id
int64 0
7k
| premises
stringlengths 118
4.1k
| paragraph
stringlengths 111
4.06k
| conclusion
stringlengths 15
240
| question
stringlengths 14
249
| label
stringclasses 3
values | arg
stringlengths 54
2.02k
| statements
stringlengths 51
1.12k
| depth
int64 1
7
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|---|---|---|---|---|---|---|---|---|
2,993 |
['At least one of two things is true: sexual intercourse is the highest risk activity for all types of STIs, or heat is generated by the friction created when knots are drawn up tight.', 'Either one or both of these statements are true: most cassowaries adapt to environments, or redevelopment is a process created to assist local governments to revitalize an area.', "Assuming most cassowaries adapt to environments, we know that the statement 'sexual intercourse is the highest risk activity for all types of STIs' can be considered false.", "So long as quality is a word used so often in advertising that it sometimes becomes diluted, 'if redevelopment is a process created to assist local governments to revitalize an area, then the statement 'sexual intercourse is the highest risk activity for all types of STIs' can be considered false' is true.", 'quality is a word used so often in advertising that it sometimes becomes diluted.']
|
At least one of two things is true: sexual intercourse is the highest risk activity for all types of STIs, or heat is generated by the friction created when knots are drawn up tight. Either one or both of these statements are true: most cassowaries adapt to environments, or redevelopment is a process created to assist local governments to revitalize an area. Assuming most cassowaries adapt to environments, we know that the statement 'sexual intercourse is the highest risk activity for all types of STIs' can be considered false. So long as quality is a word used so often in advertising that it sometimes becomes diluted, 'if redevelopment is a process created to assist local governments to revitalize an area, then the statement 'sexual intercourse is the highest risk activity for all types of STIs' can be considered false' is true. quality is a word used so often in advertising that it sometimes becomes diluted.
|
It is reasonable to believe that heat is generated by the friction created when knots are drawn up tight.
|
The claim that heat is generated by the friction created when knots are drawn up tight is false.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (Not [1].).
If [3], then (Not [1].). [SC3-2]
Therefore, Not [1]..
[SC3-2]
Modus Ponens:
If [4], then (If [3], then (Not [1].).).
[4]
Therefore, If [3], then (Not [1].)..
|
{0: 'Heat is generated by the friction created when knots are drawn up tight.', 1: 'Sexual intercourse is the highest risk activity for all types of STIs.', 2: 'Most cassowaries adapt to environments.', 3: 'Redevelopment is a process created to assist local governments to revitalize an area.', 4: 'Quality is a word used so often in advertising that it sometimes becomes diluted.'}
| 3 |
2,859 |
["On the condition that either most banana plants produce seeds or rattles are noise, it is definitely the case that if mutation isa organism, then the notion that 'more women suffer from depression than their male counterparts' is untrue.", 'Either most banana plants produce seeds or rattles are noise.', 'We know that at least one of two things is true: basalts are dark colored, fine-grained extrusive rock, or mutation isa organism.', 'We know that the claim that basalts are dark colored, fine-grained extrusive rock is false.']
|
On the condition that either most banana plants produce seeds or rattles are noise, it is definitely the case that if mutation isa organism, then the notion that 'more women suffer from depression than their male counterparts' is untrue. Either most banana plants produce seeds or rattles are noise. We know that at least one of two things is true: basalts are dark colored, fine-grained extrusive rock, or mutation isa organism. We know that the claim that basalts are dark colored, fine-grained extrusive rock is false.
|
The notion that 'more women suffer from depression than their male counterparts' is untrue.
|
The claim that more women suffer from depression than their male counterparts is true.
|
FALSE
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1] [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If (Either [2] or [3].), then (If [1], then (Not [0].).).
Either [2] or [3].
Therefore, If [1], then (Not [0].)..
[SC2-1]
Disjunctive Syllogism:
Either [4] or [1].
Not [4].
Therefore, [1].
|
{0: 'More women suffer from depression than their male counterparts.', 1: 'Mutation isa organism.', 2: 'Most banana plants produce seeds.', 3: 'Rattles are noise.', 4: 'Basalts are dark colored, fine-grained extrusive rock.'}
| 3 |
2,298 |
['Either gooseberries bear fruit or toads normally live on land but require ponds to reproduce.', "So long as gooseberries bear fruit, 'if we know that the claim that either some caterpillars make substances or enzymes make the digestion of food possible is false, then frogs sometimes have upper teeth whereas toads have no teeth at all' is true.", 'One may reasonably assume that if toads normally live on land but require ponds to reproduce, then if we know that the claim that either some caterpillars make substances or enzymes make the digestion of food possible is false, then frogs sometimes have upper teeth whereas toads have no teeth at all.', 'Either one or both of these statements are true: aircraft pilots fly commercial, private, corporate and government airplanes and helicopters, or husbands wear rings.', 'Provided that aircraft pilots fly commercial, private, corporate and government airplanes and helicopters, we know that it is not true that frogs sometimes have upper teeth whereas toads have no teeth at all.', 'Should it be the case that husbands wear rings, it follows that it is not true that frogs sometimes have upper teeth whereas toads have no teeth at all.']
|
Either gooseberries bear fruit or toads normally live on land but require ponds to reproduce. So long as gooseberries bear fruit, 'if we know that the claim that either some caterpillars make substances or enzymes make the digestion of food possible is false, then frogs sometimes have upper teeth whereas toads have no teeth at all' is true. One may reasonably assume that if toads normally live on land but require ponds to reproduce, then if we know that the claim that either some caterpillars make substances or enzymes make the digestion of food possible is false, then frogs sometimes have upper teeth whereas toads have no teeth at all. Either one or both of these statements are true: aircraft pilots fly commercial, private, corporate and government airplanes and helicopters, or husbands wear rings. Provided that aircraft pilots fly commercial, private, corporate and government airplanes and helicopters, we know that it is not true that frogs sometimes have upper teeth whereas toads have no teeth at all. Should it be the case that husbands wear rings, it follows that it is not true that frogs sometimes have upper teeth whereas toads have no teeth at all.
|
We know that either some caterpillars make substances or enzymes make the digestion of food possible.
|
We know that either some caterpillars make substances or enzymes make the digestion of food possible.
|
TRUE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
Not [2]. [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If (Not (Either [0] or [1].).), then [2].).
If [6], then (If (Not (Either [0] or [1].).), then [2].).
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not [2].).
If [4], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Some caterpillars make substances.', 1: 'Enzymes make the digestion of food possible.', 2: 'Frogs sometimes have upper teeth whereas toads have no teeth at all.', 3: 'Aircraft pilots fly commercial, private, corporate and government airplanes and helicopters.', 4: 'Husbands wear rings.', 5: 'Gooseberries bear fruit.', 6: 'Toads normally live on land but require ponds to reproduce.'}
| 3 |
2,553 |
['Assuming prime numbers are very important in mathematics and computer science , we know that if grannies have (part) plasma membranes, then antitoxins give immediate but short-term protection, acting just like antibodies.', 'prime numbers are very important in mathematics and computer science .', 'Should it be the case that most critters have feet, it follows that the claim that antitoxins give immediate but short-term protection, acting just like antibodies does not correspond with reality.', 'most critters have feet.']
|
Assuming prime numbers are very important in mathematics and computer science , we know that if grannies have (part) plasma membranes, then antitoxins give immediate but short-term protection, acting just like antibodies. prime numbers are very important in mathematics and computer science . Should it be the case that most critters have feet, it follows that the claim that antitoxins give immediate but short-term protection, acting just like antibodies does not correspond with reality. most critters have feet.
|
Those that suggest grannies have (part) plasma membranes are wrong.
|
The statement that 'different elements have different physical properties' is incorrect.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [3], then (If [0], then [1].).
[3]
Therefore, If [0], then [1]..
[SC2-1]
Modus Ponens:
If [2], then (Not [1].).
