child to a parent well into adulthood does not correspond with reality, then some people mistakenly believe that cholesterol is a soft, waxy-like substance found in each cell of the body are wrong, then contrails are clouds does not reflect reality, we also know that we know that the claim that some ancestors leave water is false.', 'Either one or both of these statements are true: wolves normally hunt for deer, or human populations tend to modify existing ecosystems for own purposes.', 'Given that wolves normally hunt for deer, it can be inferred that if those that suggest if the claim that anger can also bind a child to a parent well into adulthood does not correspond with reality, then some people mistakenly believe that cholesterol is a soft, waxy-like substance found in each cell of the body are wrong, then the claim that contrails are clouds does not correspond with reality.', 'When human populations tend to modify existing ecosystems for own purposes is true, it follows that if those that suggest if the claim that anger can also bind a child to a parent well into adulthood does not correspond with reality, then some people mistakenly believe that cholesterol is a soft, waxy-like substance found in each cell of the body are wrong, then the claim that contrails are clouds does not correspond with reality.']
|
Provided that the claim that anger can also bind a child to a parent well into adulthood does not correspond with reality, we know that cholesterol is a soft, waxy-like substance found in each cell of the body. If the claim that if those that suggest if the claim that anger can also bind a child to a parent well into adulthood does not correspond with reality, then some people mistakenly believe that cholesterol is a soft, waxy-like substance found in each cell of the body are wrong, then contrails are clouds does not reflect reality, then some ancestors leave water. Once we know the claim that if those that suggest if the claim that anger can also bind a child to a parent well into adulthood does not correspond with reality, then some people mistakenly believe that cholesterol is a soft, waxy-like substance found in each cell of the body are wrong, then contrails are clouds does not reflect reality, we also know that we know that the claim that some ancestors leave water is false. Either one or both of these statements are true: wolves normally hunt for deer, or human populations tend to modify existing ecosystems for own purposes. Given that wolves normally hunt for deer, it can be inferred that if those that suggest if the claim that anger can also bind a child to a parent well into adulthood does not correspond with reality, then some people mistakenly believe that cholesterol is a soft, waxy-like substance found in each cell of the body are wrong, then the claim that contrails are clouds does not correspond with reality. When human populations tend to modify existing ecosystems for own purposes is true, it follows that if those that suggest if the claim that anger can also bind a child to a parent well into adulthood does not correspond with reality, then some people mistakenly believe that cholesterol is a soft, waxy-like substance found in each cell of the body are wrong, then the claim that contrails are clouds does not correspond with reality.
|
It is rational to agree that anger can also bind a child to a parent well into adulthood.
|
Anger is an emotion that usually develops between characters arising from some failing or another.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then (Not [1].).).), then [2]. [SC1-2]
If (Not (If (Not [0].), then (Not [1].).).), then (Not [2].). [SC2-2]
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If (Not (If (Not [0].), then (Not [1].).).), then [2].).), then [5].
If (Not (If (Not (If (Not [0].), then (Not [1].).).), then [2].).), then (Not [5].).
Therefore, If (Not (If (Not [0].), then (Not [1].).).), then [2]..
[SC2-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If (Not (If (Not [0].), then (Not [1].).).), then (Not [2].).).
If [4], then (If (Not (If (Not [0].), then (Not [1].).).), then (Not [2].).).
Therefore, If (Not (If (Not [0].), then (Not [1].).).), then (Not [2].)..
|
{0: 'Anger can also bind a child to a parent well into adulthood.', 1: 'Cholesterol is a soft, waxy-like substance found in each cell of the body.', 2: 'Contrails are clouds.', 3: 'Wolves normally hunt for deer.', 4: 'Human populations tend to modify existing ecosystems for own purposes.', 5: 'Some ancestors leave water.'}
| 4 |
3,355 |
['Either zip files are an industry-standard way of combining and compressing several files into one or either water potential is a quantitative measure of the binding energy of water in food or tiger mosquitoes are persistent, moderately aggressive biters.', 'Should it be the case that either water potential is a quantitative measure of the binding energy of water in food or tiger mosquitoes are persistent, moderately aggressive biters, it follows that illusory contours activate non-retinotopic areas of human visual cortex.', 'When it is not true that if zip files are an industry-standard way of combining and compressing several files into one, then illusory contours activate non-retinotopic areas of human visual cortex is true, it follows that northerns generally stick to weed beds, although they can be found at anytime and anywhere.', 'Once we know it is not true that if zip files are an industry-standard way of combining and compressing several files into one, then illusory contours activate non-retinotopic areas of human visual cortex, we also know that either emotions are electric currents or cell migration is an important process for organogenesis.', "It is rational to believe that either iraqi doctors says they've documented increased cases of leukemia and deformed babies or most flames contain gases.", "On the condition that iraqi doctors says they've documented increased cases of leukemia and deformed babies, it is definitely the case that if either emotions are electric currents or cell migration is an important process for organogenesis, then the statement that states northerns generally stick to weed beds, although they can be found at anytime and anywhere is false.", 'Once we know most flames contain gases, we also know that if either emotions are electric currents or cell migration is an important process for organogenesis, then the statement that states northerns generally stick to weed beds, although they can be found at anytime and anywhere is false.']
|
Either zip files are an industry-standard way of combining and compressing several files into one or either water potential is a quantitative measure of the binding energy of water in food or tiger mosquitoes are persistent, moderately aggressive biters. Should it be the case that either water potential is a quantitative measure of the binding energy of water in food or tiger mosquitoes are persistent, moderately aggressive biters, it follows that illusory contours activate non-retinotopic areas of human visual cortex. When it is not true that if zip files are an industry-standard way of combining and compressing several files into one, then illusory contours activate non-retinotopic areas of human visual cortex is true, it follows that northerns generally stick to weed beds, although they can be found at anytime and anywhere. Once we know it is not true that if zip files are an industry-standard way of combining and compressing several files into one, then illusory contours activate non-retinotopic areas of human visual cortex, we also know that either emotions are electric currents or cell migration is an important process for organogenesis. It is rational to believe that either iraqi doctors says they've documented increased cases of leukemia and deformed babies or most flames contain gases. On the condition that iraqi doctors says they've documented increased cases of leukemia and deformed babies, it is definitely the case that if either emotions are electric currents or cell migration is an important process for organogenesis, then the statement that states northerns generally stick to weed beds, although they can be found at anytime and anywhere is false. Once we know most flames contain gases, we also know that if either emotions are electric currents or cell migration is an important process for organogenesis, then the statement that states northerns generally stick to weed beds, although they can be found at anytime and anywhere is false.
|
illusory contours activate non-retinotopic areas of human visual cortex.
|
Illusory contours are an example of the perceptual grouping of local features into a global percept.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (Either [2] or [3].).
If [1], then [0]. [SC2-1]
If (Either [2] or [3].), then [0].
Therefore, [0].
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [1], then [0].).), then [4].
If (Not (If [1], then [0].).), then (Not [4].). [SC2-2]
Therefore, If [1], then [0]..
[SC2-2]
Hypothetical Syllogism:
If (Not (If [1], then [0].).), then (Either [5] or [6].).
If (Either [5] or [6].), then (Not [4].). [SC2-3]
Therefore, If (Not (If [1], then [0].).), then (Not [4].)..
[SC2-3]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If (Either [5] or [6].), then (Not [4].).).
If [8], then (If (Either [5] or [6].), then (Not [4].).).
Therefore, If (Either [5] or [6].), then (Not [4].)..
|
{0: 'Illusory contours activate non-retinotopic areas of human visual cortex.', 1: 'Zip files are an industry-standard way of combining and compressing several files into one.', 2: 'Water potential is a quantitative measure of the binding energy of water in food.', 3: 'Tiger mosquitoes are persistent, moderately aggressive biters.', 4: 'Northerns generally stick to weed beds, although they can be found at anytime and anywhere.', 5: 'Emotions are electric currents.', 6: 'Cell migration is an important process for organogenesis.', 7: "Iraqi doctors says they've documented increased cases of leukemia and deformed babies.", 8: 'Most flames contain gases.'}
| 4 |
3,877 |
['On the condition that some fraternities even perform acts of hazing that are both dangerous and illegal, it is definitely the case that if barons are aristocrats, then seismic waves propagate through a body at the sound velocity.', 'The claim that some fraternities even perform acts of hazing that are both dangerous and illegal is true.', 'One may reasonably assume that if religious sacredness is preserved in ritual, in dress and the arrangements of the places of worship, then if barons are aristocrats, then the claim that seismic waves propagate through a body at the sound velocity has no merit.', "Whenever it is true that chloride ions increase etch rates in etching solutions, 'if barons are aristocrats, then the claim that seismic waves propagate through a body at the sound velocity has no merit' is true.", 'On the condition that rainforests are a key element of global weather systems, it is definitely the case that either religious sacredness is preserved in ritual, in dress and the arrangements of the places of worship or chloride ions increase etch rates in etching solutions.', 'The statement that states rainforests are a key element of global weather systems is right.']
|
On the condition that some fraternities even perform acts of hazing that are both dangerous and illegal, it is definitely the case that if barons are aristocrats, then seismic waves propagate through a body at the sound velocity. The claim that some fraternities even perform acts of hazing that are both dangerous and illegal is true. One may reasonably assume that if religious sacredness is preserved in ritual, in dress and the arrangements of the places of worship, then if barons are aristocrats, then the claim that seismic waves propagate through a body at the sound velocity has no merit. Whenever it is true that chloride ions increase etch rates in etching solutions, 'if barons are aristocrats, then the claim that seismic waves propagate through a body at the sound velocity has no merit' is true. On the condition that rainforests are a key element of global weather systems, it is definitely the case that either religious sacredness is preserved in ritual, in dress and the arrangements of the places of worship or chloride ions increase etch rates in etching solutions. The statement that states rainforests are a key element of global weather systems is right.
|
The statement 'barons are aristocrats' can be considered false.
|
The statement 'barons are aristocrats' is true.
|
FALSE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [4], then (If [0], then [1].).
[4]
Therefore, If [0], then [1]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3]. [SC1-2]
If [2], then (If [0], then (Not [1].).).
If [3], then (If [0], then (Not [1].).).
Therefore, If [0], then (Not [1].)..
[SC1-2]
Modus Ponens:
If [5], then (Either [2] or [3].).
[5]
Therefore, Either [2] or [3]..
|
{0: 'Barons are aristocrats.', 1: 'Seismic waves propagate through a body at the sound velocity.', 2: 'Religious sacredness is preserved in ritual, in dress and the arrangements of the places of worship.', 3: 'Chloride ions increase etch rates in etching solutions.', 4: 'Some fraternities even perform acts of hazing that are both dangerous and illegal.', 5: 'Rainforests are a key element of global weather systems.'}
| 4 |
3,768 |
["Whenever it is true that either postmodernism says it is arrogant to judge another religion as wrong or inferior or iguanas have excellent vision and can see long distances, shapes, shadows, color and movement, 'a common ground is a basis' is true.", 'On the condition that some people mistakenly believe that if all young children handle their genitals, then if either postmodernism says it is arrogant to judge another religion as wrong or inferior or iguanas have excellent vision and can see long distances, shapes, shadows, color and movement, then the statement that states a common ground is a basis is false, it is definitely the case that either schools have buildings or platforms are stages.', 'It is not the case that either schools have buildings or platforms are stages.', 'Given that colonoscopy is safe procedure, with a low risk of complications, but potentially big rewards, it can be inferred that all young children handle their genitals.', "The statement 'colonoscopy is safe procedure, with a low risk of complications, but potentially big rewards' can be considered true."]
|
Whenever it is true that either postmodernism says it is arrogant to judge another religion as wrong or inferior or iguanas have excellent vision and can see long distances, shapes, shadows, color and movement, 'a common ground is a basis' is true. On the condition that some people mistakenly believe that if all young children handle their genitals, then if either postmodernism says it is arrogant to judge another religion as wrong or inferior or iguanas have excellent vision and can see long distances, shapes, shadows, color and movement, then the statement that states a common ground is a basis is false, it is definitely the case that either schools have buildings or platforms are stages. It is not the case that either schools have buildings or platforms are stages. Given that colonoscopy is safe procedure, with a low risk of complications, but potentially big rewards, it can be inferred that all young children handle their genitals. The statement 'colonoscopy is safe procedure, with a low risk of complications, but potentially big rewards' can be considered true.
|
It is not true that either postmodernism says it is arrogant to judge another religion as wrong or inferior or iguanas have excellent vision and can see long distances, shapes, shadows, color and movement.
|
It is not true that either postmodernism says it is arrogant to judge another religion as wrong or inferior or iguanas have excellent vision and can see long distances, shapes, shadows, color and movement.
|
TRUE
|
Reductio Ad Absurdum:
If (Either [0] or [1].), then [2].
If (Either [0] or [1].), then (Not [2].). [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC2-1]
Modus Ponens:
If [3], then (If (Either [0] or [1].), then (Not [2].).). [SC1-2]
[3] [SC2-2]
Therefore, If (Either [0] or [1].), then (Not [2].)..
[SC1-2]
Modus Tonens:
If (Not (If [3], then (If (Either [0] or [1].), then (Not [2].).).).), then (Either [4] or [5].).
Not (Either [4] or [5].).
Therefore, If [3], then (If (Either [0] or [1].), then (Not [2].).)..
[SC2-2]
Modus Ponens:
If [6], then [3].
[6]
Therefore, [3].
|
{0: 'Postmodernism says it is arrogant to judge another religion as wrong or inferior.', 1: 'Iguanas have excellent vision and can see long distances, shapes, shadows, color and movement.', 2: 'A common ground is a basis.', 3: 'All young children handle their genitals.', 4: 'Schools have buildings.', 5: 'Platforms are stages.', 6: 'Colonoscopy is safe procedure, with a low risk of complications, but potentially big rewards.'}
| 4 |
3,836 |
['Given that syncrometer testing makes it possible to know exactly which toxins cause the patient s cancer, it can be inferred that methanol is one of the safest and most environmentally sound fuels available.', 'It is a fact that either bathing is a good way to clean the skin and wash the toxins away or either central body consists of brain case and primary organ housing armored within a bone cage or syncrometer testing makes it possible to know exactly which toxins cause the patient s cancer.', 'Either one or both of these statements are true: cosmic dust is a cloud, or breast cancer is a malignant form of cancer that develops in breast tissue.', 'Provided that cosmic dust is a cloud, we know that if central body consists of brain case and primary organ housing armored within a bone cage, then methanol is one of the safest and most environmentally sound fuels available.', 'If breast cancer is a malignant form of cancer that develops in breast tissue, then if central body consists of brain case and primary organ housing armored within a bone cage, then methanol is one of the safest and most environmentally sound fuels available.', 'Given that bathing is a good way to clean the skin and wash the toxins away, it can be inferred that system mechanics play minor roles.', 'Assuming bathing is a good way to clean the skin and wash the toxins away, we know that the claim that system mechanics play minor roles does not correspond with reality.']
|
Given that syncrometer testing makes it possible to know exactly which toxins cause the patient s cancer, it can be inferred that methanol is one of the safest and most environmentally sound fuels available. It is a fact that either bathing is a good way to clean the skin and wash the toxins away or either central body consists of brain case and primary organ housing armored within a bone cage or syncrometer testing makes it possible to know exactly which toxins cause the patient s cancer. Either one or both of these statements are true: cosmic dust is a cloud, or breast cancer is a malignant form of cancer that develops in breast tissue. Provided that cosmic dust is a cloud, we know that if central body consists of brain case and primary organ housing armored within a bone cage, then methanol is one of the safest and most environmentally sound fuels available. If breast cancer is a malignant form of cancer that develops in breast tissue, then if central body consists of brain case and primary organ housing armored within a bone cage, then methanol is one of the safest and most environmentally sound fuels available. Given that bathing is a good way to clean the skin and wash the toxins away, it can be inferred that system mechanics play minor roles. Assuming bathing is a good way to clean the skin and wash the toxins away, we know that the claim that system mechanics play minor roles does not correspond with reality.
|
The claim that methanol is one of the safest and most environmentally sound fuels available holds true.
|
Methanol is metabolized primarily in the liver.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [5] or (Either [1] or [2].).
Not [5]. [SC2-2]
Therefore, Either [1] or [2]..
[SC2-2]
Reductio Ad Absurdum:
If [5], then [6].
If [5], then (Not [6].).
Therefore, Not [5]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If [1], then [0].).
If [4], then (If [1], then [0].).
Therefore, If [1], then [0]..
|
{0: 'Methanol is one of the safest and most environmentally sound fuels available.', 1: 'Central body consists of brain case and primary organ housing armored within a bone cage.', 2: 'Syncrometer testing makes it possible to know exactly which toxins cause the patient s cancer.', 3: 'Cosmic dust is a cloud.', 4: 'Breast cancer is a malignant form of cancer that develops in breast tissue.', 5: 'Bathing is a good way to clean the skin and wash the toxins away.', 6: 'System mechanics play minor roles.'}
| 4 |
3,561 |
['When the claim that selenium deficiency is associated with cardiomyopathy, muscular dystrophy and cystic fibrosis is false is true, it follows that most large cities have stock exchanges.', 'Those that suggest egg yolk is the customary emulsifying ingredient in hollandaise sauce are wrong.', 'Should it be the case that most snails have holes, it follows that either egg yolk is the customary emulsifying ingredient in hollandaise sauce or if the claim that selenium deficiency is associated with cardiomyopathy, muscular dystrophy and cystic fibrosis is false, then the claim that most large cities have stock exchanges does not reflect reality.', 'On the condition that testicles are smooth, oval- shaped, and somewhat firm to the touch, it is definitely the case that either egg yolk is the customary emulsifying ingredient in hollandaise sauce or if the claim that selenium deficiency is associated with cardiomyopathy, muscular dystrophy and cystic fibrosis is false, then the claim that most large cities have stock exchanges does not reflect reality.', 'It is a fact that either most frogs eat food or either most snails have holes or testicles are smooth, oval- shaped, and somewhat firm to the touch.', 'It is not the case that most frogs eat food.']
|
When the claim that selenium deficiency is associated with cardiomyopathy, muscular dystrophy and cystic fibrosis is false is true, it follows that most large cities have stock exchanges. Those that suggest egg yolk is the customary emulsifying ingredient in hollandaise sauce are wrong. Should it be the case that most snails have holes, it follows that either egg yolk is the customary emulsifying ingredient in hollandaise sauce or if the claim that selenium deficiency is associated with cardiomyopathy, muscular dystrophy and cystic fibrosis is false, then the claim that most large cities have stock exchanges does not reflect reality. On the condition that testicles are smooth, oval- shaped, and somewhat firm to the touch, it is definitely the case that either egg yolk is the customary emulsifying ingredient in hollandaise sauce or if the claim that selenium deficiency is associated with cardiomyopathy, muscular dystrophy and cystic fibrosis is false, then the claim that most large cities have stock exchanges does not reflect reality. It is a fact that either most frogs eat food or either most snails have holes or testicles are smooth, oval- shaped, and somewhat firm to the touch. It is not the case that most frogs eat food.
|
We can assume that selenium deficiency is associated with cardiomyopathy, muscular dystrophy and cystic fibrosis.
|
We can assume that selenium deficiency is associated with cardiomyopathy, muscular dystrophy and cystic fibrosis.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or (If (Not [0].), then (Not [1].).). [SC1-2]
Not [2].