[2]
Therefore, Not [1]..
|
{0: 'Grannies have (part) plasma membranes.', 1: 'Antitoxins give immediate but short-term protection, acting just like antibodies.', 2: 'Most critters have feet.', 3: 'Prime numbers are very important in mathematics and computer science .'}
| 3 |
2,672 |
['One may reasonably assume that if a stein is a mug, then a golem is a mythical being.', 'We know that at least one of two things is true: extrinsic reinforcement can destroy inner motivation, or if games have different rules, then language learning entails building relationships.', 'Given that extrinsic reinforcement can destroy inner motivation, it can be inferred that faith is the channel on which the boats of answered prayer sail.', 'When if games have different rules, then language learning entails building relationships is true, it follows that a stein is a mug.', 'One may reasonably assume that if some people mistakenly believe that if faith is the channel on which the boats of answered prayer sail, then a golem is a mythical being, then dams have both positive and negative ecological impacts.', "The statement that 'dams have both positive and negative ecological impacts' is incorrect."]
|
One may reasonably assume that if a stein is a mug, then a golem is a mythical being. We know that at least one of two things is true: extrinsic reinforcement can destroy inner motivation, or if games have different rules, then language learning entails building relationships. Given that extrinsic reinforcement can destroy inner motivation, it can be inferred that faith is the channel on which the boats of answered prayer sail. When if games have different rules, then language learning entails building relationships is true, it follows that a stein is a mug. One may reasonably assume that if some people mistakenly believe that if faith is the channel on which the boats of answered prayer sail, then a golem is a mythical being, then dams have both positive and negative ecological impacts. The statement that 'dams have both positive and negative ecological impacts' is incorrect.
|
The idea that a golem is a mythical being is true.
|
The statement, a golem is a mythical being, does not hold.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either [3] or (If [4], then [5].).
If [3], then [1].
If (If [4], then [5].), then [2].
Therefore, Either [1] or [2]..
[SC2-1]
Modus Tonens:
If (Not (If [1], then [0].).), then [6].
Not [6].
Therefore, If [1], then [0]..
|
{0: 'A golem is a mythical being.', 1: 'Faith is the channel on which the boats of answered prayer sail.', 2: 'A stein is a mug.', 3: 'Extrinsic reinforcement can destroy inner motivation.', 4: 'Games have different rules.', 5: 'Language learning entails building relationships.', 6: 'Dams have both positive and negative ecological impacts.'}
| 3 |
2,971 |
["Whenever it is true that discover magazines have articles, 'either if aerobic exercise is best for burning fat, then zip lines used for entertainment or accessibility to nature enhances human enjoyment and relaxation or gardening is a healthy recreational activity in which all can participate' is true.", 'The claim that discover magazines have articles holds true.', 'It is rational to believe that either poets are the lawgivers of the ages or positive current is defined as flowing into each terminal.', 'When poets are the lawgivers of the ages is true, it follows that the claim that if aerobic exercise is best for burning fat, then zip lines used for entertainment or accessibility to nature enhances human enjoyment and relaxation does not correspond with reality.', 'Given that positive current is defined as flowing into each terminal, it can be inferred that the claim that if aerobic exercise is best for burning fat, then zip lines used for entertainment or accessibility to nature enhances human enjoyment and relaxation does not correspond with reality.']
|
Whenever it is true that discover magazines have articles, 'either if aerobic exercise is best for burning fat, then zip lines used for entertainment or accessibility to nature enhances human enjoyment and relaxation or gardening is a healthy recreational activity in which all can participate' is true. The claim that discover magazines have articles holds true. It is rational to believe that either poets are the lawgivers of the ages or positive current is defined as flowing into each terminal. When poets are the lawgivers of the ages is true, it follows that the claim that if aerobic exercise is best for burning fat, then zip lines used for entertainment or accessibility to nature enhances human enjoyment and relaxation does not correspond with reality. Given that positive current is defined as flowing into each terminal, it can be inferred that the claim that if aerobic exercise is best for burning fat, then zip lines used for entertainment or accessibility to nature enhances human enjoyment and relaxation does not correspond with reality.
|
It is reasonable to believe that gardening is a healthy recreational activity in which all can participate.
|
The notion that 'gardening is a healthy recreational activity in which all can participate' is untrue.
|
FALSE
|
Disjunctive Syllogism:
Either (If [1], then [2].) or [0]. [SC1-1]
Not (If [1], then [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [5], then (Either (If [1], then [2].) or [0].).
[5]
Therefore, Either (If [1], then [2].) or [0]..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not (If [1], then [2].).).
If [4], then (Not (If [1], then [2].).).
Therefore, Not (If [1], then [2].)..
|
{0: 'Gardening is a healthy recreational activity in which all can participate.', 1: 'Aerobic exercise is best for burning fat.', 2: 'Zip lines used for entertainment or accessibility to nature enhances human enjoyment and relaxation.', 3: 'Poets are the lawgivers of the ages.', 4: 'Positive current is defined as flowing into each terminal.', 5: 'Discover magazines have articles.'}
| 3 |
2,027 |
['Either one or both of these statements are true: weddings are life cycle events, or volcanic activity can change without warning.', 'If weddings are life cycle events, then if it is not the case that antihistamines are medicines which help against allergies, then all major religions approve of organ and tissue donation and consider it a gift, an act of charity.', 'On the condition that volcanic activity can change without warning, it is definitely the case that if it is not the case that antihistamines are medicines which help against allergies, then all major religions approve of organ and tissue donation and consider it a gift, an act of charity.', 'We know that at least one of two things is true: most injuries are to the soft tissue and occur most frequently in the lower extremities, or the statement that states all major religions approve of organ and tissue donation and consider it a gift, an act of charity is false.', 'It is not true that most injuries are to the soft tissue and occur most frequently in the lower extremities.']
|
Either one or both of these statements are true: weddings are life cycle events, or volcanic activity can change without warning. If weddings are life cycle events, then if it is not the case that antihistamines are medicines which help against allergies, then all major religions approve of organ and tissue donation and consider it a gift, an act of charity. On the condition that volcanic activity can change without warning, it is definitely the case that if it is not the case that antihistamines are medicines which help against allergies, then all major religions approve of organ and tissue donation and consider it a gift, an act of charity. We know that at least one of two things is true: most injuries are to the soft tissue and occur most frequently in the lower extremities, or the statement that states all major religions approve of organ and tissue donation and consider it a gift, an act of charity is false. It is not true that most injuries are to the soft tissue and occur most frequently in the lower extremities.
|
We can assume that antihistamines are medicines which help against allergies.
|
We can assume that antihistamines are medicines which help against allergies.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If (Not [0].), then [1].).
If [4], then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Disjunctive Syllogism:
Either [2] or (Not [1].).
Not [2].
Therefore, Not [1]..
|
{0: 'Antihistamines are medicines which help against allergies.', 1: 'All major religions approve of organ and tissue donation and consider it a gift, an act of charity.', 2: 'Most injuries are to the soft tissue and occur most frequently in the lower extremities.', 3: 'Weddings are life cycle events.', 4: 'Volcanic activity can change without warning.'}
| 3 |
2,231 |
["Once we know the claim that ozone is North Carolina's most widespread air quality problem does not correspond with reality, we also know that diversity is tied to genes , which are the basic units of heredity .", 'The claim that either caterpillars spend most of their time eating or some blood vessels surround renal tubules does not reflect reality.', "Either one or both of these statements are true: if psychoanalysis is impractical and ineffectual, going back to the past and ignoring present problems, then canned tuna is one of nature's healthiest and pure foods, or some minerals have chemicals.", "Provided that if psychoanalysis is impractical and ineffectual, going back to the past and ignoring present problems, then canned tuna is one of nature's healthiest and pure foods, we know that either either caterpillars spend most of their time eating or some blood vessels surround renal tubules or if the claim that ozone is North Carolina's most widespread air quality problem does not correspond with reality, then it is a common misconception that diversity is tied to genes , which are the basic units of heredity .", "Provided that some minerals have chemicals, we know that either either caterpillars spend most of their time eating or some blood vessels surround renal tubules or if the claim that ozone is North Carolina's most widespread air quality problem does not correspond with reality, then it is a common misconception that diversity is tied to genes , which are the basic units of heredity ."]