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Disjunction Elimination:
Either [3] or [4]. [SC1-3]
If [3], then (Either [2] or (If (Not [0].), then (Not [1].).).).
If [4], then (Either [2] or (If (Not [0].), then (Not [1].).).).
Therefore, Either [2] or (If (Not [0].), then (Not [1].).)..
[SC1-3]
Disjunctive Syllogism:
Either [5] or (Either [3] or [4].).
Not [5].
Therefore, Either [3] or [4]..
|
{0: 'Selenium deficiency is associated with cardiomyopathy, muscular dystrophy and cystic fibrosis.', 1: 'Most large cities have stock exchanges.', 2: 'Egg yolk is the customary emulsifying ingredient in hollandaise sauce.', 3: 'Most snails have holes.', 4: 'Testicles are smooth, oval- shaped, and somewhat firm to the touch.', 5: 'Most frogs eat food.'}
| 4 |
3,892 |
["Whenever it is true that construction is commercial enterprises, 'either some tadpoles hatch on land and then are transported to streams by their parents or eagles can sight their prey while soaring high in the air' is true.", 'It is a fact that either some people live in houses or dogs are den animals, and they like small, enclosed places.', 'Assuming some people live in houses, we know that either siblings create identities or construction is commercial enterprises.', 'Assuming it is a common misconception that if siblings create identities, then either some tadpoles hatch on land and then are transported to streams by their parents or eagles can sight their prey while soaring high in the air, we know that foul is violations.', "When it is a common misconception that if siblings create identities, then either some tadpoles hatch on land and then are transported to streams by their parents or eagles can sight their prey while soaring high in the air is true, it follows that the statement that 'foul is violations' is incorrect.", "We know that at least one of two things is true: if red clover is a short-lived perennial legume that's a key element in potato rotations, then chartreuse is liqueurs, or if dogs are den animals, and they like small, enclosed places, then either siblings create identities or construction is commercial enterprises.", "The statement, if red clover is a short-lived perennial legume that's a key element in potato rotations, then chartreuse is liqueurs, does not hold."]
|
Whenever it is true that construction is commercial enterprises, 'either some tadpoles hatch on land and then are transported to streams by their parents or eagles can sight their prey while soaring high in the air' is true. It is a fact that either some people live in houses or dogs are den animals, and they like small, enclosed places. Assuming some people live in houses, we know that either siblings create identities or construction is commercial enterprises. Assuming it is a common misconception that if siblings create identities, then either some tadpoles hatch on land and then are transported to streams by their parents or eagles can sight their prey while soaring high in the air, we know that foul is violations. When it is a common misconception that if siblings create identities, then either some tadpoles hatch on land and then are transported to streams by their parents or eagles can sight their prey while soaring high in the air is true, it follows that the statement that 'foul is violations' is incorrect. We know that at least one of two things is true: if red clover is a short-lived perennial legume that's a key element in potato rotations, then chartreuse is liqueurs, or if dogs are den animals, and they like small, enclosed places, then either siblings create identities or construction is commercial enterprises. The statement, if red clover is a short-lived perennial legume that's a key element in potato rotations, then chartreuse is liqueurs, does not hold.
|
We know that either some tadpoles hatch on land and then are transported to streams by their parents or eagles can sight their prey while soaring high in the air.
|
Some people mistakenly believe that either some tadpoles hatch on land and then are transported to streams by their parents or eagles can sight their prey while soaring high in the air.
|
FALSE
|
Disjunction Elimination:
Either [2] or [3]. [SC1-1]
If [2], then (Either [0] or [1].). [SC2-1]
If [3], then (Either [0] or [1].).
Therefore, Either [0] or [1]..
[SC1-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Either [2] or [3].).
If [5], then (Either [2] or [3].). [SC3-2]
Therefore, Either [2] or [3]..
[SC3-2]
Disjunctive Syllogism:
Either (If [7], then [8].) or (If [5], then (Either [2] or [3].).).
Not (If [7], then [8].).
Therefore, If [5], then (Either [2] or [3].)..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [2], then (Either [0] or [1].).).), then [6].
If (Not (If [2], then (Either [0] or [1].).).), then (Not [6].).
Therefore, If [2], then (Either [0] or [1].)..
|
{0: 'Some tadpoles hatch on land and then are transported to streams by their parents.', 1: 'Eagles can sight their prey while soaring high in the air.', 2: 'Siblings create identities.', 3: 'Construction is commercial enterprises.', 4: 'Some people live in houses.', 5: 'Dogs are den animals, and they like small, enclosed places.', 6: 'Foul is violations.', 7: "Red clover is a short-lived perennial legume that's a key element in potato rotations.", 8: 'Chartreuse is liqueurs.'}
| 4 |
3,225 |
['The statement that states strategies include assessments is right.', "Whenever it is true that the statement that 'prickly heat can occur in children and adults who sweat profusely' is incorrect, 'spirits are the intelligent Beings of creation' is true.", 'The claim that spirits are the intelligent Beings of creation does not correspond with reality.', 'If those that suggest if strategies include assessments, then if prickly heat can occur in children and adults who sweat profusely, then environments provide experience are wrong, then bolivian farmers grow potatoes and wheat and raise cows, sheep, and llamas.', 'Should it be the case that those that suggest if strategies include assessments, then if prickly heat can occur in children and adults who sweat profusely, then environments provide experience are wrong, it follows that it is not the case that bolivian farmers grow potatoes and wheat and raise cows, sheep, and llamas.']
|
The statement that states strategies include assessments is right. Whenever it is true that the statement that 'prickly heat can occur in children and adults who sweat profusely' is incorrect, 'spirits are the intelligent Beings of creation' is true. The claim that spirits are the intelligent Beings of creation does not correspond with reality. If those that suggest if strategies include assessments, then if prickly heat can occur in children and adults who sweat profusely, then environments provide experience are wrong, then bolivian farmers grow potatoes and wheat and raise cows, sheep, and llamas. Should it be the case that those that suggest if strategies include assessments, then if prickly heat can occur in children and adults who sweat profusely, then environments provide experience are wrong, it follows that it is not the case that bolivian farmers grow potatoes and wheat and raise cows, sheep, and llamas.
|
It is the case that environments provide experience.
|
Some environments lead to evolution.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (If [1], then [0].). [SC1-2]
[2]
Therefore, If [1], then [0]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [2], then (If [1], then [0].).).), then [4].
If (Not (If [2], then (If [1], then [0].).).), then (Not [4].).
Therefore, If [2], then (If [1], then [0].)..
[SC2-1]
Modus Tonens:
If (Not [1].), then [3].
Not [3].
Therefore, [1].
|
{0: 'Environments provide experience.', 1: 'Prickly heat can occur in children and adults who sweat profusely.', 2: 'Strategies include assessments.', 3: 'Spirits are the intelligent Beings of creation.', 4: 'Bolivian farmers grow potatoes and wheat and raise cows, sheep, and llamas.'}
| 4 |
3,820 |
["The statement that 'kill can involve laughs' is incorrect.", 'The claim that koalas look like bears but they are marsupials, carrying their young in a pouch is false.', "The statement 'most spiders live only one or two years' can be considered true.", 'If most spiders live only one or two years, then neutrinos oscillate from one type to another without physical explanation.', 'When neutrinos oscillate from one type to another without physical explanation is true, it follows that either koalas look like bears but they are marsupials, carrying their young in a pouch or either kill can involve laughs or it is not the case that gullies can remove significant areas of land from high value cultivation.']
|
The statement that 'kill can involve laughs' is incorrect. The claim that koalas look like bears but they are marsupials, carrying their young in a pouch is false. The statement 'most spiders live only one or two years' can be considered true. If most spiders live only one or two years, then neutrinos oscillate from one type to another without physical explanation. When neutrinos oscillate from one type to another without physical explanation is true, it follows that either koalas look like bears but they are marsupials, carrying their young in a pouch or either kill can involve laughs or it is not the case that gullies can remove significant areas of land from high value cultivation.
|
It is not the case that gullies can remove significant areas of land from high value cultivation.
|
It is not the case that gullies can remove significant areas of land from high value cultivation.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [2] or (Either [1] or (Not [0].).). [SC1-2]
Not [2].
Therefore, Either [1] or (Not [0].)..
[SC1-2]
Modus Ponens:
If [3], then (Either [2] or (Either [1] or (Not [0].).).). [SC1-3]
[3]
Therefore, Either [2] or (Either [1] or (Not [0].).)..
[SC1-3]
Hypothetical Syllogism:
If [3], then [4].
If [4], then (Either [2] or (Either [1] or (Not [0].).).).
Therefore, If [3], then (Either [2] or (Either [1] or (Not [0].).).)..
|
{0: 'Gullies can remove significant areas of land from high value cultivation.', 1: 'Kill can involve laughs.', 2: 'Koalas look like bears but they are marsupials, carrying their young in a pouch.', 3: 'Most spiders live only one or two years.', 4: 'Neutrinos oscillate from one type to another without physical explanation.'}
| 4 |
3,369 |
['Should it be the case that the claim that either some bulbs create heat or fellowship is what happens when people become colleagues in the mission of the church is false, it follows that either bedrooms have (part) walls or some people even kidnap animals to sell as exotic pets.', 'One may reasonably assume that if the claim that either some bulbs create heat or fellowship is what happens when people become colleagues in the mission of the church is false, then the claim that either bedrooms have (part) walls or some people even kidnap animals to sell as exotic pets has no merit.', 'If some mammals use wood, then if some bulbs create heat, then food is a fuel used by living things to supply useful energy for movement and keeping warm.', 'It is fair to say that some mammals use wood.', 'At least one of two things is true: muscle contraction is a shortening, or if fellowship is what happens when people become colleagues in the mission of the church, then food is a fuel used by living things to supply useful energy for movement and keeping warm.', 'It is a common misconception that muscle contraction is a shortening.']
|
Should it be the case that the claim that either some bulbs create heat or fellowship is what happens when people become colleagues in the mission of the church is false, it follows that either bedrooms have (part) walls or some people even kidnap animals to sell as exotic pets. One may reasonably assume that if the claim that either some bulbs create heat or fellowship is what happens when people become colleagues in the mission of the church is false, then the claim that either bedrooms have (part) walls or some people even kidnap animals to sell as exotic pets has no merit. If some mammals use wood, then if some bulbs create heat, then food is a fuel used by living things to supply useful energy for movement and keeping warm. It is fair to say that some mammals use wood. At least one of two things is true: muscle contraction is a shortening, or if fellowship is what happens when people become colleagues in the mission of the church, then food is a fuel used by living things to supply useful energy for movement and keeping warm. It is a common misconception that muscle contraction is a shortening.
|
It is reasonable to believe that food is a fuel used by living things to supply useful energy for movement and keeping warm.
|
Most food contains proteins.
|
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]
Reductio Ad Absurdum:
If (Not (Either [1] or [2].).), then (Either [3] or [4].).
If (Not (Either [1] or [2].).), then (Not (Either [3] or [4].).).
Therefore, Either [1] or [2]..
[SC2-1]
Modus Ponens:
If [5], then (If [1], then [0].).
[5]
Therefore, If [1], then [0]..
[SC3-1]
Disjunctive Syllogism:
Either [6] or (If [2], then [0].).
Not [6].
Therefore, If [2], then [0]..
|
{0: 'Food is a fuel used by living things to supply useful energy for movement and keeping warm.', 1: 'Some bulbs create heat.', 2: 'Fellowship is what happens when people become colleagues in the mission of the church.', 3: 'Bedrooms have (part) walls.', 4: 'Some people even kidnap animals to sell as exotic pets.', 5: 'Some mammals use wood.', 6: 'Muscle contraction is a shortening.'}
| 4 |
3,681 |
['Once we know mite predators play significant roles, we also know that hedgehogs are nocturnal and some can get very irate if woken up during the day.', 'The claim that cats can wear stretch collars with flat tags that are riveted directly into the collar is false.', "When we know that the claim that either cats can wear stretch collars with flat tags that are riveted directly into the collar or the statement 'hedgehogs are nocturnal and some can get very irate if woken up during the day' can be considered false is false is true, it follows that animals reach certain minimum size.", 'It is rational to believe that either some echidnas have cord or most male orangutans have development.', "Whenever it is true that some echidnas have cord, 'it is a common misconception that animals reach certain minimum size' is true.", 'Once we know most male orangutans have development, we also know that it is a common misconception that animals reach certain minimum size.']
|
Once we know mite predators play significant roles, we also know that hedgehogs are nocturnal and some can get very irate if woken up during the day. The claim that cats can wear stretch collars with flat tags that are riveted directly into the collar is false. When we know that the claim that either cats can wear stretch collars with flat tags that are riveted directly into the collar or the statement 'hedgehogs are nocturnal and some can get very irate if woken up during the day' can be considered false is false is true, it follows that animals reach certain minimum size. It is rational to believe that either some echidnas have cord or most male orangutans have development. Whenever it is true that some echidnas have cord, 'it is a common misconception that animals reach certain minimum size' is true. Once we know most male orangutans have development, we also know that it is a common misconception that animals reach certain minimum size.
|
The claim that mite predators play significant roles does not reflect reality.
|
The claim that most mite predators play roles does not correspond with reality.
|
Uncertain
|
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].
Therefore, Not [1]..
[SC1-2]
Modus Tonens:
If (Not (Either [2] or (Not [1].).).), then [3].
Not [3]. [SC2-3]
Therefore, Either [2] or (Not [1].)..
[SC2-3]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Not [3].).
If [5], then (Not [3].).
Therefore, Not [3]..
|
{0: 'Mite predators play significant roles.', 1: 'Hedgehogs are nocturnal and some can get very irate if woken up during the day.', 2: 'Cats can wear stretch collars with flat tags that are riveted directly into the collar.', 3: 'Animals reach certain minimum size.', 4: 'Some echidnas have cord.', 5: 'Most male orangutans have development.'}
| 4 |
3,339 |
['When either renal failure is common or most bull sharks grow to size is true, it follows that states also have occupational health and safety laws and agencies.', 'Once we know either palladium is used in everything from cell phones to dental work, but auto makers dominate demand or some fireweeds have taproots, we also know that states also have occupational health and safety laws and agencies.', "Whenever it is true that the claim that either either renal failure is common or most bull sharks grow to size or either palladium is used in everything from cell phones to dental work, but auto makers dominate demand or some fireweeds have taproots does not correspond with reality, 'it is not true that either utility is an economic concept that describes consumer satisfaction or bluebirds have (part) cytoplasm' is true.", 'It is reasonable to believe that radiation is the method by which the sun heats the earth.', 'We know that either babies show early signs of hunger, even when still asleep or entire plants get nutrients.', 'Given that babies show early signs of hunger, even when still asleep, it can be inferred that if radiation is the method by which the sun heats the earth, then if the claim that either either renal failure is common or most bull sharks grow to size or either palladium is used in everything from cell phones to dental work, but auto makers dominate demand or some fireweeds have taproots does not correspond with reality, then either utility is an economic concept that describes consumer satisfaction or bluebirds have (part) cytoplasm.', 'If entire plants get nutrients, then if radiation is the method by which the sun heats the earth, then if the claim that either either renal failure is common or most bull sharks grow to size or either palladium is used in everything from cell phones to dental work, but auto makers dominate demand or some fireweeds have taproots does not correspond with reality, then either utility is an economic concept that describes consumer satisfaction or bluebirds have (part) cytoplasm.']
|
When either renal failure is common or most bull sharks grow to size is true, it follows that states also have occupational health and safety laws and agencies. Once we know either palladium is used in everything from cell phones to dental work, but auto makers dominate demand or some fireweeds have taproots, we also know that states also have occupational health and safety laws and agencies. Whenever it is true that the claim that either either renal failure is common or most bull sharks grow to size or either palladium is used in everything from cell phones to dental work, but auto makers dominate demand or some fireweeds have taproots does not correspond with reality, 'it is not true that either utility is an economic concept that describes consumer satisfaction or bluebirds have (part) cytoplasm' is true. It is reasonable to believe that radiation is the method by which the sun heats the earth. We know that either babies show early signs of hunger, even when still asleep or entire plants get nutrients. Given that babies show early signs of hunger, even when still asleep, it can be inferred that if radiation is the method by which the sun heats the earth, then if the claim that either either renal failure is common or most bull sharks grow to size or either palladium is used in everything from cell phones to dental work, but auto makers dominate demand or some fireweeds have taproots does not correspond with reality, then either utility is an economic concept that describes consumer satisfaction or bluebirds have (part) cytoplasm. If entire plants get nutrients, then if radiation is the method by which the sun heats the earth, then if the claim that either either renal failure is common or most bull sharks grow to size or either palladium is used in everything from cell phones to dental work, but auto makers dominate demand or some fireweeds have taproots does not correspond with reality, then either utility is an economic concept that describes consumer satisfaction or bluebirds have (part) cytoplasm.
|
It is reasonable to believe that states also have occupational health and safety laws and agencies.
|
Many states have their own equal credit opportunity laws.
|
Uncertain
|
Disjunction Elimination:
Either (Either [1] or [2].) or (Either [3] or [4].). [SC1-1]
If (Either [1] or [2].), then [0].
If (Either [3] or [4].), then [0].
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either (Either [1] or [2].) or (Either [3] or [4].).).), then (Either [5] or [6].). [SC1-2]
If (Not (Either (Either [1] or [2].) or (Either [3] or [4].).).), then (Not (Either [5] or [6].).).
Therefore, Either (Either [1] or [2].) or (Either [3] or [4].)..
[SC1-2]
Modus Ponens:
If [7], then (If (Not (Either (Either [1] or [2].) or (Either [3] or [4].).).), then (Either [5] or [6].).). [SC1-3]
[7]
Therefore, If (Not (Either (Either [1] or [2].) or (Either [3] or [4].).).), then (Either [5] or [6].)..
[SC1-3]
Disjunction Elimination:
Either [8] or [9].
If [8], then (If [7], then (If (Not (Either (Either [1] or [2].) or (Either [3] or [4].).).), then (Either [5] or [6].).).).
If [9], then (If [7], then (If (Not (Either (Either [1] or [2].) or (Either [3] or [4].).).), then (Either [5] or [6].).).).