|
Once we know the claim that ozone is North Carolina's most widespread air quality problem does not correspond with reality, we also know that diversity is tied to genes , which are the basic units of heredity . The claim that either caterpillars spend most of their time eating or some blood vessels surround renal tubules does not reflect reality. Either one or both of these statements are true: if psychoanalysis is impractical and ineffectual, going back to the past and ignoring present problems, then canned tuna is one of nature's healthiest and pure foods, or some minerals have chemicals. Provided that if psychoanalysis is impractical and ineffectual, going back to the past and ignoring present problems, then canned tuna is one of nature's healthiest and pure foods, we know that either either caterpillars spend most of their time eating or some blood vessels surround renal tubules or if the claim that ozone is North Carolina's most widespread air quality problem does not correspond with reality, then it is a common misconception that diversity is tied to genes , which are the basic units of heredity . Provided that some minerals have chemicals, we know that either either caterpillars spend most of their time eating or some blood vessels surround renal tubules or if the claim that ozone is North Carolina's most widespread air quality problem does not correspond with reality, then it is a common misconception that diversity is tied to genes , which are the basic units of heredity .
|
The claim that ozone is North Carolina's most widespread air quality problem holds true.
|
Ozone filters many UV rays from the sun.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either (Either [2] or [3].) or (If (Not [0].), then (Not [1].).). [SC1-2]
Not (Either [2] or [3].).
Therefore, If (Not [0].), then (Not [1].)..
[SC1-2]
Disjunction Elimination:
Either (If [4], then [5].) or [6].
If (If [4], then [5].), then (Either (Either [2] or [3].) or (If (Not [0].), then (Not [1].).).).
If [6], then (Either (Either [2] or [3].) or (If (Not [0].), then (Not [1].).).).
Therefore, Either (Either [2] or [3].) or (If (Not [0].), then (Not [1].).)..
|
{0: "Ozone is North Carolina's most widespread air quality problem.", 1: 'Diversity is tied to genes , which are the basic units of heredity .', 2: 'Caterpillars spend most of their time eating.', 3: 'Some blood vessels surround renal tubules.', 4: 'Psychoanalysis is impractical and ineffectual, going back to the past and ignoring present problems.', 5: "Canned tuna is one of nature's healthiest and pure foods.", 6: 'Some minerals have chemicals.'}
| 3 |
2,306 |
['We know that at least one of two things is true: either bats specialize in different foods or giant pandas eat bamboo , or either habitat loss is still an issue, as is lead poisoning or if silver is somewhat harder than gold and is second only to gold in malleability and ductility, then fibroids can cause severe pain, heavy bleeding and abdominal swelling, among other symptoms.', 'The claim that either bats specialize in different foods or giant pandas eat bamboo has no merit.', 'One may reasonably assume that if spheres have poles, then the claim that habitat loss is still an issue, as is lead poisoning has no merit.', 'The claim that spheres have poles holds true.']
|
We know that at least one of two things is true: either bats specialize in different foods or giant pandas eat bamboo , or either habitat loss is still an issue, as is lead poisoning or if silver is somewhat harder than gold and is second only to gold in malleability and ductility, then fibroids can cause severe pain, heavy bleeding and abdominal swelling, among other symptoms. The claim that either bats specialize in different foods or giant pandas eat bamboo has no merit. One may reasonably assume that if spheres have poles, then the claim that habitat loss is still an issue, as is lead poisoning has no merit. The claim that spheres have poles holds true.
|
On the condition that silver is somewhat harder than gold and is second only to gold in malleability and ductility, it is definitely the case that fibroids can cause severe pain, heavy bleeding and abdominal swelling, among other symptoms.
|
When silver is somewhat harder than gold and is second only to gold in malleability and ductility is true, it follows that fibroids are the most frequently diagnosed tumor of the female pelvis.
|
Uncertain
|
Disjunctive Syllogism:
Either [2] or (If [0], then [1].). [SC1-1]
Not [2]. [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Disjunctive Syllogism:
Either (Either [4] or [5].) or (Either [2] or (If [0], then [1].).).
Not (Either [4] or [5].).
Therefore, Either [2] or (If [0], then [1].)..
[SC2-1]
Modus Ponens:
If [3], then (Not [2].).
[3]
Therefore, Not [2]..
|
{0: 'Silver is somewhat harder than gold and is second only to gold in malleability and ductility.', 1: 'Fibroids can cause severe pain, heavy bleeding and abdominal swelling, among other symptoms.', 2: 'Habitat loss is still an issue, as is lead poisoning.', 3: 'Spheres have poles.', 4: 'Bats specialize in different foods.', 5: 'Giant pandas eat bamboo .'}
| 3 |
2,706 |
['Either one or both of these statements are true: either some cells go through repeated cell cycles or light falling on objects, is redirected in another direction, or either rationalism is the keystone of all our freedoms or academic fraud is a growing problem as researchers fight to keep an unspoken ethical code.', "The statement 'animals live in groups' is true.", 'It is rational to believe that either either some people have a long life, and some a short life or springs generally emerge from slopes on the downdip sides of hills or goldenseal root is antiseptic and hemostatic, which means it stops bleeding.', 'One may reasonably assume that if either some people have a long life, and some a short life or springs generally emerge from slopes on the downdip sides of hills, then if animals live in groups, then it is a common misconception that either some cells go through repeated cell cycles or light falling on objects, is redirected in another direction.', 'Provided that goldenseal root is antiseptic and hemostatic, which means it stops bleeding, we know that if animals live in groups, then it is a common misconception that either some cells go through repeated cell cycles or light falling on objects, is redirected in another direction.']
|
Either one or both of these statements are true: either some cells go through repeated cell cycles or light falling on objects, is redirected in another direction, or either rationalism is the keystone of all our freedoms or academic fraud is a growing problem as researchers fight to keep an unspoken ethical code. The statement 'animals live in groups' is true. It is rational to believe that either either some people have a long life, and some a short life or springs generally emerge from slopes on the downdip sides of hills or goldenseal root is antiseptic and hemostatic, which means it stops bleeding. One may reasonably assume that if either some people have a long life, and some a short life or springs generally emerge from slopes on the downdip sides of hills, then if animals live in groups, then it is a common misconception that either some cells go through repeated cell cycles or light falling on objects, is redirected in another direction. Provided that goldenseal root is antiseptic and hemostatic, which means it stops bleeding, we know that if animals live in groups, then it is a common misconception that either some cells go through repeated cell cycles or light falling on objects, is redirected in another direction.
|
Either rationalism is the keystone of all our freedoms or academic fraud is a growing problem as researchers fight to keep an unspoken ethical code.
|
Either rationalism implies an openness to correct one's positions, based on real-world experience or argentina has (part) pampases.
|
Uncertain
|
Disjunctive Syllogism:
Either (Either [2] or [3].) or (Either [0] or [1].).
Not (Either [2] or [3].). [SC2-1]
Therefore, Either [0] or [1]..
[SC2-1]
Modus Ponens:
If [4], then (Not (Either [2] or [3].).). [SC1-2]
[4]
Therefore, Not (Either [2] or [3].)..
[SC1-2]
Disjunction Elimination:
Either (Either [5] or [6].) or [7].
If (Either [5] or [6].), then (If [4], then (Not (Either [2] or [3].).).).
If [7], then (If [4], then (Not (Either [2] or [3].).).).
Therefore, If [4], then (Not (Either [2] or [3].).)..
|
{0: 'Rationalism is the keystone of all our freedoms.', 1: 'Academic fraud is a growing problem as researchers fight to keep an unspoken ethical code.', 2: 'Some cells go through repeated cell cycles.', 3: 'Light falling on objects, is redirected in another direction.', 4: 'Animals live in groups.', 5: 'Some people have a long life, and some a short life.', 6: 'Springs generally emerge from slopes on the downdip sides of hills.', 7: 'Goldenseal root is antiseptic and hemostatic, which means it stops bleeding.'}
| 3 |
2,496 |
['On the condition that a bushman is a pioneer, it is definitely the case that if most judges are lawyers who are able to understand the law, then solar flares have no known effect on the earth.', 'Many people rightly believe that a bushman is a pioneer.', 'It is a fact that either some silica has low density or love is the supreme meaning of our life.', 'On the condition that some silica has low density, it is definitely the case that most judges are lawyers who are able to understand the law.', 'Once we know love is the supreme meaning of our life, we also know that most judges are lawyers who are able to understand the law.']
|
On the condition that a bushman is a pioneer, it is definitely the case that if most judges are lawyers who are able to understand the law, then solar flares have no known effect on the earth. Many people rightly believe that a bushman is a pioneer. It is a fact that either some silica has low density or love is the supreme meaning of our life. On the condition that some silica has low density, it is definitely the case that most judges are lawyers who are able to understand the law. Once we know love is the supreme meaning of our life, we also know that most judges are lawyers who are able to understand the law.
|
The statement that states solar flares have no known effect on the earth is right.
|
Solar flares are brief, enormous outbursts of power.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [4], then (If [1], then [0].).
[4]
Therefore, If [1], then [0]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then [1].
If [3], then [1].
Therefore, [1].
|
{0: 'Solar flares have no known effect on the earth.', 1: 'Most judges are lawyers who are able to understand the law.', 2: 'Some silica has low density.', 3: 'Love is the supreme meaning of our life.', 4: 'A bushman is a pioneer.'}
| 3 |
2,558 |
['Should it be the case that some people mistakenly believe that if sunflower seeds are usually a dark brown to black, or large, grey and white striped, then elongated snouts account for the name bottlenose, it follows that likeness isa similarity.', 'The claim that likeness isa similarity does not reflect reality.', 'Should it be the case that caulk can be difficult to keep in vertical joints and on a variety of substrates, it follows that sunflower seeds are usually a dark brown to black, or large, grey and white striped.', 'caulk can be difficult to keep in vertical joints and on a variety of substrates.']
|
Should it be the case that some people mistakenly believe that if sunflower seeds are usually a dark brown to black, or large, grey and white striped, then elongated snouts account for the name bottlenose, it follows that likeness isa similarity. The claim that likeness isa similarity does not reflect reality. Should it be the case that caulk can be difficult to keep in vertical joints and on a variety of substrates, it follows that sunflower seeds are usually a dark brown to black, or large, grey and white striped. caulk can be difficult to keep in vertical joints and on a variety of substrates.
|
The statement that states elongated snouts account for the name bottlenose is right.
|
The statement that states elongated snouts account for the name bottlenose is right.
|
TRUE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If [1], then [0].).), then [2].
Not [2].
Therefore, If [1], then [0]..
[SC2-1]
Modus Ponens:
If [3], then [1].
[3]
Therefore, [1].
|
{0: 'Elongated snouts account for the name bottlenose.', 1: 'Sunflower seeds are usually a dark brown to black, or large, grey and white striped.', 2: 'Likeness isa similarity.', 3: 'Caulk can be difficult to keep in vertical joints and on a variety of substrates.'}
| 3 |
2,784 |
['It is rational to believe that either plants need little attention or ankles have (part) lobes.', 'Assuming plants need little attention, we know that coral calcium is a salt of calcium derived from fossilized coral reefs.', 'The claim that osprey courtship begins at food and nest locations does not correspond with reality.', "If the statement that 'if ankles have (part) lobes, then coral calcium is a salt of calcium derived from fossilized coral reefs' is incorrect, then if exercise increases oxygen consumption and causes oxygen stores to be depleted faster than usual, then myths reflect their time, place, and race.", 'When if exercise increases oxygen consumption and causes oxygen stores to be depleted faster than usual, then myths reflect their time, place, and race is true, it follows that osprey courtship begins at food and nest locations.']
|
It is rational to believe that either plants need little attention or ankles have (part) lobes. Assuming plants need little attention, we know that coral calcium is a salt of calcium derived from fossilized coral reefs. The claim that osprey courtship begins at food and nest locations does not correspond with reality. If the statement that 'if ankles have (part) lobes, then coral calcium is a salt of calcium derived from fossilized coral reefs' is incorrect, then if exercise increases oxygen consumption and causes oxygen stores to be depleted faster than usual, then myths reflect their time, place, and race. When if exercise increases oxygen consumption and causes oxygen stores to be depleted faster than usual, then myths reflect their time, place, and race is true, it follows that osprey courtship begins at food and nest locations.
|
Those that suggest coral calcium is a salt of calcium derived from fossilized coral reefs are right.
|
The statement, coral calcium is a salt of calcium derived from fossilized coral reefs, does not hold.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC3-1]
Modus Tonens:
If (Not (If [2], then [0].).), then [3]. [SC1-2]
Not [3].
Therefore, If [2], then [0]..
[SC1-2]
Hypothetical Syllogism:
If (Not (If [2], then [0].).), then (If [4], then [5].).
If (If [4], then [5].), then [3].
Therefore, If (Not (If [2], then [0].).), then [3]..
|
{0: 'Coral calcium is a salt of calcium derived from fossilized coral reefs.', 1: 'Plants need little attention.', 2: 'Ankles have (part) lobes.', 3: 'Osprey courtship begins at food and nest locations.', 4: 'Exercise increases oxygen consumption and causes oxygen stores to be depleted faster than usual.', 5: 'Myths reflect their time, place, and race.'}
| 3 |
2,239 |
['At least one of two things is true: corporate foundations are separate legal organizations, sometimes with an endowment, or carriers have limits.', 'On the condition that corporate foundations are separate legal organizations, sometimes with an endowment, it is definitely the case that if most conifers contain resin, then training are practice.', 'When carriers have limits is true, it follows that if most conifers contain resin, then training are practice.', 'We know that at least one of two things is true: most parents train children, or most conifers contain resin.', 'The claim that most parents train children does not reflect reality.']
|
At least one of two things is true: corporate foundations are separate legal organizations, sometimes with an endowment, or carriers have limits. On the condition that corporate foundations are separate legal organizations, sometimes with an endowment, it is definitely the case that if most conifers contain resin, then training are practice. When carriers have limits is true, it follows that if most conifers contain resin, then training are practice. We know that at least one of two things is true: most parents train children, or most conifers contain resin. The claim that most parents train children does not reflect reality.
|
The statement that states training are practice is right.
|
The statement that states training are practice is right.
|
TRUE
|
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]
Disjunctive Syllogism:
Either [4] or [1].
Not [4].
Therefore, [1].
|
{0: 'Training are practice.', 1: 'Most conifers contain resin.', 2: 'Corporate foundations are separate legal organizations, sometimes with an endowment.', 3: 'Carriers have limits.', 4: 'Most parents train children.'}
| 3 |
2,578 |
["On the condition that the claim that if the notion that 'caterpillars prefer sticks' is untrue, then citizenship requires practice through active involvement in the community has no merit, it is definitely the case that spiders extend legs.", "The statement 'spiders extend legs' can be considered false.", "Whenever it is true that citizenship requires practice through active involvement in the community, 'sheep readily consume top growth of woad until the flowering stage' is true.", "Assuming citizenship requires practice through active involvement in the community, we know that the statement that 'sheep readily consume top growth of woad until the flowering stage' is incorrect."]
|
On the condition that the claim that if the notion that 'caterpillars prefer sticks' is untrue, then citizenship requires practice through active involvement in the community has no merit, it is definitely the case that spiders extend legs. The statement 'spiders extend legs' can be considered false. Whenever it is true that citizenship requires practice through active involvement in the community, 'sheep readily consume top growth of woad until the flowering stage' is true. Assuming citizenship requires practice through active involvement in the community, we know that the statement that 'sheep readily consume top growth of woad until the flowering stage' is incorrect.
|
It is fair to say that caterpillars prefer sticks.
|
The claim that caterpillars prefer sticks has no merit.
|
FALSE
|
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].