Therefore, If [7], then (If (Not (Either (Either [1] or [2].) or (Either [3] or [4].).).), then (Either [5] or [6].).)..
|
{0: 'States also have occupational health and safety laws and agencies.', 1: 'Renal failure is common.', 2: 'Most bull sharks grow to size.', 3: 'Palladium is used in everything from cell phones to dental work, but auto makers dominate demand.', 4: 'Some fireweeds have taproots.', 5: 'Utility is an economic concept that describes consumer satisfaction.', 6: 'Bluebirds have (part) cytoplasm.', 7: 'Radiation is the method by which the sun heats the earth.', 8: 'Babies show early signs of hunger, even when still asleep.', 9: 'Entire plants get nutrients.'}
| 4 |
3,419 |
['Assuming humanists believe in using reason and compassion to solve problems, we know that it is not true that river pollution is a reflection of the ways in which the surrounding land is used.', 'When the claim that if humanists believe in using reason and compassion to solve problems, then river pollution is a reflection of the ways in which the surrounding land is used is false is true, it follows that if light energy is wasted, and the cells produce only a weak dribble of current, then trace minerals are crucial to proper endocrine function.', "If the statement that 'if the claim that if humanists believe in using reason and compassion to solve problems, then river pollution is a reflection of the ways in which the surrounding land is used is false, then the statement that 'if light energy is wasted, and the cells produce only a weak dribble of current, then trace minerals are crucial to proper endocrine function' is incorrect' is incorrect, then temperatures fall sharply at night.", 'Either one or both of these statements are true: rotors are part of jet engines, or the statement that states temperatures fall sharply at night is false.', 'The statement that states rotors are part of jet engines is false.']
|
Assuming humanists believe in using reason and compassion to solve problems, we know that it is not true that river pollution is a reflection of the ways in which the surrounding land is used. When the claim that if humanists believe in using reason and compassion to solve problems, then river pollution is a reflection of the ways in which the surrounding land is used is false is true, it follows that if light energy is wasted, and the cells produce only a weak dribble of current, then trace minerals are crucial to proper endocrine function. If the statement that 'if the claim that if humanists believe in using reason and compassion to solve problems, then river pollution is a reflection of the ways in which the surrounding land is used is false, then the statement that 'if light energy is wasted, and the cells produce only a weak dribble of current, then trace minerals are crucial to proper endocrine function' is incorrect' is incorrect, then temperatures fall sharply at night. Either one or both of these statements are true: rotors are part of jet engines, or the statement that states temperatures fall sharply at night is false. The statement that states rotors are part of jet engines is false.
|
Some people mistakenly believe that humanists believe in using reason and compassion to solve problems.
|
Some people mistakenly believe that humanists believe in using reason and compassion to solve problems.
|
TRUE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].).
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then (If [2], then [3].).
If (Not (If [0], then [1].).), then (Not (If [2], then [3].).). [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Modus Tonens:
If (Not (If (Not (If [0], then [1].).), then (Not (If [2], then [3].).).).), then [4].
Not [4]. [SC2-3]
Therefore, If (Not (If [0], then [1].).), then (Not (If [2], then [3].).)..
[SC2-3]
Disjunctive Syllogism:
Either [5] or (Not [4].).
Not [5].
Therefore, Not [4]..
|
{0: 'Humanists believe in using reason and compassion to solve problems.', 1: 'River pollution is a reflection of the ways in which the surrounding land is used.', 2: 'Light energy is wasted, and the cells produce only a weak dribble of current.', 3: 'Trace minerals are crucial to proper endocrine function.', 4: 'Temperatures fall sharply at night.', 5: 'Rotors are part of jet engines.'}
| 4 |
3,829 |
['Once we know hardness increases somewhat with higher atomic number, we also know that mechanized agriculture requires more fossil energy.', "We know that either natural law designates the parent as a child's primary caregiver and teacher or nuclear missiles are weapons that can be launched across great distances.", 'Provided that nuclear missiles are weapons that can be launched across great distances, we know that hardness increases somewhat with higher atomic number.', "Either one or both of these statements are true: either turkey vultures use current or some women have yeast infection, or if natural law designates the parent as a child's primary caregiver and teacher, then hardness increases somewhat with higher atomic number.", 'There is good reason to believe that either some emotional symptoms associate with disorder or if religious rituals are often re-enactments of a Myth , then affected rabbits are listless, anoretic, and dehydrated.', 'Given that some emotional symptoms associate with disorder, it can be inferred that those that suggest either turkey vultures use current or some women have yeast infection are wrong.', 'Should it be the case that if religious rituals are often re-enactments of a Myth , then affected rabbits are listless, anoretic, and dehydrated, it follows that those that suggest either turkey vultures use current or some women have yeast infection are wrong.']
|
Once we know hardness increases somewhat with higher atomic number, we also know that mechanized agriculture requires more fossil energy. We know that either natural law designates the parent as a child's primary caregiver and teacher or nuclear missiles are weapons that can be launched across great distances. Provided that nuclear missiles are weapons that can be launched across great distances, we know that hardness increases somewhat with higher atomic number. Either one or both of these statements are true: either turkey vultures use current or some women have yeast infection, or if natural law designates the parent as a child's primary caregiver and teacher, then hardness increases somewhat with higher atomic number. There is good reason to believe that either some emotional symptoms associate with disorder or if religious rituals are often re-enactments of a Myth , then affected rabbits are listless, anoretic, and dehydrated. Given that some emotional symptoms associate with disorder, it can be inferred that those that suggest either turkey vultures use current or some women have yeast infection are wrong. Should it be the case that if religious rituals are often re-enactments of a Myth , then affected rabbits are listless, anoretic, and dehydrated, it follows that those that suggest either turkey vultures use current or some women have yeast infection are wrong.
|
The idea that mechanized agriculture requires more fossil energy is true.
|
It is a common misconception that mechanized agriculture requires more fossil energy.
|
FALSE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then [1]. [SC2-2]
If [3], then [1].
Therefore, [1].
[SC2-2]
Disjunctive Syllogism:
Either (Either [4] or [5].) or (If [2], then [1].).
Not (Either [4] or [5].). [SC2-3]
Therefore, If [2], then [1]..
[SC2-3]
Disjunction Elimination:
Either [6] or (If [7], then [8].).
If [6], then (Not (Either [4] or [5].).).
If (If [7], then [8].), then (Not (Either [4] or [5].).).
Therefore, Not (Either [4] or [5].)..
|
{0: 'Mechanized agriculture requires more fossil energy.', 1: 'Hardness increases somewhat with higher atomic number.', 2: "Natural law designates the parent as a child's primary caregiver and teacher.", 3: 'Nuclear missiles are weapons that can be launched across great distances.', 4: 'Turkey vultures use current.', 5: 'Some women have yeast infection.', 6: 'Some emotional symptoms associate with disorder.', 7: 'Religious rituals are often re-enactments of a Myth .', 8: 'Affected rabbits are listless, anoretic, and dehydrated.'}
| 4 |
3,951 |
['Provided that many species attend aphids and coccids in strongly mutualistic associations, we know that most creatures hide from predators.', 'Once we know some people mistakenly believe that many species attend aphids and coccids in strongly mutualistic associations, we also know that if squirrels have (part) sterna, then mushrooms grow under trees.', "Whenever it is true that if squirrels have (part) sterna, then mushrooms grow under trees, 'a digestive tract is a duct' is true.", 'We know that at least one of two things is true: potassium is the major intracellular electrolyte, or some people mistakenly believe that a digestive tract is a duct.', 'It is not the case that potassium is the major intracellular electrolyte.']
|
Provided that many species attend aphids and coccids in strongly mutualistic associations, we know that most creatures hide from predators. Once we know some people mistakenly believe that many species attend aphids and coccids in strongly mutualistic associations, we also know that if squirrels have (part) sterna, then mushrooms grow under trees. Whenever it is true that if squirrels have (part) sterna, then mushrooms grow under trees, 'a digestive tract is a duct' is true. We know that at least one of two things is true: potassium is the major intracellular electrolyte, or some people mistakenly believe that a digestive tract is a duct. It is not the case that potassium is the major intracellular electrolyte.
|
The claim that most creatures hide from predators holds true.
|
The claim that most creatures hide from predators holds true.
|
TRUE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not [1].), then [2]. [SC1-2]
Not [2]. [SC2-2]
Therefore, [1].
[SC1-2]
Hypothetical Syllogism:
If (Not [1].), then (If [4], then [5].).
If (If [4], then [5].), then [2].
Therefore, If (Not [1].), then [2]..
[SC2-2]
Disjunctive Syllogism:
Either [3] or (Not [2].).
Not [3].
Therefore, Not [2]..
|
{0: 'Most creatures hide from predators.', 1: 'Many species attend aphids and coccids in strongly mutualistic associations.', 2: 'A digestive tract is a duct.', 3: 'Potassium is the major intracellular electrolyte.', 4: 'Squirrels have (part) sterna.', 5: 'Mushrooms grow under trees.'}
| 4 |
3,454 |
['On the condition that the claim that either if oral sex is performed on the young woman, then some people can put numbing creams on or wear double condoms or boys begin puberty does not reflect reality, it is definitely the case that garlic mustard is a rapidly spreading woodland weed.', "The statement 'garlic mustard is a rapidly spreading woodland weed' can be considered false.", 'We know that at least one of two things is true: most men infect with viruses, or smoking can involve coughing.', 'One may reasonably assume that if most men infect with viruses, then if if oral sex is performed on the young woman, then some people can put numbing creams on or wear double condoms, then tear ducts are vestigial.', 'Should it be the case that smoking can involve coughing, it follows that if if oral sex is performed on the young woman, then some people can put numbing creams on or wear double condoms, then tear ducts are vestigial.', "When the statement 'if boys begin puberty, then tear ducts are vestigial' can be considered false is true, it follows that some vegetables contain a larger amount of carbohydrate thus increasing calories.", 'Some people mistakenly believe that some vegetables contain a larger amount of carbohydrate thus increasing calories.']
|
On the condition that the claim that either if oral sex is performed on the young woman, then some people can put numbing creams on or wear double condoms or boys begin puberty does not reflect reality, it is definitely the case that garlic mustard is a rapidly spreading woodland weed. The statement 'garlic mustard is a rapidly spreading woodland weed' can be considered false. We know that at least one of two things is true: most men infect with viruses, or smoking can involve coughing. One may reasonably assume that if most men infect with viruses, then if if oral sex is performed on the young woman, then some people can put numbing creams on or wear double condoms, then tear ducts are vestigial. Should it be the case that smoking can involve coughing, it follows that if if oral sex is performed on the young woman, then some people can put numbing creams on or wear double condoms, then tear ducts are vestigial. When the statement 'if boys begin puberty, then tear ducts are vestigial' can be considered false is true, it follows that some vegetables contain a larger amount of carbohydrate thus increasing calories. Some people mistakenly believe that some vegetables contain a larger amount of carbohydrate thus increasing calories.
|
The statement that states tear ducts are vestigial is right.
|
The statement that states tear ducts are vestigial is right.
|
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]. [SC3-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either (If [1], then [2].) or [3].).), then [4].
Not [4].
Therefore, Either (If [1], then [2].) or [3]..
[SC2-1]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (If [1], then [2].), then [0].).
If [6], then (If (If [1], then [2].), then [0].).
Therefore, If (If [1], then [2].), then [0]..
[SC3-1]
Modus Tonens:
If (Not (If [3], then [0].).), then [7].
Not [7].
Therefore, If [3], then [0]..
|
{0: 'Tear ducts are vestigial.', 1: 'Oral sex is performed on the young woman.', 2: 'Some people can put numbing creams on or wear double condoms.', 3: 'Boys begin puberty.', 4: 'Garlic mustard is a rapidly spreading woodland weed.', 5: 'Most men infect with viruses.', 6: 'Smoking can involve coughing.', 7: 'Some vegetables contain a larger amount of carbohydrate thus increasing calories.'}
| 4 |
3,063 |
["Provided that the statement that 'canonisation is sanctification' is incorrect, we know that it is not the case that otters share the sea with whales, harbor seals, sea lions, and Dall porpoises.", "There is good reason to believe that either counseling is one of the specialty areas within the discipline of psychology or if the statement that 'if the statement that 'canonisation is sanctification' is incorrect, then otters share the sea with whales, harbor seals, sea lions, and Dall porpoises' is incorrect, then clinicians recognize that antisocial personality disorder is very difficult to treat.", 'We know that the claim that counseling is one of the specialty areas within the discipline of psychology is false.', "One may reasonably assume that if moldova isa thing, then if the statement that 'if the statement that 'canonisation is sanctification' is incorrect, then otters share the sea with whales, harbor seals, sea lions, and Dall porpoises' is incorrect, then the statement that 'clinicians recognize that antisocial personality disorder is very difficult to treat' is incorrect.", 'It is rational to agree that moldova isa thing.']
|
Provided that the statement that 'canonisation is sanctification' is incorrect, we know that it is not the case that otters share the sea with whales, harbor seals, sea lions, and Dall porpoises. There is good reason to believe that either counseling is one of the specialty areas within the discipline of psychology or if the statement that 'if the statement that 'canonisation is sanctification' is incorrect, then otters share the sea with whales, harbor seals, sea lions, and Dall porpoises' is incorrect, then clinicians recognize that antisocial personality disorder is very difficult to treat. We know that the claim that counseling is one of the specialty areas within the discipline of psychology is false. One may reasonably assume that if moldova isa thing, then if the statement that 'if the statement that 'canonisation is sanctification' is incorrect, then otters share the sea with whales, harbor seals, sea lions, and Dall porpoises' is incorrect, then the statement that 'clinicians recognize that antisocial personality disorder is very difficult to treat' is incorrect. It is rational to agree that moldova isa thing.
|
It is true that canonisation is sanctification.
|
It is true that canonisation is sanctification.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then [1].).), then [2]. [SC1-2]
If (Not (If (Not [0].), then [1].).), then (Not [2].). [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunctive Syllogism:
Either [3] or (If (Not (If (Not [0].), then [1].).), then [2].).
Not [3].
Therefore, If (Not (If (Not [0].), then [1].).), then [2]..
[SC2-2]
Modus Ponens:
If [4], then (If (Not (If (Not [0].), then [1].).), then (Not [2].).).
[4]
Therefore, If (Not (If (Not [0].), then [1].).), then (Not [2].)..
|
{0: 'Canonisation is sanctification.', 1: 'Otters share the sea with whales, harbor seals, sea lions, and Dall porpoises.', 2: 'Clinicians recognize that antisocial personality disorder is very difficult to treat.', 3: 'Counseling is one of the specialty areas within the discipline of psychology.', 4: 'Moldova isa thing.'}
| 4 |
3,759 |
["So long as red clover is the most widely used in frost seeding and has proven to be good in establishment, 'it is not true that some lunar rocks contain high concentrations of the dioxide' is true.", 'On the condition that it is a common misconception that red clover is the most widely used in frost seeding and has proven to be good in establishment, it is definitely the case that the claim that many neonatal caregivers are afraid of bilirubin has no merit.', 'It is not true that bobcat kittens weigh ounces.', "When glue boards lose their effectiveness in dusty areas unless covered is true, it follows that if the notion that 'if it is a common misconception that red clover is the most widely used in frost seeding and has proven to be good in establishment, then many neonatal caregivers are afraid of bilirubin' is untrue, then bobcat kittens weigh ounces.", 'It is a simple truth that glue boards lose their effectiveness in dusty areas unless covered.']
|
So long as red clover is the most widely used in frost seeding and has proven to be good in establishment, 'it is not true that some lunar rocks contain high concentrations of the dioxide' is true. On the condition that it is a common misconception that red clover is the most widely used in frost seeding and has proven to be good in establishment, it is definitely the case that the claim that many neonatal caregivers are afraid of bilirubin has no merit. It is not true that bobcat kittens weigh ounces. When glue boards lose their effectiveness in dusty areas unless covered is true, it follows that if the notion that 'if it is a common misconception that red clover is the most widely used in frost seeding and has proven to be good in establishment, then many neonatal caregivers are afraid of bilirubin' is untrue, then bobcat kittens weigh ounces. It is a simple truth that glue boards lose their effectiveness in dusty areas unless covered.
|
It is not true that some lunar rocks contain high concentrations of the dioxide.
|
We can assume that some lunar rocks contain high concentrations of the dioxide.
|
FALSE
|
Modus Ponens:
If [1], then (Not [0].).
[1] [SC2-1]
Therefore, Not [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then [2]. [SC1-2]
If (Not [1].), then (Not [2].).
Therefore, [1].
[SC1-2]
Modus Tonens:
If (Not (If (Not [1].), then [2].).), then [3]. [SC1-3]
Not [3].
Therefore, If (Not [1].), then [2]..
[SC1-3]
Modus Ponens:
If [4], then (If (Not (If (Not [1].), then [2].).), then [3].).
[4]
Therefore, If (Not (If (Not [1].), then [2].).), then [3]..
|
{0: 'Some lunar rocks contain high concentrations of the dioxide.', 1: 'Red clover is the most widely used in frost seeding and has proven to be good in establishment.', 2: 'Many neonatal caregivers are afraid of bilirubin.', 3: 'Bobcat kittens weigh ounces.', 4: 'Glue boards lose their effectiveness in dusty areas unless covered.'}
| 4 |
3,360 |
["The notion that 'either carbohydrates are either simple like sugar, or complex like starch or falcons has-part claws' is untrue.", 'There is good reason to believe that either either cheetahs eat mammalian herbivores or factors affect atmospheres or either bags are located in shopping malls or unions work for equal treatment and fight discrimination.', 'Given that either bags are located in shopping malls or unions work for equal treatment and fight discrimination, it can be inferred that if the claim that tortoises prefer sandy habitats does not reflect reality, then either carbohydrates are either simple like sugar, or complex like starch or falcons has-part claws.', 'One may reasonably assume that if either cheetahs eat mammalian herbivores or factors affect atmospheres, then if alcoholism is an illness, just like asthma or diabetes , then heat produced by the digestive process affects deer behavior.', 'It is a fact that either kangaroos have (part) cell membranes or most parents protect babies.', 'When kangaroos have (part) cell membranes is true, it follows that if if alcoholism is an illness, just like asthma or diabetes , then heat produced by the digestive process affects deer behavior, then if the claim that tortoises prefer sandy habitats does not reflect reality, then either carbohydrates are either simple like sugar, or complex like starch or falcons has-part claws.', 'Should it be the case that most parents protect babies, it follows that if if alcoholism is an illness, just like asthma or diabetes , then heat produced by the digestive process affects deer behavior, then if the claim that tortoises prefer sandy habitats does not reflect reality, then either carbohydrates are either simple like sugar, or complex like starch or falcons has-part claws.']
|
The notion that 'either carbohydrates are either simple like sugar, or complex like starch or falcons has-part claws' is untrue. There is good reason to believe that either either cheetahs eat mammalian herbivores or factors affect atmospheres or either bags are located in shopping malls or unions work for equal treatment and fight discrimination. Given that either bags are located in shopping malls or unions work for equal treatment and fight discrimination, it can be inferred that if the claim that tortoises prefer sandy habitats does not reflect reality, then either carbohydrates are either simple like sugar, or complex like starch or falcons has-part claws. One may reasonably assume that if either cheetahs eat mammalian herbivores or factors affect atmospheres, then if alcoholism is an illness, just like asthma or diabetes , then heat produced by the digestive process affects deer behavior. It is a fact that either kangaroos have (part) cell membranes or most parents protect babies. When kangaroos have (part) cell membranes is true, it follows that if if alcoholism is an illness, just like asthma or diabetes , then heat produced by the digestive process affects deer behavior, then if the claim that tortoises prefer sandy habitats does not reflect reality, then either carbohydrates are either simple like sugar, or complex like starch or falcons has-part claws. Should it be the case that most parents protect babies, it follows that if if alcoholism is an illness, just like asthma or diabetes , then heat produced by the digestive process affects deer behavior, then if the claim that tortoises prefer sandy habitats does not reflect reality, then either carbohydrates are either simple like sugar, or complex like starch or falcons has-part claws.
|
We can assume that tortoises prefer sandy habitats.
|
The statement that states tortoises prefer sandy habitats is false.
|
FALSE
|
Modus Tonens:
If (Not [0].), then (Either [1] or [2].). [SC1-1]
Not (Either [1] or [2].).