Not [2].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Reductio Ad Absurdum:
If [1], then [3].
If [1], then (Not [3].).
Therefore, Not [1]..
|
{0: 'Caterpillars prefer sticks.', 1: 'Citizenship requires practice through active involvement in the community.', 2: 'Spiders extend legs.', 3: 'Sheep readily consume top growth of woad until the flowering stage.'}
| 3 |
2,055 |
["Given that wetlands are capable of reducing sulfate to sulfide, it can be inferred that if the notion that 'different batons are used by different people , for different things ' is untrue, then mixed incontinence is a combination of stress and urge incontinence.", 'It is reasonable to believe that wetlands are capable of reducing sulfate to sulfide.', "Once we know the notion that 'different batons are used by different people , for different things ' is untrue, we also know that irradiation is known as a cold process.", "Assuming irradiation is known as a cold process, we know that the statement 'mixed incontinence is a combination of stress and urge incontinence' can be considered false."]
|
Given that wetlands are capable of reducing sulfate to sulfide, it can be inferred that if the notion that 'different batons are used by different people , for different things ' is untrue, then mixed incontinence is a combination of stress and urge incontinence. It is reasonable to believe that wetlands are capable of reducing sulfate to sulfide. Once we know the notion that 'different batons are used by different people , for different things ' is untrue, we also know that irradiation is known as a cold process. Assuming irradiation is known as a cold process, we know that the statement 'mixed incontinence is a combination of stress and urge incontinence' can be considered false.
|
It is rational to agree that different batons are used by different people , for different things .
|
Those that suggest different batons are used by different people , for different things are wrong.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (If (Not [0].), then [1].).
[2]
Therefore, If (Not [0].), then [1]..
[SC2-1]
Hypothetical Syllogism:
If (Not [0].), then [3].
If [3], then (Not [1].).
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Different batons are used by different people , for different things .', 1: 'Mixed incontinence is a combination of stress and urge incontinence.', 2: 'Wetlands are capable of reducing sulfate to sulfide.', 3: 'Irradiation is known as a cold process.'}
| 3 |
2,906 |
['Provided that seeds vary greatly in color, texture, longevity, and methods of dispersal, we know that domestic noise is a major and increasing source of complaints to local authorities.', 'It is not the case that mangabeys give birth to monkeys.', 'We know that at least one of two things is true: deep breathing works anyplace, anytime to increase the supply of oxygen to muscles and organs, or either some infection destroys cause brains or corn snakes are native to the United States.', 'If deep breathing works anyplace, anytime to increase the supply of oxygen to muscles and organs, then either mangabeys give birth to monkeys or seeds vary greatly in color, texture, longevity, and methods of dispersal.', 'Should it be the case that either some infection destroys cause brains or corn snakes are native to the United States, it follows that either mangabeys give birth to monkeys or seeds vary greatly in color, texture, longevity, and methods of dispersal.']
|
Provided that seeds vary greatly in color, texture, longevity, and methods of dispersal, we know that domestic noise is a major and increasing source of complaints to local authorities. It is not the case that mangabeys give birth to monkeys. We know that at least one of two things is true: deep breathing works anyplace, anytime to increase the supply of oxygen to muscles and organs, or either some infection destroys cause brains or corn snakes are native to the United States. If deep breathing works anyplace, anytime to increase the supply of oxygen to muscles and organs, then either mangabeys give birth to monkeys or seeds vary greatly in color, texture, longevity, and methods of dispersal. Should it be the case that either some infection destroys cause brains or corn snakes are native to the United States, it follows that either mangabeys give birth to monkeys or seeds vary greatly in color, texture, longevity, and methods of dispersal.
|
The idea that domestic noise is a major and increasing source of complaints to local authorities is true.
|
We know that the claim that domestic noise is a major and increasing source of complaints to local authorities is false.
|
FALSE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or [1]. [SC1-2]
Not [2].
Therefore, [1].
[SC1-2]
Disjunction Elimination:
Either [3] or (Either [4] or [5].).
If [3], then (Either [2] or [1].).
If (Either [4] or [5].), then (Either [2] or [1].).
Therefore, Either [2] or [1]..
|
{0: 'Domestic noise is a major and increasing source of complaints to local authorities.', 1: 'Seeds vary greatly in color, texture, longevity, and methods of dispersal.', 2: 'Mangabeys give birth to monkeys.', 3: 'Deep breathing works anyplace, anytime to increase the supply of oxygen to muscles and organs.', 4: 'Some infection destroys cause brains.', 5: 'Corn snakes are native to the United States.'}
| 3 |
2,175 |
['Given that most people know about eating sensibly and exercising more, it can be inferred that a bank loan is a loan.', 'There is good reason to believe that either military planes are the most sophisticated and fastest planes used by people or most people know about eating sensibly and exercising more.', 'There is good reason to believe that either lawns are more harmful to lakes than toxic substances or waste from individual sewage systems or it is a common misconception that military planes are the most sophisticated and fastest planes used by people.', "The notion that 'lawns are more harmful to lakes than toxic substances or waste from individual sewage systems' is untrue."]
|
Given that most people know about eating sensibly and exercising more, it can be inferred that a bank loan is a loan. There is good reason to believe that either military planes are the most sophisticated and fastest planes used by people or most people know about eating sensibly and exercising more. There is good reason to believe that either lawns are more harmful to lakes than toxic substances or waste from individual sewage systems or it is a common misconception that military planes are the most sophisticated and fastest planes used by people. The notion that 'lawns are more harmful to lakes than toxic substances or waste from individual sewage systems' is untrue.
|
It is reasonable to believe that a bank loan is a loan.
|
It is reasonable to believe that a bank loan is a loan.
|
TRUE
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or [1].
Not [2]. [SC2-2]
Therefore, [1].
[SC2-2]
Disjunctive Syllogism:
Either [3] or (Not [2].).
Not [3].
Therefore, Not [2]..
|
{0: 'A bank loan is a loan.', 1: 'Most people know about eating sensibly and exercising more.', 2: 'Military planes are the most sophisticated and fastest planes used by people.', 3: 'Lawns are more harmful to lakes than toxic substances or waste from individual sewage systems.'}
| 3 |
2,014 |
['Once we know the claim that if we know that the claim that either fruit bats enter zones or european countries pretend to be democratic is false, then if people die every year from eating tasty but poisonous mushrooms, then transcendental numbers are also irrational has no merit, we also know that if appeal is attractiveness, then compact discs are sound recordings.', 'The claim that if appeal is attractiveness, then compact discs are sound recordings does not correspond with reality.', 'There is good reason to believe that either some lesser kudus have white stripes or a mirror image is similarity.', 'On the condition that some lesser kudus have white stripes, it is definitely the case that the statement, if people die every year from eating tasty but poisonous mushrooms, then transcendental numbers are also irrational, does not hold.', 'Once we know a mirror image is similarity, we also know that the statement, if people die every year from eating tasty but poisonous mushrooms, then transcendental numbers are also irrational, does not hold.']
|
Once we know the claim that if we know that the claim that either fruit bats enter zones or european countries pretend to be democratic is false, then if people die every year from eating tasty but poisonous mushrooms, then transcendental numbers are also irrational has no merit, we also know that if appeal is attractiveness, then compact discs are sound recordings. The claim that if appeal is attractiveness, then compact discs are sound recordings does not correspond with reality. There is good reason to believe that either some lesser kudus have white stripes or a mirror image is similarity. On the condition that some lesser kudus have white stripes, it is definitely the case that the statement, if people die every year from eating tasty but poisonous mushrooms, then transcendental numbers are also irrational, does not hold. Once we know a mirror image is similarity, we also know that the statement, if people die every year from eating tasty but poisonous mushrooms, then transcendental numbers are also irrational, does not hold.
|
We know that at least one of two things is true: fruit bats enter zones, or european countries pretend to be democratic.
|
We know that at least one of two things is true: fruit bats enter zones, or european countries pretend to be democratic.
|
TRUE
|
Modus Tonens:
If (Not (Either [0] or [1].).), then (If [2], then [3].). [SC1-1]
Not (If [2], then [3].). [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Modus Tonens:
If (Not (If (Not (Either [0] or [1].).), then (If [2], then [3].).).), then (If [4], then [5].).
Not (If [4], then [5].).
Therefore, If (Not (Either [0] or [1].).), then (If [2], then [3].)..
[SC2-1]
Disjunction Elimination:
Either [6] or [7].
If [6], then (Not (If [2], then [3].).).
If [7], then (Not (If [2], then [3].).).
Therefore, Not (If [2], then [3].)..
|
{0: 'Fruit bats enter zones.', 1: 'European countries pretend to be democratic.', 2: 'People die every year from eating tasty but poisonous mushrooms.', 3: 'Transcendental numbers are also irrational.', 4: 'Appeal is attractiveness.', 5: 'Compact discs are sound recordings.', 6: 'Some lesser kudus have white stripes.', 7: 'A mirror image is similarity.'}
| 3 |
2,077 |
["The claim that cosmic rays are atomic nuclei that enter the Earth's atmosphere at nearly the speed of light is true.", "The notion that 'filters create electronic noise, the deeper the filter, the greater the noise' is untrue.", "Should it be the case that the claim that either filters create electronic noise, the deeper the filter, the greater the noise or if cosmic rays are atomic nuclei that enter the Earth's atmosphere at nearly the speed of light, then children experience gastrointestinal difficulty has no merit, it follows that wick has (part) sections.", "Should it be the case that the claim that either filters create electronic noise, the deeper the filter, the greater the noise or if cosmic rays are atomic nuclei that enter the Earth's atmosphere at nearly the speed of light, then children experience gastrointestinal difficulty has no merit, it follows that the notion that 'wick has (part) sections' is untrue."]
|
The claim that cosmic rays are atomic nuclei that enter the Earth's atmosphere at nearly the speed of light is true. The notion that 'filters create electronic noise, the deeper the filter, the greater the noise' is untrue. Should it be the case that the claim that either filters create electronic noise, the deeper the filter, the greater the noise or if cosmic rays are atomic nuclei that enter the Earth's atmosphere at nearly the speed of light, then children experience gastrointestinal difficulty has no merit, it follows that wick has (part) sections. Should it be the case that the claim that either filters create electronic noise, the deeper the filter, the greater the noise or if cosmic rays are atomic nuclei that enter the Earth's atmosphere at nearly the speed of light, then children experience gastrointestinal difficulty has no merit, it follows that the notion that 'wick has (part) sections' is untrue.
|
It is fair to say that children experience gastrointestinal difficulty.
|
Children play sexually with their own and the opposite sex, and occasionally even with siblings.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [1], then [0].). [SC1-2]
Not [2].
Therefore, If [1], then [0]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [2] or (If [1], then [0].).).), then [3].
If (Not (Either [2] or (If [1], then [0].).).), then (Not [3].).
Therefore, Either [2] or (If [1], then [0].)..
|
{0: 'Children experience gastrointestinal difficulty.', 1: "Cosmic rays are atomic nuclei that enter the Earth's atmosphere at nearly the speed of light.", 2: 'Filters create electronic noise, the deeper the filter, the greater the noise.', 3: 'Wick has (part) sections.'}
| 3 |
2,031 |
['One may reasonably assume that if electric circuits are used to distribute energy quickly and conveniently to distant locations, then hard leather is best on carpeting but can sometimes be too slippery.', 'It is a fact that either salvadoran tortillas are smaller and much thicker than Mexican tortillas or snares placed in trails or under fences can successfully capture furbearers.', 'Provided that salvadoran tortillas are smaller and much thicker than Mexican tortillas, we know that either electric circuits are used to distribute energy quickly and conveniently to distant locations or most marine environments have characteristics.', 'When snares placed in trails or under fences can successfully capture furbearers is true, it follows that either electric circuits are used to distribute energy quickly and conveniently to distant locations or most marine environments have characteristics.', 'Given that it is not the case that if most marine environments have characteristics, then hard leather is best on carpeting but can sometimes be too slippery, it can be inferred that either main minerals are diamond, gold, uranium, steel, limestone, copper and manganese or arthritis is an ailment often dealt with best at home.', 'When it is not the case that if most marine environments have characteristics, then hard leather is best on carpeting but can sometimes be too slippery is true, it follows that we know that the claim that either main minerals are diamond, gold, uranium, steel, limestone, copper and manganese or arthritis is an ailment often dealt with best at home is false.']
|
One may reasonably assume that if electric circuits are used to distribute energy quickly and conveniently to distant locations, then hard leather is best on carpeting but can sometimes be too slippery. It is a fact that either salvadoran tortillas are smaller and much thicker than Mexican tortillas or snares placed in trails or under fences can successfully capture furbearers. Provided that salvadoran tortillas are smaller and much thicker than Mexican tortillas, we know that either electric circuits are used to distribute energy quickly and conveniently to distant locations or most marine environments have characteristics. When snares placed in trails or under fences can successfully capture furbearers is true, it follows that either electric circuits are used to distribute energy quickly and conveniently to distant locations or most marine environments have characteristics. Given that it is not the case that if most marine environments have characteristics, then hard leather is best on carpeting but can sometimes be too slippery, it can be inferred that either main minerals are diamond, gold, uranium, steel, limestone, copper and manganese or arthritis is an ailment often dealt with best at home. When it is not the case that if most marine environments have characteristics, then hard leather is best on carpeting but can sometimes be too slippery is true, it follows that we know that the claim that either main minerals are diamond, gold, uranium, steel, limestone, copper and manganese or arthritis is an ailment often dealt with best at home is false.
|
The idea that hard leather is best on carpeting but can sometimes be too slippery is true.
|
Tables provide results.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Either [1] or [2].).
If [4], then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then [0].).), then (Either [5] or [6].).
If (Not (If [2], then [0].).), then (Not (Either [5] or [6].).).
Therefore, If [2], then [0]..
|
{0: 'Hard leather is best on carpeting but can sometimes be too slippery.', 1: 'Electric circuits are used to distribute energy quickly and conveniently to distant locations.', 2: 'Most marine environments have characteristics.', 3: 'Salvadoran tortillas are smaller and much thicker than Mexican tortillas.', 4: 'Snares placed in trails or under fences can successfully capture furbearers.', 5: 'Main minerals are diamond, gold, uranium, steel, limestone, copper and manganese.', 6: 'Arthritis is an ailment often dealt with best at home.'}
| 3 |
2,481 |
['We know that at least one of two things is true: metastatic lesions respond to chemotherapy or localized radiation therapy, or fire can be a threat to humans.', 'One may reasonably assume that if metastatic lesions respond to chemotherapy or localized radiation therapy, then astronomy is the only science that can really travel in the past.', 'We know that either criminal law involves a citizen or a business and the state or analyses reveal motion.', 'When criminal law involves a citizen or a business and the state is true, it follows that we know that the claim that astronomy is the only science that can really travel in the past is false.', 'Provided that analyses reveal motion, we know that we know that the claim that astronomy is the only science that can really travel in the past is false.']
|
We know that at least one of two things is true: metastatic lesions respond to chemotherapy or localized radiation therapy, or fire can be a threat to humans. One may reasonably assume that if metastatic lesions respond to chemotherapy or localized radiation therapy, then astronomy is the only science that can really travel in the past. We know that either criminal law involves a citizen or a business and the state or analyses reveal motion. When criminal law involves a citizen or a business and the state is true, it follows that we know that the claim that astronomy is the only science that can really travel in the past is false. Provided that analyses reveal motion, we know that we know that the claim that astronomy is the only science that can really travel in the past is false.
|
fire can be a threat to humans.
|
Fire does damage.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0].