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [3] or [4].) or (Either [5] or [6].).
If (Either [3] or [4].), then (If (Not [0].), then (Either [1] or [2].).). [SC2-2]
If (Either [5] or [6].), then (If (Not [0].), then (Either [1] or [2].).).
Therefore, If (Not [0].), then (Either [1] or [2].)..
[SC2-2]
Hypothetical Syllogism:
If (Either [3] or [4].), then (If [7], then [8].).
If (If [7], then [8].), then (If (Not [0].), then (Either [1] or [2].).). [SC2-3]
Therefore, If (Either [3] or [4].), then (If (Not [0].), then (Either [1] or [2].).)..
[SC2-3]
Disjunction Elimination:
Either [9] or [10].
If [9], then (If (If [7], then [8].), then (If (Not [0].), then (Either [1] or [2].).).).
If [10], then (If (If [7], then [8].), then (If (Not [0].), then (Either [1] or [2].).).).
Therefore, If (If [7], then [8].), then (If (Not [0].), then (Either [1] or [2].).)..
|
{0: 'Tortoises prefer sandy habitats.', 1: 'Carbohydrates are either simple like sugar, or complex like starch.', 2: 'Falcons has-part claws.', 3: 'Cheetahs eat mammalian herbivores.', 4: 'Factors affect atmospheres.', 5: 'Bags are located in shopping malls.', 6: 'Unions work for equal treatment and fight discrimination.', 7: 'Alcoholism is an illness, just like asthma or diabetes .', 8: 'Heat produced by the digestive process affects deer behavior.', 9: 'Kangaroos have (part) cell membranes.', 10: 'Most parents protect babies.'}
| 4 |
3,237 |
['We know that at least one of two things is true: corporate building happens through connectedness, or if inflation hurts people on fixed-incomes because it means they can buy less, then pharmaceutical companies base their prices on local supply and demand.', 'Assuming corporate building happens through connectedness, we know that either golf has (part) second periods or mammals associated with wetlands include muskrat, otter, and beaver.', 'Assuming if inflation hurts people on fixed-incomes because it means they can buy less, then pharmaceutical companies base their prices on local supply and demand, we know that either golf has (part) second periods or mammals associated with wetlands include muskrat, otter, and beaver.', 'There is good reason to believe that either vinegar lasts indefinitely in the pantry without refrigeration or rodeo is a great sport with dedicated, talented performers.', 'When vinegar lasts indefinitely in the pantry without refrigeration is true, it follows that if golf has (part) second periods, then koalas are very good swimmers.', 'Provided that rodeo is a great sport with dedicated, talented performers, we know that if golf has (part) second periods, then koalas are very good swimmers.', 'If we know that the claim that if mammals associated with wetlands include muskrat, otter, and beaver, then koalas are very good swimmers is false, then most children recover from chicken pox uneventfully in less than two weeks.', 'When we know that the claim that if mammals associated with wetlands include muskrat, otter, and beaver, then koalas are very good swimmers is false is true, it follows that the statement, most children recover from chicken pox uneventfully in less than two weeks, does not hold.']
|
We know that at least one of two things is true: corporate building happens through connectedness, or if inflation hurts people on fixed-incomes because it means they can buy less, then pharmaceutical companies base their prices on local supply and demand. Assuming corporate building happens through connectedness, we know that either golf has (part) second periods or mammals associated with wetlands include muskrat, otter, and beaver. Assuming if inflation hurts people on fixed-incomes because it means they can buy less, then pharmaceutical companies base their prices on local supply and demand, we know that either golf has (part) second periods or mammals associated with wetlands include muskrat, otter, and beaver. There is good reason to believe that either vinegar lasts indefinitely in the pantry without refrigeration or rodeo is a great sport with dedicated, talented performers. When vinegar lasts indefinitely in the pantry without refrigeration is true, it follows that if golf has (part) second periods, then koalas are very good swimmers. Provided that rodeo is a great sport with dedicated, talented performers, we know that if golf has (part) second periods, then koalas are very good swimmers. If we know that the claim that if mammals associated with wetlands include muskrat, otter, and beaver, then koalas are very good swimmers is false, then most children recover from chicken pox uneventfully in less than two weeks. When we know that the claim that if mammals associated with wetlands include muskrat, otter, and beaver, then koalas are very good swimmers is false is true, it follows that the statement, most children recover from chicken pox uneventfully in less than two weeks, does not hold.
|
It is rational to agree that koalas are very good swimmers.
|
Some koalas reach maturity.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [6] or (If [7], then [8].).
If [6], then (Either [1] or [2].).
If (If [7], then [8].), then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If [1], then [0].).
If [4], then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then [0].).), then [5].
If (Not (If [2], then [0].).), then (Not [5].).
Therefore, If [2], then [0]..
|
{0: 'Koalas are very good swimmers.', 1: 'Golf has (part) second periods.', 2: 'Mammals associated with wetlands include muskrat, otter, and beaver.', 3: 'Vinegar lasts indefinitely in the pantry without refrigeration.', 4: 'Rodeo is a great sport with dedicated, talented performers.', 5: 'Most children recover from chicken pox uneventfully in less than two weeks.', 6: 'Corporate building happens through connectedness.', 7: 'Inflation hurts people on fixed-incomes because it means they can buy less.', 8: 'Pharmaceutical companies base their prices on local supply and demand.'}
| 4 |
3,112 |
['Either one or both of these statements are true: some rainwater has kinetic energy, or some mushrooms produce mushrooms.', 'On the condition that some rainwater has kinetic energy, it is definitely the case that either if meerkats have middle ear bones, then limitations affect population growth or some cysts cause kidney damage.', 'One may reasonably assume that if some mushrooms produce mushrooms, then either if meerkats have middle ear bones, then limitations affect population growth or some cysts cause kidney damage.', 'Given that if pigs weigh about two and a half pounds at birth, and usually double their weight the first week, then hot lather comes from volcanoes, and when it cools, it turns into rocks, it can be inferred that if if meerkats have middle ear bones, then limitations affect population growth, then banks dominate the asset management industry.', 'Assuming pigs weigh about two and a half pounds at birth, and usually double their weight the first week, we know that hot lather comes from volcanoes, and when it cools, it turns into rocks.', 'When the claim that if some cysts cause kidney damage, then banks dominate the asset management industry is false is true, it follows that river blindness is endemic in many parts of Africa and South America.', 'The statement, river blindness is endemic in many parts of Africa and South America, does not hold.']
|
Either one or both of these statements are true: some rainwater has kinetic energy, or some mushrooms produce mushrooms. On the condition that some rainwater has kinetic energy, it is definitely the case that either if meerkats have middle ear bones, then limitations affect population growth or some cysts cause kidney damage. One may reasonably assume that if some mushrooms produce mushrooms, then either if meerkats have middle ear bones, then limitations affect population growth or some cysts cause kidney damage. Given that if pigs weigh about two and a half pounds at birth, and usually double their weight the first week, then hot lather comes from volcanoes, and when it cools, it turns into rocks, it can be inferred that if if meerkats have middle ear bones, then limitations affect population growth, then banks dominate the asset management industry. Assuming pigs weigh about two and a half pounds at birth, and usually double their weight the first week, we know that hot lather comes from volcanoes, and when it cools, it turns into rocks. When the claim that if some cysts cause kidney damage, then banks dominate the asset management industry is false is true, it follows that river blindness is endemic in many parts of Africa and South America. The statement, river blindness is endemic in many parts of Africa and South America, does not hold.
|
The claim that banks dominate the asset management industry holds true.
|
The claim that banks dominate the asset management industry holds true.
|
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]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Either (If [1], then [2].) or [3].).
If [5], then (Either (If [1], then [2].) or [3].).
Therefore, Either (If [1], then [2].) or [3]..
[SC2-1]
Modus Ponens:
If (If [7], then [8].), then (If (If [1], then [2].), then [0].).
If [7], then [8].
Therefore, If (If [1], then [2].), then [0]..
[SC3-1]
Modus Tonens:
If (Not (If [3], then [0].).), then [6].
Not [6].
Therefore, If [3], then [0]..
|
{0: 'Banks dominate the asset management industry.', 1: 'Meerkats have middle ear bones.', 2: 'Limitations affect population growth.', 3: 'Some cysts cause kidney damage.', 4: 'Some rainwater has kinetic energy.', 5: 'Some mushrooms produce mushrooms.', 6: 'River blindness is endemic in many parts of Africa and South America.', 7: 'Pigs weigh about two and a half pounds at birth, and usually double their weight the first week.', 8: 'Hot lather comes from volcanoes, and when it cools, it turns into rocks.'}
| 4 |
3,640 |
['Once we know governments provide the policy and fiscal framework which motivates private investment, we also know that magnetic fields are the same as electric fields.', 'It is rational to believe that either naturalists believe in rubbing evening primrose oil onto the cervix or governments provide the policy and fiscal framework which motivates private investment.', 'Some people mistakenly believe that naturalists believe in rubbing evening primrose oil onto the cervix.', 'On the condition that it is not true that if magnetic fields are the same as electric fields, then either scientists use hypotheses or creatine also plays an important role in nerve cell function, it is definitely the case that if some people believe baptism can be accomplished by sprinking or pouring, then an ukulele is a guitar.', 'The claim that if some people believe baptism can be accomplished by sprinking or pouring, then an ukulele is a guitar does not correspond with reality.']
|
Once we know governments provide the policy and fiscal framework which motivates private investment, we also know that magnetic fields are the same as electric fields. It is rational to believe that either naturalists believe in rubbing evening primrose oil onto the cervix or governments provide the policy and fiscal framework which motivates private investment. Some people mistakenly believe that naturalists believe in rubbing evening primrose oil onto the cervix. On the condition that it is not true that if magnetic fields are the same as electric fields, then either scientists use hypotheses or creatine also plays an important role in nerve cell function, it is definitely the case that if some people believe baptism can be accomplished by sprinking or pouring, then an ukulele is a guitar. The claim that if some people believe baptism can be accomplished by sprinking or pouring, then an ukulele is a guitar does not correspond with reality.
|
It is a fact that either scientists use hypotheses or creatine also plays an important role in nerve cell function.
|
It is a fact that either scientists use hypotheses or creatine also plays an important role in nerve cell function.
|
TRUE
|
Modus Ponens:
If [2], then (Either [0] or [1].). [SC1-1]
[2] [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Hypothetical Syllogism:
If [2], then [3].
If [3], then (Either [0] or [1].). [SC2-2]
Therefore, If [2], then (Either [0] or [1].)..
[SC2-2]
Modus Tonens:
If (Not (If [3], then (Either [0] or [1].).).), then (If [5], then [6].).
Not (If [5], then [6].).
Therefore, If [3], then (Either [0] or [1].)..
[SC2-1]
Disjunctive Syllogism:
Either [4] or [2].
Not [4].
Therefore, [2].
|
{0: 'Scientists use hypotheses.', 1: 'Creatine also plays an important role in nerve cell function.', 2: 'Governments provide the policy and fiscal framework which motivates private investment.', 3: 'Magnetic fields are the same as electric fields.', 4: 'Naturalists believe in rubbing evening primrose oil onto the cervix.', 5: 'Some people believe baptism can be accomplished by sprinking or pouring.', 6: 'An ukulele is a guitar.'}
| 4 |
3,532 |
["When most viral hepatitis leads to liver damage is true, it follows that if some malaria lasts for months, then protein is composed of amino acids and serve as the body's workhorses.", "If carps have (part) tail fins, then if some malaria lasts for months, then protein is composed of amino acids and serve as the body's workhorses.", 'On the condition that the statement, either most viral hepatitis leads to liver damage or carps have (part) tail fins, does not hold, it is definitely the case that some people mistakenly believe that witch hunts are about images and social control.', 'On the condition that biomedical engineers develop aids for the deaf and blind, it is definitely the case that if the statement, either most viral hepatitis leads to liver damage or carps have (part) tail fins, does not hold, then witch hunts are about images and social control.', 'Provided that some cervixes produce fluid, we know that if the statement, either most viral hepatitis leads to liver damage or carps have (part) tail fins, does not hold, then witch hunts are about images and social control.', "So long as some people feel the effects of aging earlier than others, 'either biomedical engineers develop aids for the deaf and blind or some cervixes produce fluid' is true.", 'Those that suggest some people feel the effects of aging earlier than others are right.']
|
When most viral hepatitis leads to liver damage is true, it follows that if some malaria lasts for months, then protein is composed of amino acids and serve as the body's workhorses. If carps have (part) tail fins, then if some malaria lasts for months, then protein is composed of amino acids and serve as the body's workhorses. On the condition that the statement, either most viral hepatitis leads to liver damage or carps have (part) tail fins, does not hold, it is definitely the case that some people mistakenly believe that witch hunts are about images and social control. On the condition that biomedical engineers develop aids for the deaf and blind, it is definitely the case that if the statement, either most viral hepatitis leads to liver damage or carps have (part) tail fins, does not hold, then witch hunts are about images and social control. Provided that some cervixes produce fluid, we know that if the statement, either most viral hepatitis leads to liver damage or carps have (part) tail fins, does not hold, then witch hunts are about images and social control. So long as some people feel the effects of aging earlier than others, 'either biomedical engineers develop aids for the deaf and blind or some cervixes produce fluid' is true. Those that suggest some people feel the effects of aging earlier than others are right.
|
If some malaria lasts for months, then protein is composed of amino acids and serve as the body's workhorses.
|
If some malaria lasts for months, then protein is composed of amino acids and serve as the body's workhorses.
|
TRUE
|
Disjunction Elimination:
Either [2] or [3]. [SC1-1]
If [2], then (If [0], then [1].).
If [3], then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [2] or [3].).), then [4]. [SC1-2]
If (Not (Either [2] or [3].).), then (Not [4].).
Therefore, Either [2] or [3]..
[SC1-2]
Disjunction Elimination:
Either [5] or [6]. [SC1-3]
If [5], then (If (Not (Either [2] or [3].).), then [4].).
If [6], then (If (Not (Either [2] or [3].).), then [4].).
Therefore, If (Not (Either [2] or [3].).), then [4]..
[SC1-3]
Modus Ponens:
If [7], then (Either [5] or [6].).
[7]
Therefore, Either [5] or [6]..
|
{0: 'Some malaria lasts for months.', 1: "Protein is composed of amino acids and serve as the body's workhorses.", 2: 'Most viral hepatitis leads to liver damage.', 3: 'Carps have (part) tail fins.', 4: 'Witch hunts are about images and social control.', 5: 'Biomedical engineers develop aids for the deaf and blind.', 6: 'Some cervixes produce fluid.', 7: 'Some people feel the effects of aging earlier than others.'}
| 4 |
3,126 |
["So long as some people mistakenly believe that if the notion that 'if most states have statutes and regulations governing licensure to practice medicine, then adenoviruses are a common cause of gastroenteritis ' is untrue, then occupancy is a residence, 'the statement 'most carnivores seek prey' can be considered false' is true.", 'It is a fact that either either separation is based on electrical charge and molecular weight of the enzymes or hamsters have runny noses or precipitation reaches surfaces.', 'Should it be the case that either separation is based on electrical charge and molecular weight of the enzymes or hamsters have runny noses, it follows that those that suggest occupancy is a residence are wrong.', 'On the condition that precipitation reaches surfaces, it is definitely the case that those that suggest occupancy is a residence are wrong.', "So long as some people mistakenly believe that if the notion that 'if most states have statutes and regulations governing licensure to practice medicine, then adenoviruses are a common cause of gastroenteritis ' is untrue, then occupancy is a residence, 'if informatics is the study and use of computers and information in health care, then kidney stones form from chemicals in the urine' is true.", 'Given that if informatics is the study and use of computers and information in health care, then kidney stones form from chemicals in the urine, it can be inferred that most carnivores seek prey.']
|
So long as some people mistakenly believe that if the notion that 'if most states have statutes and regulations governing licensure to practice medicine, then adenoviruses are a common cause of gastroenteritis ' is untrue, then occupancy is a residence, 'the statement 'most carnivores seek prey' can be considered false' is true. It is a fact that either either separation is based on electrical charge and molecular weight of the enzymes or hamsters have runny noses or precipitation reaches surfaces. Should it be the case that either separation is based on electrical charge and molecular weight of the enzymes or hamsters have runny noses, it follows that those that suggest occupancy is a residence are wrong. On the condition that precipitation reaches surfaces, it is definitely the case that those that suggest occupancy is a residence are wrong. So long as some people mistakenly believe that if the notion that 'if most states have statutes and regulations governing licensure to practice medicine, then adenoviruses are a common cause of gastroenteritis ' is untrue, then occupancy is a residence, 'if informatics is the study and use of computers and information in health care, then kidney stones form from chemicals in the urine' is true. Given that if informatics is the study and use of computers and information in health care, then kidney stones form from chemicals in the urine, it can be inferred that most carnivores seek prey.
|
If most states have statutes and regulations governing licensure to practice medicine, then adenoviruses are a common cause of gastroenteritis .
|
Given that most states have statutes and regulations governing licensure to practice medicine, it can be inferred that adenoviruses cause illnesses.
|
Uncertain
|
Modus Tonens:
If (Not (If [0], then [1].).), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not (If [0], then [1].).), then [2].).), then [6]. [SC1-2]
If (Not (If (Not (If [0], then [1].).), then [2].).), then (Not [6].).
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC1-2]
Hypothetical Syllogism:
If (Not (If (Not (If [0], then [1].).), then [2].).), then (If [7], then [8].).
If (If [7], then [8].), then [6].
Therefore, If (Not (If (Not (If [0], then [1].).), then [2].).), then [6]..
[SC2-1]
Disjunction Elimination:
Either (Either [3] or [4].) or [5].
If (Either [3] or [4].), then (Not [2].).
If [5], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Most states have statutes and regulations governing licensure to practice medicine.', 1: 'Adenoviruses are a common cause of gastroenteritis .', 2: 'Occupancy is a residence.', 3: 'Separation is based on electrical charge and molecular weight of the enzymes.', 4: 'Hamsters have runny noses.', 5: 'Precipitation reaches surfaces.', 6: 'Most carnivores seek prey.', 7: 'Informatics is the study and use of computers and information in health care.', 8: 'Kidney stones form from chemicals in the urine.'}
| 4 |
3,259 |
['Either sleep also allows the joints to rest or either teraFLOPs are the total amount of calculations needed to complete a work unit or conservatism seems to be a conglomerate of opinions on race.', "The statement 'sleep also allows the joints to rest' can be considered false.", 'When bacteria survive in the knots and are readily washed off at all times of the year is true, it follows that if teraFLOPs are the total amount of calculations needed to complete a work unit, then the statement that states pigments are light-fast and made specifically for hand papermaking is false.', 'The claim that bacteria survive in the knots and are readily washed off at all times of the year is true.', 'We know that either values depend on factors or if conservatism seems to be a conglomerate of opinions on race, then the statement that states pigments are light-fast and made specifically for hand papermaking is false.', "The statement that 'values depend on factors' is incorrect."]
|
Either sleep also allows the joints to rest or either teraFLOPs are the total amount of calculations needed to complete a work unit or conservatism seems to be a conglomerate of opinions on race. The statement 'sleep also allows the joints to rest' can be considered false. When bacteria survive in the knots and are readily washed off at all times of the year is true, it follows that if teraFLOPs are the total amount of calculations needed to complete a work unit, then the statement that states pigments are light-fast and made specifically for hand papermaking is false. The claim that bacteria survive in the knots and are readily washed off at all times of the year is true. We know that either values depend on factors or if conservatism seems to be a conglomerate of opinions on race, then the statement that states pigments are light-fast and made specifically for hand papermaking is false. The statement that 'values depend on factors' is incorrect.
|
The statement that states pigments are light-fast and made specifically for hand papermaking is false.
|
The statement that states pigments are light-fast and made specifically for hand papermaking is false.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].). [SC2-1]
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [5] or (Either [1] or [2].).
Not [5].
Therefore, Either [1] or [2]..
[SC2-1]
Modus Ponens:
If [3], then (If [1], then (Not [0].).).
[3]
Therefore, If [1], then (Not [0].)..
[SC3-1]
Disjunctive Syllogism:
Either [4] or (If [2], then (Not [0].).).
Not [4].
Therefore, If [2], then (Not [0].)..
|
{0: 'Pigments are light-fast and made specifically for hand papermaking.', 1: 'TeraFLOPs are the total amount of calculations needed to complete a work unit.', 2: 'Conservatism seems to be a conglomerate of opinions on race.', 3: 'Bacteria survive in the knots and are readily washed off at all times of the year.', 4: 'Values depend on factors.', 5: 'Sleep also allows the joints to rest.'}
| 4 |
3,742 |
["Assuming those that suggest if ground water is a vast resource that underlies the earth's surface, then related substances act as antibiotics are wrong, we know that the statement that states either sexual intercourse includes an exchange of emotional electricity or intellectual honesty is an aspect of truthfulness is false.", "Given that those that suggest either either fertilization occurs when the male sex cell joins the female sex cell or spider crabs are known for having long, spindly legs or if those that suggest if ground water is a vast resource that underlies the earth's surface, then related substances act as antibiotics are wrong, then either sexual intercourse includes an exchange of emotional electricity or intellectual honesty is an aspect of truthfulness are wrong, it can be inferred that researchers to study effects.", "If those that suggest either either fertilization occurs when the male sex cell joins the female sex cell or spider crabs are known for having long, spindly legs or if those that suggest if ground water is a vast resource that underlies the earth's surface, then related substances act as antibiotics are wrong, then either sexual intercourse includes an exchange of emotional electricity or intellectual honesty is an aspect of truthfulness are wrong, then we know that the claim that researchers to study effects is false.", 'At least one of two things is true: economic literacy is part of everyday living, or nasal congestion is one of the consequences of such disease.', 'One may reasonably assume that if economic literacy is part of everyday living, then some people mistakenly believe that either fertilization occurs when the male sex cell joins the female sex cell or spider crabs are known for having long, spindly legs.', 'When nasal congestion is one of the consequences of such disease is true, it follows that some people mistakenly believe that either fertilization occurs when the male sex cell joins the female sex cell or spider crabs are known for having long, spindly legs.']
|
Assuming those that suggest if ground water is a vast resource that underlies the earth's surface, then related substances act as antibiotics are wrong, we know that the statement that states either sexual intercourse includes an exchange of emotional electricity or intellectual honesty is an aspect of truthfulness is false. Given that those that suggest either either fertilization occurs when the male sex cell joins the female sex cell or spider crabs are known for having long, spindly legs or if those that suggest if ground water is a vast resource that underlies the earth's surface, then related substances act as antibiotics are wrong, then either sexual intercourse includes an exchange of emotional electricity or intellectual honesty is an aspect of truthfulness are wrong, it can be inferred that researchers to study effects. If those that suggest either either fertilization occurs when the male sex cell joins the female sex cell or spider crabs are known for having long, spindly legs or if those that suggest if ground water is a vast resource that underlies the earth's surface, then related substances act as antibiotics are wrong, then either sexual intercourse includes an exchange of emotional electricity or intellectual honesty is an aspect of truthfulness are wrong, then we know that the claim that researchers to study effects is false. At least one of two things is true: economic literacy is part of everyday living, or nasal congestion is one of the consequences of such disease. One may reasonably assume that if economic literacy is part of everyday living, then some people mistakenly believe that either fertilization occurs when the male sex cell joins the female sex cell or spider crabs are known for having long, spindly legs. When nasal congestion is one of the consequences of such disease is true, it follows that some people mistakenly believe that either fertilization occurs when the male sex cell joins the female sex cell or spider crabs are known for having long, spindly legs.
|
On the condition that ground water is a vast resource that underlies the earth's surface, it is definitely the case that related substances act as antibiotics.
|
The statement, if ground water is a vast resource that underlies the earth's surface, then related substances act as antibiotics, does not hold.
|
FALSE
|
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then (Either [2] or [3].). [SC1-1]
If (Not (If [0], then [1].).), then (Not (Either [2] or [3].).).
Therefore, If [0], then [1]..
[SC1-1]
Disjunctive Syllogism:
Either (Either [4] or [5].) or (If (Not (If [0], then [1].).), then (Either [2] or [3].).). [SC1-2]
Not (Either [4] or [5].). [SC2-2]
Therefore, If (Not (If [0], then [1].).), then (Either [2] or [3].)..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either (Either [4] or [5].) or (If (Not (If [0], then [1].).), then (Either [2] or [3].).).).), then [8].
If (Not (Either (Either [4] or [5].) or (If (Not (If [0], then [1].).), then (Either [2] or [3].).).).), then (Not [8].).
Therefore, Either (Either [4] or [5].) or (If (Not (If [0], then [1].).), then (Either [2] or [3].).)..
[SC2-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Not (Either [4] or [5].).).
If [7], then (Not (Either [4] or [5].).).
Therefore, Not (Either [4] or [5].)..
|
{0: "Ground water is a vast resource that underlies the earth's surface.", 1: 'Related substances act as antibiotics.', 2: 'Sexual intercourse includes an exchange of emotional electricity.', 3: 'Intellectual honesty is an aspect of truthfulness.', 4: 'Fertilization occurs when the male sex cell joins the female sex cell.', 5: 'Spider crabs are known for having long, spindly legs.', 6: 'Economic literacy is part of everyday living.', 7: 'Nasal congestion is one of the consequences of such disease.', 8: 'Researchers to study effects.'}
| 4 |
3,761 |
['It is a common misconception that either goats show characteristics or most rat snakes feed on rodents.', 'Provided that it is not the case that either mineral turpentine contains a high percentage of aromatic solvent, as does white spirit or if rams can spread disease throughout the national flock, then either goats show characteristics or most rat snakes feed on rodents, we know that child begins to experience body changes during puberty.', 'The claim that child begins to experience body changes during puberty has no merit.', "Either one or both of these statements are true: internal parasites can have major effects on their hosts, or the notion that 'mineral turpentine contains a high percentage of aromatic solvent, as does white spirit' is untrue.", 'Those that suggest internal parasites can have major effects on their hosts are wrong.']
|
It is a common misconception that either goats show characteristics or most rat snakes feed on rodents. Provided that it is not the case that either mineral turpentine contains a high percentage of aromatic solvent, as does white spirit or if rams can spread disease throughout the national flock, then either goats show characteristics or most rat snakes feed on rodents, we know that child begins to experience body changes during puberty. The claim that child begins to experience body changes during puberty has no merit. Either one or both of these statements are true: internal parasites can have major effects on their hosts, or the notion that 'mineral turpentine contains a high percentage of aromatic solvent, as does white spirit' is untrue. Those that suggest internal parasites can have major effects on their hosts are wrong.
|
The statement that 'rams can spread disease throughout the national flock' is incorrect.
|
Some people mistakenly believe that rams have horns that are massive and tightly curled close to the face.
|
Uncertain
|
Modus Tonens:
If [0], then (Either [1] or [2].). [SC1-1]
Not (Either [1] or [2].).
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [3] or (If [0], then (Either [1] or [2].).). [SC1-2]
Not [3]. [SC2-2]
Therefore, If [0], then (Either [1] or [2].)..
[SC1-2]
Modus Tonens:
If (Not (Either [3] or (If [0], then (Either [1] or [2].).).).), then [4].
Not [4].
Therefore, Either [3] or (If [0], then (Either [1] or [2].).)..
[SC2-2]
Disjunctive Syllogism:
Either [5] or (Not [3].).
Not [5].
Therefore, Not [3]..
|
{0: 'Rams can spread disease throughout the national flock.', 1: 'Goats show characteristics.', 2: 'Most rat snakes feed on rodents.', 3: 'Mineral turpentine contains a high percentage of aromatic solvent, as does white spirit.', 4: 'Child begins to experience body changes during puberty.', 5: 'Internal parasites can have major effects on their hosts.'}
| 4 |
3,137 |
["The notion that 'most foxes eat gerbils' is untrue.", 'The claim that if computer software is one example of a complex system with emergent properties, then discount rates are interest rates is false.', 'At least one of two things is true: either results indicate boundary conditions or love is the driving factor, yet can be the ultimate force of destruction, or daughter isa individual.', "Assuming either results indicate boundary conditions or love is the driving factor, yet can be the ultimate force of destruction, we know that if the statement that 'if the statement that states arctic air is created over the frozen snowfields of central and northern Canada is false, then most foxes eat gerbils' is incorrect, then if computer software is one example of a complex system with emergent properties, then discount rates are interest rates.", 'There is good reason to believe that either finnish culture is rooted in shamanism or psychiatrists are, first and foremost, medical doctors.', "On the condition that finnish culture is rooted in shamanism, it is definitely the case that if daughter isa individual, then if the statement that 'if the statement that states arctic air is created over the frozen snowfields of central and northern Canada is false, then most foxes eat gerbils' is incorrect, then if computer software is one example of a complex system with emergent properties, then discount rates are interest rates.", "One may reasonably assume that if psychiatrists are, first and foremost, medical doctors, then if daughter isa individual, then if the statement that 'if the statement that states arctic air is created over the frozen snowfields of central and northern Canada is false, then most foxes eat gerbils' is incorrect, then if computer software is one example of a complex system with emergent properties, then discount rates are interest rates."]
|
The notion that 'most foxes eat gerbils' is untrue. The claim that if computer software is one example of a complex system with emergent properties, then discount rates are interest rates is false. At least one of two things is true: either results indicate boundary conditions or love is the driving factor, yet can be the ultimate force of destruction, or daughter isa individual. Assuming either results indicate boundary conditions or love is the driving factor, yet can be the ultimate force of destruction, we know that if the statement that 'if the statement that states arctic air is created over the frozen snowfields of central and northern Canada is false, then most foxes eat gerbils' is incorrect, then if computer software is one example of a complex system with emergent properties, then discount rates are interest rates. There is good reason to believe that either finnish culture is rooted in shamanism or psychiatrists are, first and foremost, medical doctors. On the condition that finnish culture is rooted in shamanism, it is definitely the case that if daughter isa individual, then if the statement that 'if the statement that states arctic air is created over the frozen snowfields of central and northern Canada is false, then most foxes eat gerbils' is incorrect, then if computer software is one example of a complex system with emergent properties, then discount rates are interest rates. One may reasonably assume that if psychiatrists are, first and foremost, medical doctors, then if daughter isa individual, then if the statement that 'if the statement that states arctic air is created over the frozen snowfields of central and northern Canada is false, then most foxes eat gerbils' is incorrect, then if computer software is one example of a complex system with emergent properties, then discount rates are interest rates.
|
The claim that arctic air is created over the frozen snowfields of central and northern Canada holds true.
|
The claim that arctic air is created over the frozen snowfields of central and northern Canada holds true.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Not [0].), then [1].).), then (If [2], then [3].). [SC1-2]
Not (If [2], then [3].).
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunction Elimination:
Either (Either [4] or [5].) or [6].
If (Either [4] or [5].), then (If (Not (If (Not [0].), then [1].).), then (If [2], then [3].).).
If [6], then (If (Not (If (Not [0].), then [1].).), then (If [2], then [3].).). [SC3-3]
Therefore, If (Not (If (Not [0].), then [1].).), then (If [2], then [3].)..
[SC3-3]
Disjunction Elimination:
Either [7] or [8].
If [7], then (If [6], then (If (Not (If (Not [0].), then [1].).), then (If [2], then [3].).).).
If [8], then (If [6], then (If (Not (If (Not [0].), then [1].).), then (If [2], then [3].).).).
Therefore, If [6], then (If (Not (If (Not [0].), then [1].).), then (If [2], then [3].).)..
|
{0: 'Arctic air is created over the frozen snowfields of central and northern Canada.', 1: 'Most foxes eat gerbils.', 2: 'Computer software is one example of a complex system with emergent properties.', 3: 'Discount rates are interest rates.', 4: 'Results indicate boundary conditions.', 5: 'Love is the driving factor, yet can be the ultimate force of destruction.', 6: 'Daughter isa individual.', 7: 'Finnish culture is rooted in shamanism.', 8: 'Psychiatrists are, first and foremost, medical doctors.'}
| 4 |
3,007 |
["Whenever it is true that some people mistakenly believe that practical horoscopy is the life-blood of any attempt to explain 'how astrology works', 'if earthquakes mostly happen along the boundaries between tectonic plates, then most spiders has-part mouthparts' is true.", "Assuming iodometric reactions are rapid and quantitative, we know that if some people mistakenly believe that practical horoscopy is the life-blood of any attempt to explain 'how astrology works', then those that suggest if earthquakes mostly happen along the boundaries between tectonic plates, then most spiders has-part mouthparts are wrong.", 'It is a fact that either voles have short life spans, ranging from two to sixteen months or either case analysis is used to emphasize the relationship of financial theory and the firm or most people love themselves and,thus, feel that they are distinct and unique.', 'On the condition that voles have short life spans, ranging from two to sixteen months, it is definitely the case that either stewardship is the Christian way of life or iodometric reactions are rapid and quantitative.', 'One may reasonably assume that if either case analysis is used to emphasize the relationship of financial theory and the firm or most people love themselves and,thus, feel that they are distinct and unique, then either stewardship is the Christian way of life or iodometric reactions are rapid and quantitative.', "So long as if lactic acid builds up in the muscles, causing that sore and tired feeling, then computer applications exceed a barrier, below which a person uses a computer system to do something, 'if stewardship is the Christian way of life, then if some people mistakenly believe that practical horoscopy is the life-blood of any attempt to explain 'how astrology works', then those that suggest if earthquakes mostly happen along the boundaries between tectonic plates, then most spiders has-part mouthparts are wrong' is true.", 'Should it be the case that lactic acid builds up in the muscles, causing that sore and tired feeling, it follows that computer applications exceed a barrier, below which a person uses a computer system to do something.']
|
Whenever it is true that some people mistakenly believe that practical horoscopy is the life-blood of any attempt to explain 'how astrology works', 'if earthquakes mostly happen along the boundaries between tectonic plates, then most spiders has-part mouthparts' is true. Assuming iodometric reactions are rapid and quantitative, we know that if some people mistakenly believe that practical horoscopy is the life-blood of any attempt to explain 'how astrology works', then those that suggest if earthquakes mostly happen along the boundaries between tectonic plates, then most spiders has-part mouthparts are wrong. It is a fact that either voles have short life spans, ranging from two to sixteen months or either case analysis is used to emphasize the relationship of financial theory and the firm or most people love themselves and,thus, feel that they are distinct and unique. On the condition that voles have short life spans, ranging from two to sixteen months, it is definitely the case that either stewardship is the Christian way of life or iodometric reactions are rapid and quantitative. One may reasonably assume that if either case analysis is used to emphasize the relationship of financial theory and the firm or most people love themselves and,thus, feel that they are distinct and unique, then either stewardship is the Christian way of life or iodometric reactions are rapid and quantitative. So long as if lactic acid builds up in the muscles, causing that sore and tired feeling, then computer applications exceed a barrier, below which a person uses a computer system to do something, 'if stewardship is the Christian way of life, then if some people mistakenly believe that practical horoscopy is the life-blood of any attempt to explain 'how astrology works', then those that suggest if earthquakes mostly happen along the boundaries between tectonic plates, then most spiders has-part mouthparts are wrong' is true. Should it be the case that lactic acid builds up in the muscles, causing that sore and tired feeling, it follows that computer applications exceed a barrier, below which a person uses a computer system to do something.
|
The claim that practical horoscopy is the life-blood of any attempt to explain 'how astrology works' holds true.
|
The claim that practical horoscopy is the life-blood of any attempt to explain 'how astrology works' does not correspond with reality.
|
FALSE
|
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]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (If (Not [0].), then (Not (If [1], then [2].).).). [SC2-2]
If [4], then (If (Not [0].), then (Not (If [1], then [2].).).).
Therefore, If (Not [0].), then (Not (If [1], then [2].).)..
[SC1-2]
Disjunction Elimination:
Either [7] or (Either [8] or [9].).
If [7], then (Either [3] or [4].).
If (Either [8] or [9].), then (Either [3] or [4].).
Therefore, Either [3] or [4]..
[SC2-2]
Modus Ponens:
If (If [5], then [6].), then (If [3], then (If (Not [0].), then (Not (If [1], then [2].).).).).
If [5], then [6].