Not [1]. [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If [1], then [2].
Not [2]. [SC2-2]
Therefore, Not [1]..
[SC2-2]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Not [2].).
If [4], then (Not [2].).
Therefore, Not [2]..
|
{0: 'Fire can be a threat to humans.', 1: 'Metastatic lesions respond to chemotherapy or localized radiation therapy.', 2: 'Astronomy is the only science that can really travel in the past.', 3: 'Criminal law involves a citizen or a business and the state.', 4: 'Analyses reveal motion.'}
| 3 |
2,310 |
['Either one or both of these statements are true: teenagers are teenagers, or sedges have a superficial resemblance to grasses.', 'Assuming sedges have a superficial resemblance to grasses, we know that we know that the claim that most nutrias have long tails is false.', 'It is rational to believe that either resistance is associated with past pesticide use patterns or if teenagers are teenagers, then we know that the claim that most nutrias have long tails is false.', 'Either logical calculuses differ according as they concentrate on different kinds of valid argument forms or the claim that resistance is associated with past pesticide use patterns does not correspond with reality.', 'The statement that states logical calculuses differ according as they concentrate on different kinds of valid argument forms is false.']
|
Either one or both of these statements are true: teenagers are teenagers, or sedges have a superficial resemblance to grasses. Assuming sedges have a superficial resemblance to grasses, we know that we know that the claim that most nutrias have long tails is false. It is rational to believe that either resistance is associated with past pesticide use patterns or if teenagers are teenagers, then we know that the claim that most nutrias have long tails is false. Either logical calculuses differ according as they concentrate on different kinds of valid argument forms or the claim that resistance is associated with past pesticide use patterns does not correspond with reality. The statement that states logical calculuses differ according as they concentrate on different kinds of valid argument forms is false.
|
We know that the claim that most nutrias have long tails is false.
|
The statement that states nutrias have claw toes is false.
|
Uncertain
|
Disjunction Elimination:
Either [1] or [2].
If [1], then (Not [0].). [SC2-1]
If [2], then (Not [0].).
Therefore, Not [0]..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (If [1], then (Not [0].).).
Not [3]. [SC2-2]
Therefore, If [1], then (Not [0].)..
[SC2-2]
Disjunctive Syllogism:
Either [4] or (Not [3].).
Not [4].
Therefore, Not [3]..
|
{0: 'Most nutrias have long tails.', 1: 'Teenagers are teenagers.', 2: 'Sedges have a superficial resemblance to grasses.', 3: 'Resistance is associated with past pesticide use patterns.', 4: 'Logical calculuses differ according as they concentrate on different kinds of valid argument forms.'}
| 3 |
2,311 |
['Either antelopes have (part) cells or if homosexuals are the only group to claim minority status based on behavior, then cougar numbers are at high population levels.', 'The claim that antelopes have (part) cells does not reflect reality.', 'Given that some people mistakenly believe that homosexuals are the only group to claim minority status based on behavior, it can be inferred that most computer systems support floating point in hardware today.', "Assuming some people mistakenly believe that homosexuals are the only group to claim minority status based on behavior, we know that the notion that 'most computer systems support floating point in hardware today' is untrue."]
|
Either antelopes have (part) cells or if homosexuals are the only group to claim minority status based on behavior, then cougar numbers are at high population levels. The claim that antelopes have (part) cells does not reflect reality. Given that some people mistakenly believe that homosexuals are the only group to claim minority status based on behavior, it can be inferred that most computer systems support floating point in hardware today. Assuming some people mistakenly believe that homosexuals are the only group to claim minority status based on behavior, we know that the notion that 'most computer systems support floating point in hardware today' is untrue.
|
It is reasonable to believe that cougar numbers are at high population levels.
|
Driveshafts are fairly heavy, they can be quite long, and they turn at high speeds.
|
Uncertain
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1] [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [1], then [0].).
Not [2].
Therefore, If [1], then [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Not [1].), then [3].
If (Not [1].), then (Not [3].).
Therefore, [1].
|
{0: 'Cougar numbers are at high population levels.', 1: 'Homosexuals are the only group to claim minority status based on behavior.', 2: 'Antelopes have (part) cells.', 3: 'Most computer systems support floating point in hardware today.'}
| 3 |
2,883 |
['We know that the claim that some organic polymers can exhibit strong ceramic qualities, forming bonds in three dimensions is false.', 'We know that either either albumin is synthesized by the liver and secreted into the blood or many stars occur in pairs, multiple systems, and star cluster s or sheep eat grass.', 'Provided that sheep eat grass, we know that if it is not true that some fields have poles, then some organic polymers can exhibit strong ceramic qualities, forming bonds in three dimensions.', 'Once we know the statement that states if either albumin is synthesized by the liver and secreted into the blood or many stars occur in pairs, multiple systems, and star cluster s , then if it is not true that some fields have poles, then some organic polymers can exhibit strong ceramic qualities, forming bonds in three dimensions is false, we also know that either many drugs commonly used today are of herbal medicine origin or remediation is a tool to assist students in becoming more academically successful.', 'If the statement that states if either albumin is synthesized by the liver and secreted into the blood or many stars occur in pairs, multiple systems, and star cluster s , then if it is not true that some fields have poles, then some organic polymers can exhibit strong ceramic qualities, forming bonds in three dimensions is false, then the claim that either many drugs commonly used today are of herbal medicine origin or remediation is a tool to assist students in becoming more academically successful has no merit.']
|
We know that the claim that some organic polymers can exhibit strong ceramic qualities, forming bonds in three dimensions is false. We know that either either albumin is synthesized by the liver and secreted into the blood or many stars occur in pairs, multiple systems, and star cluster s or sheep eat grass. Provided that sheep eat grass, we know that if it is not true that some fields have poles, then some organic polymers can exhibit strong ceramic qualities, forming bonds in three dimensions. Once we know the statement that states if either albumin is synthesized by the liver and secreted into the blood or many stars occur in pairs, multiple systems, and star cluster s , then if it is not true that some fields have poles, then some organic polymers can exhibit strong ceramic qualities, forming bonds in three dimensions is false, we also know that either many drugs commonly used today are of herbal medicine origin or remediation is a tool to assist students in becoming more academically successful. If the statement that states if either albumin is synthesized by the liver and secreted into the blood or many stars occur in pairs, multiple systems, and star cluster s , then if it is not true that some fields have poles, then some organic polymers can exhibit strong ceramic qualities, forming bonds in three dimensions is false, then the claim that either many drugs commonly used today are of herbal medicine origin or remediation is a tool to assist students in becoming more academically successful has no merit.
|
We can assume that some fields have poles.
|
Fields consist of trees.
|
Uncertain
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either (Either [2] or [3].) or [4].
If (Either [2] or [3].), then (If (Not [0].), then [1].). [SC2-2]
If [4], then (If (Not [0].), then [1].).
Therefore, If (Not [0].), then [1]..
[SC2-2]
Reductio Ad Absurdum:
If (Not (If (Either [2] or [3].), then (If (Not [0].), then [1].).).), then (Either [5] or [6].).
If (Not (If (Either [2] or [3].), then (If (Not [0].), then [1].).).), then (Not (Either [5] or [6].).).