Therefore, If [3], then (If (Not [0].), then (Not (If [1], then [2].).).)..
|
{0: "Practical horoscopy is the life-blood of any attempt to explain 'how astrology works'.", 1: 'Earthquakes mostly happen along the boundaries between tectonic plates.', 2: 'Most spiders has-part mouthparts.', 3: 'Stewardship is the Christian way of life.', 4: 'Iodometric reactions are rapid and quantitative.', 5: 'Lactic acid builds up in the muscles, causing that sore and tired feeling.', 6: 'Computer applications exceed a barrier, below which a person uses a computer system to do something.', 7: 'Voles have short life spans, ranging from two to sixteen months.', 8: 'Case analysis is used to emphasize the relationship of financial theory and the firm.', 9: 'Most people love themselves and,thus, feel that they are distinct and unique.'}
| 4 |
3,502 |
['On the condition that centipedes are common in most gardens across America, Europe and Asia, it is definitely the case that if the claim that anolis lizards communicate with displays consisting of motion of the head and body does not correspond with reality, then either coral reefs are restricted to warm, shallow water or cellular effects vary with the changing bio-rhythms of cell cycles and cell functions.', "So long as alabaster is gypsums, 'if the claim that anolis lizards communicate with displays consisting of motion of the head and body does not correspond with reality, then the statement, either coral reefs are restricted to warm, shallow water or cellular effects vary with the changing bio-rhythms of cell cycles and cell functions, does not hold' is true.", 'It is rational to agree that alabaster is gypsums.', 'Once we know capybaras are very useful animals, we also know that centipedes are common in most gardens across America, Europe and Asia.', 'It is true that capybaras are very useful animals.']
|
On the condition that centipedes are common in most gardens across America, Europe and Asia, it is definitely the case that if the claim that anolis lizards communicate with displays consisting of motion of the head and body does not correspond with reality, then either coral reefs are restricted to warm, shallow water or cellular effects vary with the changing bio-rhythms of cell cycles and cell functions. So long as alabaster is gypsums, 'if the claim that anolis lizards communicate with displays consisting of motion of the head and body does not correspond with reality, then the statement, either coral reefs are restricted to warm, shallow water or cellular effects vary with the changing bio-rhythms of cell cycles and cell functions, does not hold' is true. It is rational to agree that alabaster is gypsums. Once we know capybaras are very useful animals, we also know that centipedes are common in most gardens across America, Europe and Asia. It is true that capybaras are very useful animals.
|
The claim that anolis lizards communicate with displays consisting of motion of the head and body is true.
|
The claim that anolis lizards communicate with displays consisting of motion of the head and body is true.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then (Either [1] or [2].). [SC1-1]
If (Not [0].), then (Not (Either [1] or [2].).). [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (If (Not [0].), then (Either [1] or [2].).).
[3] [SC2-2]
Therefore, If (Not [0].), then (Either [1] or [2].)..
[SC2-2]
Modus Ponens:
If [5], then [3].
[5]
Therefore, [3].
[SC2-1]
Modus Ponens:
If [4], then (If (Not [0].), then (Not (Either [1] or [2].).).).
[4]
Therefore, If (Not [0].), then (Not (Either [1] or [2].).)..
|
{0: 'Anolis lizards communicate with displays consisting of motion of the head and body.', 1: 'Coral reefs are restricted to warm, shallow water.', 2: 'Cellular effects vary with the changing bio-rhythms of cell cycles and cell functions.', 3: 'Centipedes are common in most gardens across America, Europe and Asia.', 4: 'Alabaster is gypsums.', 5: 'Capybaras are very useful animals.'}
| 4 |
3,831 |
['Assuming either armyworms continue to be found sporadically in barley and wheat fields or garages have (part) courtyards, we know that olive oil is super for use on and in pasta and breads.', "There is good reason to believe that either psychologists say parental exaggeration plays a vital role in a child's development or the claim that good care helps prevent hearing problems and holes in the eardrum does not reflect reality.", "The claim that psychologists say parental exaggeration plays a vital role in a child's development has no merit.", 'On the condition that most fish feed on fish, it is definitely the case that if olive oil is super for use on and in pasta and breads, then good care helps prevent hearing problems and holes in the eardrum.', 'It is a simple truth that most fish feed on fish.']
|
Assuming either armyworms continue to be found sporadically in barley and wheat fields or garages have (part) courtyards, we know that olive oil is super for use on and in pasta and breads. There is good reason to believe that either psychologists say parental exaggeration plays a vital role in a child's development or the claim that good care helps prevent hearing problems and holes in the eardrum does not reflect reality. The claim that psychologists say parental exaggeration plays a vital role in a child's development has no merit. On the condition that most fish feed on fish, it is definitely the case that if olive oil is super for use on and in pasta and breads, then good care helps prevent hearing problems and holes in the eardrum. It is a simple truth that most fish feed on fish.
|
The statement, either armyworms continue to be found sporadically in barley and wheat fields or garages have (part) courtyards, does not hold.
|
It is rational to believe that either armyworms continue to be found sporadically in barley and wheat fields or garages have (part) courtyards.
|
FALSE
|
Modus Tonens:
If (Either [0] or [1].), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Hypothetical Syllogism:
If (Either [0] or [1].), then [4].
If [4], then [2]. [SC2-2]
Therefore, If (Either [0] or [1].), then [2]..
[SC2-2]
Modus Ponens:
If [5], then (If [4], then [2].).
[5]
Therefore, If [4], then [2]..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (Not [2].).
Not [3].
Therefore, Not [2]..
|
{0: 'Armyworms continue to be found sporadically in barley and wheat fields.', 1: 'Garages have (part) courtyards.', 2: 'Good care helps prevent hearing problems and holes in the eardrum.', 3: "Psychologists say parental exaggeration plays a vital role in a child's development.", 4: 'Olive oil is super for use on and in pasta and breads.', 5: 'Most fish feed on fish.'}
| 4 |
3,762 |
['The claim that density is also important in the industry that keeps the world moving, petroleum is false.', 'When the claim that either forests remove carbon dioxide from the atmosphere as trees take it in and breathe out oxygen or paints are the result of innovative pigment technology does not reflect reality is true, it follows that either heavy rainfall reduces mite populations in soybeans or some chemicals use in treatments.', 'Assuming either heavy rainfall reduces mite populations in soybeans or some chemicals use in treatments, we know that some isotopes are stable and remain unchanged through time.', 'One may reasonably assume that if some people mistakenly believe that if some isotopes are stable and remain unchanged through time, then density is also important in the industry that keeps the world moving, petroleum, then combat isa battle.', 'Given that some people mistakenly believe that if some isotopes are stable and remain unchanged through time, then density is also important in the industry that keeps the world moving, petroleum, it can be inferred that the statement, combat isa battle, does not hold.']
|
The claim that density is also important in the industry that keeps the world moving, petroleum is false. When the claim that either forests remove carbon dioxide from the atmosphere as trees take it in and breathe out oxygen or paints are the result of innovative pigment technology does not reflect reality is true, it follows that either heavy rainfall reduces mite populations in soybeans or some chemicals use in treatments. Assuming either heavy rainfall reduces mite populations in soybeans or some chemicals use in treatments, we know that some isotopes are stable and remain unchanged through time. One may reasonably assume that if some people mistakenly believe that if some isotopes are stable and remain unchanged through time, then density is also important in the industry that keeps the world moving, petroleum, then combat isa battle. Given that some people mistakenly believe that if some isotopes are stable and remain unchanged through time, then density is also important in the industry that keeps the world moving, petroleum, it can be inferred that the statement, combat isa battle, does not hold.
|
We know that at least one of two things is true: forests remove carbon dioxide from the atmosphere as trees take it in and breathe out oxygen, or paints are the result of innovative pigment technology.
|
The claim that either forests remove carbon dioxide from the atmosphere as trees take it in and breathe out oxygen or paints are the result of innovative pigment technology does not correspond with reality.
|
FALSE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
Not [2].
Therefore, Either [0] or [1]..
[SC1-1]
Hypothetical Syllogism:
If (Not (Either [0] or [1].).), then [3]. [SC1-2]
If [3], then [2]. [SC2-2]
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC1-2]
Hypothetical Syllogism:
If (Not (Either [0] or [1].).), then (Either [4] or [5].).
If (Either [4] or [5].), then [3].
Therefore, If (Not (Either [0] or [1].).), then [3]..
[SC2-2]
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]..
|
{0: 'Forests remove carbon dioxide from the atmosphere as trees take it in and breathe out oxygen.', 1: 'Paints are the result of innovative pigment technology.', 2: 'Density is also important in the industry that keeps the world moving, petroleum.', 3: 'Some isotopes are stable and remain unchanged through time.', 4: 'Heavy rainfall reduces mite populations in soybeans.', 5: 'Some chemicals use in treatments.', 6: 'Combat isa battle.'}
| 4 |
3,851 |
["Whenever it is true that the claim that either inflation is an invisible form of taxation that irresponsible governments inflict on their citizens or it is a common misconception that cognitive anthropology is the study of culture and mind does not correspond with reality, 'weight is primarily a function of food volume and exercise' is true.", 'Once we know the claim that either inflation is an invisible form of taxation that irresponsible governments inflict on their citizens or it is a common misconception that cognitive anthropology is the study of culture and mind does not correspond with reality, we also know that we know that the claim that weight is primarily a function of food volume and exercise is false.', 'It is a common misconception that centipedes are found throughout the United States and the world.', 'On the condition that if obstructive conduct can vary widely in nature, degree of planning, and seriousness, then rats emerge at nights, it is definitely the case that either centipedes are found throughout the United States and the world or it is not true that inflation is an invisible form of taxation that irresponsible governments inflict on their citizens.', "Whenever it is true that obstructive conduct can vary widely in nature, degree of planning, and seriousness, 'rats emerge at nights' is true."]
|
Whenever it is true that the claim that either inflation is an invisible form of taxation that irresponsible governments inflict on their citizens or it is a common misconception that cognitive anthropology is the study of culture and mind does not correspond with reality, 'weight is primarily a function of food volume and exercise' is true. Once we know the claim that either inflation is an invisible form of taxation that irresponsible governments inflict on their citizens or it is a common misconception that cognitive anthropology is the study of culture and mind does not correspond with reality, we also know that we know that the claim that weight is primarily a function of food volume and exercise is false. It is a common misconception that centipedes are found throughout the United States and the world. On the condition that if obstructive conduct can vary widely in nature, degree of planning, and seriousness, then rats emerge at nights, it is definitely the case that either centipedes are found throughout the United States and the world or it is not true that inflation is an invisible form of taxation that irresponsible governments inflict on their citizens. Whenever it is true that obstructive conduct can vary widely in nature, degree of planning, and seriousness, 'rats emerge at nights' is true.
|
It is a common misconception that cognitive anthropology is the study of culture and mind.
|
Those that suggest cognitive anthropology is the study of culture and mind are right.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or (Not [0].). [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or (Not [0].).).), then [2].
If (Not (Either [1] or (Not [0].).).), then (Not [2].).
Therefore, Either [1] or (Not [0].)..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (Not [1].). [SC1-2]
Not [3].
Therefore, Not [1]..
[SC1-2]
Modus Ponens:
If (If [4], then [5].), then (Either [3] or (Not [1].).).
If [4], then [5].
Therefore, Either [3] or (Not [1].)..
|
{0: 'Cognitive anthropology is the study of culture and mind.', 1: 'Inflation is an invisible form of taxation that irresponsible governments inflict on their citizens.', 2: 'Weight is primarily a function of food volume and exercise.', 3: 'Centipedes are found throughout the United States and the world.', 4: 'Obstructive conduct can vary widely in nature, degree of planning, and seriousness.', 5: 'Rats emerge at nights.'}
| 4 |
3,407 |
["Assuming those that suggest homeowners use gasoline cans for their lawnmowers and other equipment are wrong, we know that the notion that 'some water passes through holes' is untrue.", 'It is true that african art takes many forms and is made from many different materials.', 'Should it be the case that the statement, if african art takes many forms and is made from many different materials, then if those that suggest homeowners use gasoline cans for their lawnmowers and other equipment are wrong, then some water passes through holes, does not hold, it follows that a scrimshaw is a carving.', 'Either food improves health or if the statement, if african art takes many forms and is made from many different materials, then if those that suggest homeowners use gasoline cans for their lawnmowers and other equipment are wrong, then some water passes through holes, does not hold, then it is not true that a scrimshaw is a carving.', 'Those that suggest food improves health are wrong.']
|
Assuming those that suggest homeowners use gasoline cans for their lawnmowers and other equipment are wrong, we know that the notion that 'some water passes through holes' is untrue. It is true that african art takes many forms and is made from many different materials. Should it be the case that the statement, if african art takes many forms and is made from many different materials, then if those that suggest homeowners use gasoline cans for their lawnmowers and other equipment are wrong, then some water passes through holes, does not hold, it follows that a scrimshaw is a carving. Either food improves health or if the statement, if african art takes many forms and is made from many different materials, then if those that suggest homeowners use gasoline cans for their lawnmowers and other equipment are wrong, then some water passes through holes, does not hold, then it is not true that a scrimshaw is a carving. Those that suggest food improves health are wrong.
|
homeowners use gasoline cans for their lawnmowers and other equipment.
|
The statement 'homeowners use gasoline cans for their lawnmowers and other equipment' can be considered false.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (If (Not [0].), then [1].). [SC1-2]
[2]
Therefore, If (Not [0].), then [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [2], then (If (Not [0].), then [1].).).), then [3].
If (Not (If [2], then (If (Not [0].), then [1].).).), then (Not [3].). [SC2-3]
Therefore, If [2], then (If (Not [0].), then [1].)..
[SC2-3]
Disjunctive Syllogism:
Either [4] or (If (Not (If [2], then (If (Not [0].), then [1].).).), then (Not [3].).).
Not [4].
Therefore, If (Not (If [2], then (If (Not [0].), then [1].).).), then (Not [3].)..
|
{0: 'Homeowners use gasoline cans for their lawnmowers and other equipment.', 1: 'Some water passes through holes.', 2: 'African art takes many forms and is made from many different materials.', 3: 'A scrimshaw is a carving.', 4: 'Food improves health.'}
| 4 |
3,692 |
['On the condition that anhydrous ammonia is a strong alkali that can cause painful skin burns, it is definitely the case that books have stories.', 'We know that either if skilled workers have different personalities, work ethics and life goals, then porn is porn no matter what form it is in or either incorrect diets can cause serious dental disease or anhydrous ammonia is a strong alkali that can cause painful skin burns.', 'The claim that if skilled workers have different personalities, work ethics and life goals, then porn is porn no matter what form it is in does not reflect reality.', 'Given that either active toys develop large and small muscles or worms are located in earth, it can be inferred that if incorrect diets can cause serious dental disease, then books have stories.', 'One may reasonably assume that if if compression occurs when the size and shape of the thoracic outlet is altered, then data publishing involves creating Web pages from information stored in a database, then if incorrect diets can cause serious dental disease, then books have stories.', 'It is a fact that either either pica is more common in people that are brain damaged or have a mental handicap or an easterner is an inhabitant or either either active toys develop large and small muscles or worms are located in earth or if compression occurs when the size and shape of the thoracic outlet is altered, then data publishing involves creating Web pages from information stored in a database.', "The statement that 'either pica is more common in people that are brain damaged or have a mental handicap or an easterner is an inhabitant' is incorrect."]
|
On the condition that anhydrous ammonia is a strong alkali that can cause painful skin burns, it is definitely the case that books have stories. We know that either if skilled workers have different personalities, work ethics and life goals, then porn is porn no matter what form it is in or either incorrect diets can cause serious dental disease or anhydrous ammonia is a strong alkali that can cause painful skin burns. The claim that if skilled workers have different personalities, work ethics and life goals, then porn is porn no matter what form it is in does not reflect reality. Given that either active toys develop large and small muscles or worms are located in earth, it can be inferred that if incorrect diets can cause serious dental disease, then books have stories. One may reasonably assume that if if compression occurs when the size and shape of the thoracic outlet is altered, then data publishing involves creating Web pages from information stored in a database, then if incorrect diets can cause serious dental disease, then books have stories. It is a fact that either either pica is more common in people that are brain damaged or have a mental handicap or an easterner is an inhabitant or either either active toys develop large and small muscles or worms are located in earth or if compression occurs when the size and shape of the thoracic outlet is altered, then data publishing involves creating Web pages from information stored in a database. The statement that 'either pica is more common in people that are brain damaged or have a mental handicap or an easterner is an inhabitant' is incorrect.
|
Those that suggest books have stories are right.
|
Some people mistakenly believe that books have stories.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either (If [3], then [4].) or (Either [1] or [2].).
Not (If [3], then [4].).
Therefore, Either [1] or [2]..
[SC2-1]
Disjunction Elimination:
Either (Either [5] or [6].) or (If [7], then [8].). [SC1-2]
If (Either [5] or [6].), then (If [1], then [0].).
If (If [7], then [8].), then (If [1], then [0].).
Therefore, If [1], then [0]..
[SC1-2]
Disjunctive Syllogism:
Either (Either [9] or [10].) or (Either (Either [5] or [6].) or (If [7], then [8].).).
Not (Either [9] or [10].).
Therefore, Either (Either [5] or [6].) or (If [7], then [8].)..
|
{0: 'Books have stories.', 1: 'Incorrect diets can cause serious dental disease.', 2: 'Anhydrous ammonia is a strong alkali that can cause painful skin burns.', 3: 'Skilled workers have different personalities, work ethics and life goals.', 4: 'Porn is porn no matter what form it is in.', 5: 'Active toys develop large and small muscles.', 6: 'Worms are located in earth.', 7: 'Compression occurs when the size and shape of the thoracic outlet is altered.', 8: 'Data publishing involves creating Web pages from information stored in a database.', 9: 'Pica is more common in people that are brain damaged or have a mental handicap.', 10: 'An easterner is an inhabitant.'}
| 4 |
3,353 |
['When raccoons have (part) cytoplasm is true, it follows that query languages based on relational calculus are nonprocedural.', 'Assuming it is not the case that if children fall from trees, ladders, roofs and other high places every day, then those that suggest query languages based on relational calculus are nonprocedural are wrong, we know that some machinery produces static electricity.', 'Those that suggest some machinery produces static electricity are wrong.', 'One may reasonably assume that if we know that the claim that if children fall from trees, ladders, roofs and other high places every day, then raccoons have (part) cytoplasm is false, then all sources of energy have negative impacts on the environment.', 'When we know that the claim that if children fall from trees, ladders, roofs and other high places every day, then raccoons have (part) cytoplasm is false is true, it follows that we know that the claim that all sources of energy have negative impacts on the environment is false.']
|
When raccoons have (part) cytoplasm is true, it follows that query languages based on relational calculus are nonprocedural. Assuming it is not the case that if children fall from trees, ladders, roofs and other high places every day, then those that suggest query languages based on relational calculus are nonprocedural are wrong, we know that some machinery produces static electricity. Those that suggest some machinery produces static electricity are wrong. One may reasonably assume that if we know that the claim that if children fall from trees, ladders, roofs and other high places every day, then raccoons have (part) cytoplasm is false, then all sources of energy have negative impacts on the environment. When we know that the claim that if children fall from trees, ladders, roofs and other high places every day, then raccoons have (part) cytoplasm is false is true, it follows that we know that the claim that all sources of energy have negative impacts on the environment is false.
|
It is not true that children fall from trees, ladders, roofs and other high places every day.
|
It is the case that children fall from trees, ladders, roofs and other high places every day.
|
FALSE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC1-1]
Hypothetical Syllogism:
If [0], then [2]. [SC1-2]
If [2], then [1].
Therefore, If [0], then [1]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [0], then [2].).), then [4].
If (Not (If [0], then [2].).), then (Not [4].).
Therefore, If [0], then [2]..
[SC2-1]
Modus Tonens:
If (Not (If [0], then (Not [1].).).), then [3].
Not [3].
Therefore, If [0], then (Not [1].)..
|
{0: 'Children fall from trees, ladders, roofs and other high places every day.', 1: 'Query languages based on relational calculus are nonprocedural.', 2: 'Raccoons have (part) cytoplasm.', 3: 'Some machinery produces static electricity.', 4: 'All sources of energy have negative impacts on the environment.'}
| 4 |
3,153 |
['There is good reason to believe that either either cyclists have (part) material bodies or some stimulants affect only a specific organ such as the heart, lungs, brain, or nervous system or either thugs are located in streets or testosterone relaxes rabbit coronary arteries and aorta.', 'One may reasonably assume that if either thugs are located in streets or testosterone relaxes rabbit coronary arteries and aorta, then either generosity is a mark of a true believer or water is located in ice.', 'Either joints are geologist jargon for cracks or the statement, generosity is a mark of a true believer, does not hold.', 'Some people mistakenly believe that joints are geologist jargon for cracks.', 'Either either carbon dioxide is an acid gas or perennial plants have yellow flowers or if either cyclists have (part) material bodies or some stimulants affect only a specific organ such as the heart, lungs, brain, or nervous system, then either generosity is a mark of a true believer or water is located in ice.', 'Some people mistakenly believe that either carbon dioxide is an acid gas or perennial plants have yellow flowers.']
|
There is good reason to believe that either either cyclists have (part) material bodies or some stimulants affect only a specific organ such as the heart, lungs, brain, or nervous system or either thugs are located in streets or testosterone relaxes rabbit coronary arteries and aorta. One may reasonably assume that if either thugs are located in streets or testosterone relaxes rabbit coronary arteries and aorta, then either generosity is a mark of a true believer or water is located in ice. Either joints are geologist jargon for cracks or the statement, generosity is a mark of a true believer, does not hold. Some people mistakenly believe that joints are geologist jargon for cracks. Either either carbon dioxide is an acid gas or perennial plants have yellow flowers or if either cyclists have (part) material bodies or some stimulants affect only a specific organ such as the heart, lungs, brain, or nervous system, then either generosity is a mark of a true believer or water is located in ice. Some people mistakenly believe that either carbon dioxide is an acid gas or perennial plants have yellow flowers.
|
The statement that states water is located in ice is right.
|
The statement that states water is located in ice is right.
|
TRUE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [2] or [3].) or (Either [4] or [5].).
If (Either [2] or [3].), then (Either [1] or [0].). [SC2-2]
If (Either [4] or [5].), then (Either [1] or [0].).
Therefore, Either [1] or [0]..
[SC2-2]
Disjunctive Syllogism:
Either (Either [7] or [8].) or (If (Either [2] or [3].), then (Either [1] or [0].).).
Not (Either [7] or [8].).
Therefore, If (Either [2] or [3].), then (Either [1] or [0].)..
[SC2-1]
Disjunctive Syllogism:
Either [6] or (Not [1].).
Not [6].
Therefore, Not [1]..
|
{0: 'Water is located in ice.', 1: 'Generosity is a mark of a true believer.', 2: 'Cyclists have (part) material bodies.', 3: 'Some stimulants affect only a specific organ such as the heart, lungs, brain, or nervous system.', 4: 'Thugs are located in streets.', 5: 'Testosterone relaxes rabbit coronary arteries and aorta.', 6: 'Joints are geologist jargon for cracks.', 7: 'Carbon dioxide is an acid gas.', 8: 'Perennial plants have yellow flowers.'}
| 4 |
3,566 |
['If buildups are accretion, then some people mistakenly believe that movement is a natural and often spontaneous response to sounds and sound patterns.', 'If if most fungi are associated with plants as saprotrophs and decomposers, then fish have fins for locomotion, then if massage reduces anxiety and lowers the blood levels of the stress hormone, cortisol, then capillaries are the largest of the blood vessels.', 'When if massage reduces anxiety and lowers the blood levels of the stress hormone, cortisol, then capillaries are the largest of the blood vessels is true, it follows that buildups are accretion.', 'Assuming some people mistakenly believe that if most fungi are associated with plants as saprotrophs and decomposers, then fish have fins for locomotion, we know that mites spin very fine webs over the places where they are feeding.', "So long as some people mistakenly believe that if most fungi are associated with plants as saprotrophs and decomposers, then fish have fins for locomotion, 'the statement that 'mites spin very fine webs over the places where they are feeding' is incorrect' is true."]
|
If buildups are accretion, then some people mistakenly believe that movement is a natural and often spontaneous response to sounds and sound patterns. If if most fungi are associated with plants as saprotrophs and decomposers, then fish have fins for locomotion, then if massage reduces anxiety and lowers the blood levels of the stress hormone, cortisol, then capillaries are the largest of the blood vessels. When if massage reduces anxiety and lowers the blood levels of the stress hormone, cortisol, then capillaries are the largest of the blood vessels is true, it follows that buildups are accretion. Assuming some people mistakenly believe that if most fungi are associated with plants as saprotrophs and decomposers, then fish have fins for locomotion, we know that mites spin very fine webs over the places where they are feeding. So long as some people mistakenly believe that if most fungi are associated with plants as saprotrophs and decomposers, then fish have fins for locomotion, 'the statement that 'mites spin very fine webs over the places where they are feeding' is incorrect' is true.
|
Some people mistakenly believe that movement is a natural and often spontaneous response to sounds and sound patterns.
|
Some people mistakenly believe that movement is a natural and often spontaneous response to sounds and sound patterns.
|
TRUE
|
Modus Ponens:
If [1], then (Not [0].).
[1] [SC2-1]
Therefore, Not [0]..
[SC2-1]
Modus Ponens:
If (If [2], then [3].), then [1]. [SC1-2]
If [2], then [3]. [SC2-2]
Therefore, [1].
[SC1-2]
Hypothetical Syllogism:
If (If [2], then [3].), then (If [4], then [5].).
If (If [4], then [5].), then [1].
Therefore, If (If [2], then [3].), then [1]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If [2], then [3].).), then [6].
If (Not (If [2], then [3].).), then (Not [6].).
Therefore, If [2], then [3]..
|
{0: 'Movement is a natural and often spontaneous response to sounds and sound patterns.', 1: 'Buildups are accretion.', 2: 'Most fungi are associated with plants as saprotrophs and decomposers.', 3: 'Fish have fins for locomotion.', 4: 'Massage reduces anxiety and lowers the blood levels of the stress hormone, cortisol.', 5: 'Capillaries are the largest of the blood vessels.', 6: 'Mites spin very fine webs over the places where they are feeding.'}
| 4 |
3,542 |
["The statement that 'plants obtain the primary and secondary nutrients and some micronutrients solely from the soil' is incorrect.", 'Given that genetic drift can lead to populations with reduced genetic variation, it can be inferred that rain is made of water.', "The statement 'rain is made of water' can be considered false.", 'At least one of two things is true: smaller lemurs eat more insects, or hippocampal lesions do the following in animals A. disrupt radial arm maze performance.', "Assuming smaller lemurs eat more insects, we know that if the claim that if the statement 'storms also tend to be stronger and often strike without warning' can be considered false, then genetic drift can lead to populations with reduced genetic variation is false, then plants obtain the primary and secondary nutrients and some micronutrients solely from the soil.", "Provided that hippocampal lesions do the following in animals A. disrupt radial arm maze performance, we know that if the claim that if the statement 'storms also tend to be stronger and often strike without warning' can be considered false, then genetic drift can lead to populations with reduced genetic variation is false, then plants obtain the primary and secondary nutrients and some micronutrients solely from the soil."]
|
The statement that 'plants obtain the primary and secondary nutrients and some micronutrients solely from the soil' is incorrect. Given that genetic drift can lead to populations with reduced genetic variation, it can be inferred that rain is made of water. The statement 'rain is made of water' can be considered false. At least one of two things is true: smaller lemurs eat more insects, or hippocampal lesions do the following in animals A. disrupt radial arm maze performance. Assuming smaller lemurs eat more insects, we know that if the claim that if the statement 'storms also tend to be stronger and often strike without warning' can be considered false, then genetic drift can lead to populations with reduced genetic variation is false, then plants obtain the primary and secondary nutrients and some micronutrients solely from the soil. Provided that hippocampal lesions do the following in animals A. disrupt radial arm maze performance, we know that if the claim that if the statement 'storms also tend to be stronger and often strike without warning' can be considered false, then genetic drift can lead to populations with reduced genetic variation is false, then plants obtain the primary and secondary nutrients and some micronutrients solely from the soil.
|
storms also tend to be stronger and often strike without warning.
|
Storms also tend to be stronger and often strike without warning.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Not [0].), then [1].).), then [2]. [SC1-2]
Not [2].
Therefore, If (Not [0].), then [1]..
[SC1-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If (Not (If (Not [0].), then [1].).), then [2].).
If [5], then (If (Not (If (Not [0].), then [1].).), then [2].).
Therefore, If (Not (If (Not [0].), then [1].).), then [2]..
[SC2-1]
Modus Tonens:
If [1], then [3].
Not [3].
Therefore, Not [1]..
|
{0: 'Storms also tend to be stronger and often strike without warning.', 1: 'Genetic drift can lead to populations with reduced genetic variation.', 2: 'Plants obtain the primary and secondary nutrients and some micronutrients solely from the soil.', 3: 'Rain is made of water.', 4: 'Smaller lemurs eat more insects.', 5: 'Hippocampal lesions do the following in animals A. disrupt radial arm maze performance.'}
| 4 |
3,343 |
["The notion that 'plierses have (part) sections' is untrue.", "One may reasonably assume that if it is a common misconception that if hammerhead sharks eat fish, then anger is the best agent for cleaning up one's emotions, then if all programming languages have functions, then educators are professionals.", 'Provided that if all programming languages have functions, then educators are professionals, we know that we know that the claim that most carpenter bees feed on nectar is false.', "One may reasonably assume that if the statement 'either plierses have (part) sections or if it is a common misconception that if hammerhead sharks eat fish, then anger is the best agent for cleaning up one's emotions, then most carpenter bees feed on nectar' can be considered false, then constructivism provides general concepts for thinking about teaching and learning.", "The notion that 'constructivism provides general concepts for thinking about teaching and learning' is untrue."]
|
The notion that 'plierses have (part) sections' is untrue. One may reasonably assume that if it is a common misconception that if hammerhead sharks eat fish, then anger is the best agent for cleaning up one's emotions, then if all programming languages have functions, then educators are professionals. Provided that if all programming languages have functions, then educators are professionals, we know that we know that the claim that most carpenter bees feed on nectar is false. One may reasonably assume that if the statement 'either plierses have (part) sections or if it is a common misconception that if hammerhead sharks eat fish, then anger is the best agent for cleaning up one's emotions, then most carpenter bees feed on nectar' can be considered false, then constructivism provides general concepts for thinking about teaching and learning. The notion that 'constructivism provides general concepts for thinking about teaching and learning' is untrue.
|
Given that hammerhead sharks eat fish, it can be inferred that anger is the best agent for cleaning up one's emotions.
|
Given that hammerhead sharks eat fish, it can be inferred that anger is the best agent for cleaning up one's emotions.
|
TRUE
|
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then [2]. [SC1-1]
If (Not (If [0], then [1].).), then (Not [2].). [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Disjunctive Syllogism:
Either [5] or (If (Not (If [0], then [1].).), then [2].). [SC1-2]
Not [5].
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC1-2]
Modus Tonens:
If (Not (Either [5] or (If (Not (If [0], then [1].).), then [2].).).), then [6].
Not [6].
Therefore, Either [5] or (If (Not (If [0], then [1].).), then [2].)..
[SC2-1]
Hypothetical Syllogism:
If (Not (If [0], then [1].).), then (If [3], then [4].).
If (If [3], then [4].), then (Not [2].).
Therefore, If (Not (If [0], then [1].).), then (Not [2].)..
|
{0: 'Hammerhead sharks eat fish.', 1: "Anger is the best agent for cleaning up one's emotions.", 2: 'Most carpenter bees feed on nectar.', 3: 'All programming languages have functions.', 4: 'Educators are professionals.', 5: 'Plierses have (part) sections.', 6: 'Constructivism provides general concepts for thinking about teaching and learning.'}
| 4 |
3,887 |
["One may reasonably assume that if the statement 'if many cars have brake pad sensors to warn of pad wear, then black cardamoms have antibacterial properties' can be considered false, then dinosaurs provide no evidence for evolution.", "Should it be the case that the statement 'if many cars have brake pad sensors to warn of pad wear, then black cardamoms have antibacterial properties' can be considered false, it follows that the statement 'dinosaurs provide no evidence for evolution' can be considered false.", 'If helium atoms have charge, then many cars have brake pad sensors to warn of pad wear.', 'One may reasonably assume that if if people desire novelty, then heating also occurs from both conduction current and radiation, then many cars have brake pad sensors to warn of pad wear.', 'We know that at least one of two things is true: either some beetles possess mechanisms or democrats see minorities mainly as large block votes at bargain prices, or some ostriches survive to adulthood.', "So long as either some beetles possess mechanisms or democrats see minorities mainly as large block votes at bargain prices, 'helium atoms have charge' is true.", "So long as some ostriches survive to adulthood, 'if people desire novelty, then heating also occurs from both conduction current and radiation' is true."]
|
One may reasonably assume that if the statement 'if many cars have brake pad sensors to warn of pad wear, then black cardamoms have antibacterial properties' can be considered false, then dinosaurs provide no evidence for evolution. Should it be the case that the statement 'if many cars have brake pad sensors to warn of pad wear, then black cardamoms have antibacterial properties' can be considered false, it follows that the statement 'dinosaurs provide no evidence for evolution' can be considered false. If helium atoms have charge, then many cars have brake pad sensors to warn of pad wear. One may reasonably assume that if if people desire novelty, then heating also occurs from both conduction current and radiation, then many cars have brake pad sensors to warn of pad wear. We know that at least one of two things is true: either some beetles possess mechanisms or democrats see minorities mainly as large block votes at bargain prices, or some ostriches survive to adulthood. So long as either some beetles possess mechanisms or democrats see minorities mainly as large block votes at bargain prices, 'helium atoms have charge' is true. So long as some ostriches survive to adulthood, 'if people desire novelty, then heating also occurs from both conduction current and radiation' is true.
|
The claim that black cardamoms have antibacterial properties is true.
|
Black cardamoms have properties.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [1], then [0].).), then [2].
If (Not (If [1], then [0].).), then (Not [2].).
Therefore, If [1], then [0]..
[SC2-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].). [SC1-2]
If [3], then [1].
If (If [4], then [5].), then [1].
Therefore, [1].
[SC1-2]
Constructive Dilemma:
Either (Either [6] or [7].) or [8].
If (Either [6] or [7].), then [3].
If [8], then (If [4], then [5].).
Therefore, Either [3] or (If [4], then [5].)..
|
{0: 'Black cardamoms have antibacterial properties.', 1: 'Many cars have brake pad sensors to warn of pad wear.', 2: 'Dinosaurs provide no evidence for evolution.', 3: 'Helium atoms have charge.', 4: 'People desire novelty.', 5: 'Heating also occurs from both conduction current and radiation.', 6: 'Some beetles possess mechanisms.', 7: 'Democrats see minorities mainly as large block votes at bargain prices.', 8: 'Some ostriches survive to adulthood.'}
| 4 |
3,997 |
['There is good reason to believe that either diseases are more common in older people or hydrangeas are susceptible leaf spots and powdery mildew.', "One may reasonably assume that if hydrangeas are susceptible leaf spots and powdery mildew, then the statement that 'fledglings have light spots all over their bodies, but otherwise resemble adults' is incorrect.", "So long as gardening can become a kind of disease, 'if either a tax collection is a collection or adolescence is immaturity, then if diseases are more common in older people , then the statement that 'fledglings have light spots all over their bodies, but otherwise resemble adults' is incorrect' is true.", 'The statement that states gardening can become a kind of disease is right.', "So long as the statement that states either a tax collection is a collection or adolescence is immaturity is false, 'horses can see well to either side, but have only a limited range of binocular vision' is true.", 'The statement, horses can see well to either side, but have only a limited range of binocular vision, does not hold.']
|
There is good reason to believe that either diseases are more common in older people or hydrangeas are susceptible leaf spots and powdery mildew. One may reasonably assume that if hydrangeas are susceptible leaf spots and powdery mildew, then the statement that 'fledglings have light spots all over their bodies, but otherwise resemble adults' is incorrect. So long as gardening can become a kind of disease, 'if either a tax collection is a collection or adolescence is immaturity, then if diseases are more common in older people , then the statement that 'fledglings have light spots all over their bodies, but otherwise resemble adults' is incorrect' is true. The statement that states gardening can become a kind of disease is right. So long as the statement that states either a tax collection is a collection or adolescence is immaturity is false, 'horses can see well to either side, but have only a limited range of binocular vision' is true. The statement, horses can see well to either side, but have only a limited range of binocular vision, does not hold.
|
The statement that 'fledglings have light spots all over their bodies, but otherwise resemble adults' is incorrect.
|
The statement that 'fledglings have light spots all over their bodies, but otherwise resemble adults' is incorrect.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then (Not [0].). [SC2-1]
If [2], then (Not [0].).
Therefore, Not [0]..
[SC2-1]
Modus Ponens:
If (Either [3] or [4].), then (If [1], then (Not [0].).). [SC1-2]
Either [3] or [4]. [SC2-2]
Therefore, If [1], then (Not [0].)..
[SC1-2]
Modus Ponens:
If [5], then (If (Either [3] or [4].), then (If [1], then (Not [0].).).).
[5]
Therefore, If (Either [3] or [4].), then (If [1], then (Not [0].).)..
[SC2-2]
Modus Tonens:
If (Not (Either [3] or [4].).), then [6].
Not [6].
Therefore, Either [3] or [4]..
|
{0: 'Fledglings have light spots all over their bodies, but otherwise resemble adults.', 1: 'Diseases are more common in older people .', 2: 'Hydrangeas are susceptible leaf spots and powdery mildew.', 3: 'A tax collection is a collection.', 4: 'Adolescence is immaturity.', 5: 'Gardening can become a kind of disease.', 6: 'Horses can see well to either side, but have only a limited range of binocular vision.'}
| 4 |
3,825 |
['When bees are a part of the Life of our planet is true, it follows that diffraction gratings are used in many analytical chemistry tools , such as a spectrometer .', 'The claim that either hate is an intense feeling of malevolence, anger, dislike, etc or throws are blankets does not reflect reality.', 'At least one of two things is true: response thresholds to sucrose predict foraging division of labor in honeybees, or if technology changes what mathematics is to be learned and when and how it is learned, then diffraction gratings are used in many analytical chemistry tools , such as a spectrometer .', 'The statement that states response thresholds to sucrose predict foraging division of labor in honeybees is false.', 'It is a fact that either water is the cheapest source of fluid for people working out an hour or less or some pediatric cardiologists see and advise congenital heart patients into adulthood.', 'Provided that water is the cheapest source of fluid for people working out an hour or less, we know that either either hate is an intense feeling of malevolence, anger, dislike, etc or throws are blankets or either bees are a part of the Life of our planet or technology changes what mathematics is to be learned and when and how it is learned.', 'Provided that some pediatric cardiologists see and advise congenital heart patients into adulthood, we know that either either hate is an intense feeling of malevolence, anger, dislike, etc or throws are blankets or either bees are a part of the Life of our planet or technology changes what mathematics is to be learned and when and how it is learned.']
|
When bees are a part of the Life of our planet is true, it follows that diffraction gratings are used in many analytical chemistry tools , such as a spectrometer . The claim that either hate is an intense feeling of malevolence, anger, dislike, etc or throws are blankets does not reflect reality. At least one of two things is true: response thresholds to sucrose predict foraging division of labor in honeybees, or if technology changes what mathematics is to be learned and when and how it is learned, then diffraction gratings are used in many analytical chemistry tools , such as a spectrometer . The statement that states response thresholds to sucrose predict foraging division of labor in honeybees is false. It is a fact that either water is the cheapest source of fluid for people working out an hour or less or some pediatric cardiologists see and advise congenital heart patients into adulthood. Provided that water is the cheapest source of fluid for people working out an hour or less, we know that either either hate is an intense feeling of malevolence, anger, dislike, etc or throws are blankets or either bees are a part of the Life of our planet or technology changes what mathematics is to be learned and when and how it is learned. Provided that some pediatric cardiologists see and advise congenital heart patients into adulthood, we know that either either hate is an intense feeling of malevolence, anger, dislike, etc or throws are blankets or either bees are a part of the Life of our planet or technology changes what mathematics is to be learned and when and how it is learned.
|
The idea that diffraction gratings are used in many analytical chemistry tools , such as a spectrometer is true.
|
Some people mistakenly believe that diffraction gratings are used in many analytical chemistry tools , such as a spectrometer .
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either (Either [4] or [5].) or (Either [1] or [2].). [SC1-2]
Not (Either [4] or [5].).
Therefore, Either [1] or [2]..
[SC1-2]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Either (Either [4] or [5].) or (Either [1] or [2].).).
If [7], then (Either (Either [4] or [5].) or (Either [1] or [2].).).
Therefore, Either (Either [4] or [5].) or (Either [1] or [2].)..
[SC3-1]
Disjunctive Syllogism:
Either [3] or (If [2], then [0].).
Not [3].
Therefore, If [2], then [0]..
|
{0: 'Diffraction gratings are used in many analytical chemistry tools , such as a spectrometer .', 1: 'Bees are a part of the Life of our planet.', 2: 'Technology changes what mathematics is to be learned and when and how it is learned.', 3: 'Response thresholds to sucrose predict foraging division of labor in honeybees.', 4: 'Hate is an intense feeling of malevolence, anger, dislike, etc.', 5: 'Throws are blankets.', 6: 'Water is the cheapest source of fluid for people working out an hour or less.', 7: 'Some pediatric cardiologists see and advise congenital heart patients into adulthood.'}
| 4 |
3,056 |
['One may reasonably assume that if erosion is the gradually taking away of dirt, soil, or sand by wind or water, then roast pork is a joint.', 'On the condition that conifer needles have a thick, waxy coating of cutin that significantly reduces water loss, it is definitely the case that murine thymidine kinase in transgenic mice.', "Should it be the case that the statement that 'either erosion is the gradually taking away of dirt, soil, or sand by wind or water or conifer needles have a thick, waxy coating of cutin that significantly reduces water loss' is incorrect, it follows that it is not the case that victims enter enclose areas.", "One may reasonably assume that if the statement that 'either erosion is the gradually taking away of dirt, soil, or sand by wind or water or conifer needles have a thick, waxy coating of cutin that significantly reduces water loss' is incorrect, then abstract landscapes evolve into strange, god-like figures whose images revert into landscapes.", "One may reasonably assume that if the statement that 'if abstract landscapes evolve into strange, god-like figures whose images revert into landscapes, then victims enter enclose areas' is incorrect, then some sources emit radiation.", 'We know that the claim that some sources emit radiation is false.']
|
One may reasonably assume that if erosion is the gradually taking away of dirt, soil, or sand by wind or water, then roast pork is a joint. On the condition that conifer needles have a thick, waxy coating of cutin that significantly reduces water loss, it is definitely the case that murine thymidine kinase in transgenic mice. Should it be the case that the statement that 'either erosion is the gradually taking away of dirt, soil, or sand by wind or water or conifer needles have a thick, waxy coating of cutin that significantly reduces water loss' is incorrect, it follows that it is not the case that victims enter enclose areas. One may reasonably assume that if the statement that 'either erosion is the gradually taking away of dirt, soil, or sand by wind or water or conifer needles have a thick, waxy coating of cutin that significantly reduces water loss' is incorrect, then abstract landscapes evolve into strange, god-like figures whose images revert into landscapes. One may reasonably assume that if the statement that 'if abstract landscapes evolve into strange, god-like figures whose images revert into landscapes, then victims enter enclose areas' is incorrect, then some sources emit radiation. We know that the claim that some sources emit radiation is false.
|
We know that at least one of two things is true: roast pork is a joint, or murine thymidine kinase in transgenic mice.
|
Those that suggest either roast pork is a joint or murine thymidine kinase in transgenic mice are wrong.
|
FALSE
|
Constructive Dilemma:
Either [2] or [3]. [SC1-1]
If [2], then [0].
If [3], then [1].
Therefore, Either [0] or [1]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [2] or [3].).), then [4]. [SC1-2]
If (Not (Either [2] or [3].).), then (Not [4].).
Therefore, Either [2] or [3]..
[SC1-2]
Hypothetical Syllogism:
If (Not (Either [2] or [3].).), then [5].
If [5], then [4]. [SC2-3]
Therefore, If (Not (Either [2] or [3].).), then [4]..
[SC2-3]
Modus Tonens:
If (Not (If [5], then [4].).), then [6].
Not [6].
Therefore, If [5], then [4]..
|
{0: 'Roast pork is a joint.', 1: 'Murine thymidine kinase in transgenic mice.', 2: 'Erosion is the gradually taking away of dirt, soil, or sand by wind or water.', 3: 'Conifer needles have a thick, waxy coating of cutin that significantly reduces water loss.', 4: 'Victims enter enclose areas.', 5: 'Abstract landscapes evolve into strange, god-like figures whose images revert into landscapes.', 6: 'Some sources emit radiation.'}
| 4 |
3,400 |
['Given that it is not true that if aphids also excrete honeydew, then users see benefits, it can be inferred that if astronomers play significant roles, then pieceworks are employment.', 'It is a common misconception that if astronomers play significant roles, then pieceworks are employment.', 'On the condition that incest is a collective name for a great variety of phenomena, it is definitely the case that the statement that states users see benefits is false.', 'When some mothers love ducks is true, it follows that the statement that states users see benefits is false.', 'We know that at least one of two things is true: if crocuses are an example of corms, then babies have (part) material bodies, or either incest is a collective name for a great variety of phenomena or some mothers love ducks.', 'Some people mistakenly believe that if crocuses are an example of corms, then babies have (part) material bodies.']
|
Given that it is not true that if aphids also excrete honeydew, then users see benefits, it can be inferred that if astronomers play significant roles, then pieceworks are employment. It is a common misconception that if astronomers play significant roles, then pieceworks are employment. On the condition that incest is a collective name for a great variety of phenomena, it is definitely the case that the statement that states users see benefits is false. When some mothers love ducks is true, it follows that the statement that states users see benefits is false. We know that at least one of two things is true: if crocuses are an example of corms, then babies have (part) material bodies, or either incest is a collective name for a great variety of phenomena or some mothers love ducks. Some people mistakenly believe that if crocuses are an example of corms, then babies have (part) material bodies.
|
The claim that aphids also excrete honeydew does not reflect reality.
|
Those that suggest aphids also excrete honeydew are right.
|
FALSE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (If [0], then [1].).), then (If [2], then [3].).
Not (If [2], then [3].).
Therefore, If [0], then [1]..
[SC2-1]
Disjunction Elimination:
Either [4] or [5]. [SC1-2]
If [4], then (Not [1].).
If [5], then (Not [1].).
Therefore, Not [1]..
[SC1-2]
Disjunctive Syllogism:
Either (If [6], then [7].) or (Either [4] or [5].).
Not (If [6], then [7].).
Therefore, Either [4] or [5]..
|
{0: 'Aphids also excrete honeydew.', 1: 'Users see benefits.', 2: 'Astronomers play significant roles.', 3: 'Pieceworks are employment.', 4: 'Incest is a collective name for a great variety of phenomena.', 5: 'Some mothers love ducks.', 6: 'Crocuses are an example of corms.', 7: 'Babies have (part) material bodies.'}
| 4 |
3,572 |
["Whenever it is true that the statement, either searchs are films or plant foods are poor sources of EFAs, does not hold, 'sambar deer possess red spots' is true.", 'Assuming the statement, either searchs are films or plant foods are poor sources of EFAs, does not hold, we know that it is not the case that sambar deer possess red spots.', 'It is rational to believe that either most death caused by influenza are in elderly people or if searchs are films, then spectators have (part) corpi.', 'Some people mistakenly believe that most death caused by influenza are in elderly people.', 'Provided that the claim that if plant foods are poor sources of EFAs, then spectators have (part) corpi does not correspond with reality, we know that dynamism can also derive from interactivity, as readers contribute their ideas or images.', 'The claim that dynamism can also derive from interactivity, as readers contribute their ideas or images is false.']
|
Whenever it is true that the statement, either searchs are films or plant foods are poor sources of EFAs, does not hold, 'sambar deer possess red spots' is true. Assuming the statement, either searchs are films or plant foods are poor sources of EFAs, does not hold, we know that it is not the case that sambar deer possess red spots. It is rational to believe that either most death caused by influenza are in elderly people or if searchs are films, then spectators have (part) corpi. Some people mistakenly believe that most death caused by influenza are in elderly people. Provided that the claim that if plant foods are poor sources of EFAs, then spectators have (part) corpi does not correspond with reality, we know that dynamism can also derive from interactivity, as readers contribute their ideas or images. The claim that dynamism can also derive from interactivity, as readers contribute their ideas or images is false.
|
Many people rightly believe that spectators have (part) corpi.
|
Many people rightly believe that spectators have (part) corpi.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either [1] or [2].).), then [5].
If (Not (Either [1] or [2].).), then (Not [5].).
Therefore, Either [1] or [2]..
[SC2-1]
Disjunctive Syllogism:
Either [4] or (If [1], then [0].).
Not [4].
Therefore, If [1], then [0]..
[SC3-1]
Modus Tonens:
If (Not (If [2], then [0].).), then [3].
Not [3].
Therefore, If [2], then [0]..
|
{0: 'Spectators have (part) corpi.', 1: 'Searchs are films.', 2: 'Plant foods are poor sources of EFAs.', 3: 'Dynamism can also derive from interactivity, as readers contribute their ideas or images.', 4: 'Most death caused by influenza are in elderly people.', 5: 'Sambar deer possess red spots.'}
| 4 |
3,473 |
['There is good reason to believe that either if corporations are creatures of both statute and contract, then waste products have functions or commerce has (part) business activities.', 'On the condition that commerce has (part) business activities, it is definitely the case that if we know that the claim that if status affects actions, then mercury evaporates easily and can become a breathable vapor, which can cause health problems is false, then lactose alone is responsible for more than one-third of the osmotic pressure of normal milk.', "So long as some people mistakenly believe that if we know that the claim that if status affects actions, then mercury evaporates easily and can become a breathable vapor, which can cause health problems is false, then those that suggest lactose alone is responsible for more than one-third of the osmotic pressure of normal milk are wrong, 'assimilation is more a biological process than a matter of choice' is true.", "The statement 'assimilation is more a biological process than a matter of choice' can be considered false.", "Whenever it is true that if corporations are creatures of both statute and contract, then waste products have functions, 'stress is a common thing that is experienced in our everyday lives' is true.", "Whenever it is true that stress is a common thing that is experienced in our everyday lives, 'if we know that the claim that if status affects actions, then mercury evaporates easily and can become a breathable vapor, which can cause health problems is false, then lactose alone is responsible for more than one-third of the osmotic pressure of normal milk' is true."]
|
There is good reason to believe that either if corporations are creatures of both statute and contract, then waste products have functions or commerce has (part) business activities. On the condition that commerce has (part) business activities, it is definitely the case that if we know that the claim that if status affects actions, then mercury evaporates easily and can become a breathable vapor, which can cause health problems is false, then lactose alone is responsible for more than one-third of the osmotic pressure of normal milk. So long as some people mistakenly believe that if we know that the claim that if status affects actions, then mercury evaporates easily and can become a breathable vapor, which can cause health problems is false, then those that suggest lactose alone is responsible for more than one-third of the osmotic pressure of normal milk are wrong, 'assimilation is more a biological process than a matter of choice' is true. The statement 'assimilation is more a biological process than a matter of choice' can be considered false. Whenever it is true that if corporations are creatures of both statute and contract, then waste products have functions, 'stress is a common thing that is experienced in our everyday lives' is true. Whenever it is true that stress is a common thing that is experienced in our everyday lives, 'if we know that the claim that if status affects actions, then mercury evaporates easily and can become a breathable vapor, which can cause health problems is false, then lactose alone is responsible for more than one-third of the osmotic pressure of normal milk' is true.
|
One may reasonably assume that if status affects actions, then mercury evaporates easily and can become a breathable vapor, which can cause health problems.
|
One may reasonably assume that if status affects actions, then mercury evaporates easily and can become a breathable vapor, which can cause health problems.
|
TRUE
|
Reductio Ad Absurdum:
If (Not (If [0], then [1].).), then [2]. [SC1-1]
If (Not (If [0], then [1].).), then (Not [2].). [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Disjunction Elimination:
Either (If [3], then [4].) or [5].
If (If [3], then [4].), then (If (Not (If [0], then [1].).), then [2].). [SC2-2]
If [5], then (If (Not (If [0], then [1].).), then [2].).
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC2-2]
Hypothetical Syllogism:
If (If [3], then [4].), then [7].
If [7], then (If (Not (If [0], then [1].).), then [2].).
Therefore, If (If [3], then [4].), then (If (Not (If [0], then [1].).), then [2].)..
[SC2-1]
Modus Tonens:
If (Not (If (Not (If [0], then [1].).), then (Not [2].).).), then [6].
Not [6].
Therefore, If (Not (If [0], then [1].).), then (Not [2].)..
|
{0: 'Status affects actions.', 1: 'Mercury evaporates easily and can become a breathable vapor, which can cause health problems.', 2: 'Lactose alone is responsible for more than one-third of the osmotic pressure of normal milk.', 3: 'Corporations are creatures of both statute and contract.', 4: 'Waste products have functions.', 5: 'Commerce has (part) business activities.', 6: 'Assimilation is more a biological process than a matter of choice.', 7: 'Stress is a common thing that is experienced in our everyday lives.'}
| 4 |
3,468 |
["Whenever it is true that either some children are afraid of firefighters or some salmon live in regions, 'either porpoises are located in water or ferns have true roots and stems and reproduce by making spores' is true.", 'It is a fact that either either solicitors are used for criminal laws or some telescopes can look at wide areas of the sky at once or arthropods rely on eyes.', 'Provided that arthropods rely on eyes, we know that either some children are afraid of firefighters or some salmon live in regions.', "When the notion that 'if either solicitors are used for criminal laws or some telescopes can look at wide areas of the sky at once, then either some children are afraid of firefighters or some salmon live in regions' is untrue is true, it follows that the claim that irradiation also inhibits the spoilage of foods, stretching the world's available food supply does not correspond with reality.", "Given that the statement that states if the notion that 'if either solicitors are used for criminal laws or some telescopes can look at wide areas of the sky at once, then either some children are afraid of firefighters or some salmon live in regions' is untrue, then irradiation also inhibits the spoilage of foods, stretching the world's available food supply is false, it can be inferred that meteorologists study the atmosphere and atmospheric phenomena, including the weather.", "Should it be the case that the statement that states if the notion that 'if either solicitors are used for criminal laws or some telescopes can look at wide areas of the sky at once, then either some children are afraid of firefighters or some salmon live in regions' is untrue, then irradiation also inhibits the spoilage of foods, stretching the world's available food supply is false, it follows that the statement that 'meteorologists study the atmosphere and atmospheric phenomena, including the weather' is incorrect."]
|
Whenever it is true that either some children are afraid of firefighters or some salmon live in regions, 'either porpoises are located in water or ferns have true roots and stems and reproduce by making spores' is true. It is a fact that either either solicitors are used for criminal laws or some telescopes can look at wide areas of the sky at once or arthropods rely on eyes. Provided that arthropods rely on eyes, we know that either some children are afraid of firefighters or some salmon live in regions. When the notion that 'if either solicitors are used for criminal laws or some telescopes can look at wide areas of the sky at once, then either some children are afraid of firefighters or some salmon live in regions' is untrue is true, it follows that the claim that irradiation also inhibits the spoilage of foods, stretching the world's available food supply does not correspond with reality. Given that the statement that states if the notion that 'if either solicitors are used for criminal laws or some telescopes can look at wide areas of the sky at once, then either some children are afraid of firefighters or some salmon live in regions' is untrue, then irradiation also inhibits the spoilage of foods, stretching the world's available food supply is false, it can be inferred that meteorologists study the atmosphere and atmospheric phenomena, including the weather. Should it be the case that the statement that states if the notion that 'if either solicitors are used for criminal laws or some telescopes can look at wide areas of the sky at once, then either some children are afraid of firefighters or some salmon live in regions' is untrue, then irradiation also inhibits the spoilage of foods, stretching the world's available food supply is false, it follows that the statement that 'meteorologists study the atmosphere and atmospheric phenomena, including the weather' is incorrect.
|
We know that at least one of two things is true: porpoises are located in water, or ferns have true roots and stems and reproduce by making spores.
|
It is not true that either porpoises are located in water or ferns have true roots and stems and reproduce by making spores.
|
FALSE
|
Modus Ponens:
If (Either [2] or [3].), then (Either [0] or [1].).
Either [2] or [3]. [SC2-1]
Therefore, Either [0] or [1]..
[SC2-1]
Disjunction Elimination:
Either (Either [4] or [5].) or [6].
If (Either [4] or [5].), then (Either [2] or [3].). [SC2-2]
If [6], then (Either [2] or [3].).
Therefore, Either [2] or [3]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Either [4] or [5].), then (Either [2] or [3].).).), then [7]. [SC1-3]
If (Not (If (Either [4] or [5].), then (Either [2] or [3].).).), then (Not [7].).
Therefore, If (Either [4] or [5].), then (Either [2] or [3].)..
[SC1-3]
Reductio Ad Absurdum:
If (Not (If (Not (If (Either [4] or [5].), then (Either [2] or [3].).).), then [7].).), then [8].
If (Not (If (Not (If (Either [4] or [5].), then (Either [2] or [3].).).), then [7].).), then (Not [8].).
Therefore, If (Not (If (Either [4] or [5].), then (Either [2] or [3].).).), then [7]..
|
{0: 'Porpoises are located in water.', 1: 'Ferns have true roots and stems and reproduce by making spores.', 2: 'Some children are afraid of firefighters.', 3: 'Some salmon live in regions.', 4: 'Solicitors are used for criminal laws.', 5: 'Some telescopes can look at wide areas of the sky at once.', 6: 'Arthropods rely on eyes.', 7: "Irradiation also inhibits the spoilage of foods, stretching the world's available food supply.", 8: 'Meteorologists study the atmosphere and atmospheric phenomena, including the weather.'}
| 4 |
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