Therefore, If (Either [2] or [3].), then (If (Not [0].), then [1].)..
|
{0: 'Some fields have poles.', 1: 'Some organic polymers can exhibit strong ceramic qualities, forming bonds in three dimensions.', 2: 'Albumin is synthesized by the liver and secreted into the blood.', 3: 'Many stars occur in pairs, multiple systems, and star cluster s .', 4: 'Sheep eat grass.', 5: 'Many drugs commonly used today are of herbal medicine origin.', 6: 'Remediation is a tool to assist students in becoming more academically successful.'}
| 3 |
2,788 |
["It is not true that friendship is a special word with a sacred meaning of 'a sincere gift of self' to the other.", "One may reasonably assume that if some animals resemble snakes, then either friendship is a special word with a sacred meaning of 'a sincere gift of self' to the other or it is a common misconception that if a steeple is a tower, then pulmonary emboli are a major cause of death following operation.", "So long as skippers are a separate group of butterflies, with many distinctive features, 'either friendship is a special word with a sacred meaning of 'a sincere gift of self' to the other or it is a common misconception that if a steeple is a tower, then pulmonary emboli are a major cause of death following operation' is true.", 'When large differences exist in the semen producing ability of bulls of the same age, weight and breed is true, it follows that either some animals resemble snakes or skippers are a separate group of butterflies, with many distinctive features.', 'The claim that large differences exist in the semen producing ability of bulls of the same age, weight and breed holds true.']
|
It is not true that friendship is a special word with a sacred meaning of 'a sincere gift of self' to the other. One may reasonably assume that if some animals resemble snakes, then either friendship is a special word with a sacred meaning of 'a sincere gift of self' to the other or it is a common misconception that if a steeple is a tower, then pulmonary emboli are a major cause of death following operation. So long as skippers are a separate group of butterflies, with many distinctive features, 'either friendship is a special word with a sacred meaning of 'a sincere gift of self' to the other or it is a common misconception that if a steeple is a tower, then pulmonary emboli are a major cause of death following operation' is true. When large differences exist in the semen producing ability of bulls of the same age, weight and breed is true, it follows that either some animals resemble snakes or skippers are a separate group of butterflies, with many distinctive features. The claim that large differences exist in the semen producing ability of bulls of the same age, weight and breed holds true.
|
It is a common misconception that if a steeple is a tower, then pulmonary emboli are a major cause of death following operation.
|
It is a common misconception that a steeple is a tower.
|
Uncertain
|
Disjunctive Syllogism:
Either [2] or (Not (If [0], then [1].).). [SC1-1]
Not [2].
Therefore, Not (If [0], then [1].)..
[SC1-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (Either [2] or (Not (If [0], then [1].).).).
If [4], then (Either [2] or (Not (If [0], then [1].).).).
Therefore, Either [2] or (Not (If [0], then [1].).)..
[SC1-2]
Modus Ponens:
If [5], then (Either [3] or [4].).
[5]
Therefore, Either [3] or [4]..
|
{0: 'A steeple is a tower.', 1: 'Pulmonary emboli are a major cause of death following operation.', 2: "Friendship is a special word with a sacred meaning of 'a sincere gift of self' to the other.", 3: 'Some animals resemble snakes.', 4: 'Skippers are a separate group of butterflies, with many distinctive features.', 5: 'Large differences exist in the semen producing ability of bulls of the same age, weight and breed.'}
| 3 |
2,045 |
['Given that clinical electrocardiograms make up such a class of signals, it can be inferred that hair needs silica to grow and as a protection for the skin and cell walls.', "Whenever it is true that some slime tubes fill with fluid, 'if if clinical electrocardiograms make up such a class of signals, then hair needs silica to grow and as a protection for the skin and cell walls, then a kitchenette is a kitchen' is true.", "Whenever it is true that moccasins are very popular for footwear, 'some slime tubes fill with fluid' is true.", 'The claim that moccasins are very popular for footwear is true.']
|
Given that clinical electrocardiograms make up such a class of signals, it can be inferred that hair needs silica to grow and as a protection for the skin and cell walls. Whenever it is true that some slime tubes fill with fluid, 'if if clinical electrocardiograms make up such a class of signals, then hair needs silica to grow and as a protection for the skin and cell walls, then a kitchenette is a kitchen' is true. Whenever it is true that moccasins are very popular for footwear, 'some slime tubes fill with fluid' is true. The claim that moccasins are very popular for footwear is true.
|
a kitchenette is a kitchen.
|
It is not true that a kitchenette is a kitchen.
|
FALSE
|
Modus Ponens:
If (If [1], then [2].), then [0]. [SC1-1]
If [1], then [2].
Therefore, [0].
[SC1-1]
Modus Ponens:
If [3], then (If (If [1], then [2].), then [0].).
[3] [SC2-2]
Therefore, If (If [1], then [2].), then [0]..
[SC2-2]
Modus Ponens:
If [4], then [3].
[4]
Therefore, [3].
|
{0: 'A kitchenette is a kitchen.', 1: 'Clinical electrocardiograms make up such a class of signals.', 2: 'Hair needs silica to grow and as a protection for the skin and cell walls.', 3: 'Some slime tubes fill with fluid.', 4: 'Moccasins are very popular for footwear.'}
| 3 |
2,103 |
['Either households give charity or if it is a common misconception that folk art is art made by self-trained artists or trained artisans, then if filing cabinets serve well for storing science materials, then some hormones control reproduction.', 'It is not true that households give charity.', 'We know that either if most weeds grow in unhealthy soil, then bestsellers are both fiction and non-fiction books that have sold well in bookstores or either clock speed is an unreliable benchmark of computer performance or prosthetic groups are non-polypeptide groups.', 'Provided that if most weeds grow in unhealthy soil, then bestsellers are both fiction and non-fiction books that have sold well in bookstores, we know that if it is a common misconception that folk art is art made by self-trained artists or trained artisans, then those that suggest if filing cabinets serve well for storing science materials, then some hormones control reproduction are wrong.', 'If either clock speed is an unreliable benchmark of computer performance or prosthetic groups are non-polypeptide groups, then if it is a common misconception that folk art is art made by self-trained artists or trained artisans, then those that suggest if filing cabinets serve well for storing science materials, then some hormones control reproduction are wrong.']
|
Either households give charity or if it is a common misconception that folk art is art made by self-trained artists or trained artisans, then if filing cabinets serve well for storing science materials, then some hormones control reproduction. It is not true that households give charity. We know that either if most weeds grow in unhealthy soil, then bestsellers are both fiction and non-fiction books that have sold well in bookstores or either clock speed is an unreliable benchmark of computer performance or prosthetic groups are non-polypeptide groups. Provided that if most weeds grow in unhealthy soil, then bestsellers are both fiction and non-fiction books that have sold well in bookstores, we know that if it is a common misconception that folk art is art made by self-trained artists or trained artisans, then those that suggest if filing cabinets serve well for storing science materials, then some hormones control reproduction are wrong. If either clock speed is an unreliable benchmark of computer performance or prosthetic groups are non-polypeptide groups, then if it is a common misconception that folk art is art made by self-trained artists or trained artisans, then those that suggest if filing cabinets serve well for storing science materials, then some hormones control reproduction are wrong.
|
The statement 'folk art is art made by self-trained artists or trained artisans' can be considered true.
|
The statement 'folk art is art made by self-trained artists or trained artisans' can be considered true.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then (If [1], then [2].). [SC1-1]
If (Not [0].), then (Not (If [1], then [2].).). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [7] or (If (Not [0].), then (If [1], then [2].).).
Not [7].
Therefore, If (Not [0].), then (If [1], then [2].)..
[SC2-1]
Disjunction Elimination:
Either (If [3], then [4].) or (Either [5] or [6].).
If (If [3], then [4].), then (If (Not [0].), then (Not (If [1], then [2].).).).
If (Either [5] or [6].), then (If (Not [0].), then (Not (If [1], then [2].).).).
Therefore, If (Not [0].), then (Not (If [1], then [2].).)..
|
{0: 'Folk art is art made by self-trained artists or trained artisans.', 1: 'Filing cabinets serve well for storing science materials.', 2: 'Some hormones control reproduction.', 3: 'Most weeds grow in unhealthy soil.', 4: 'Bestsellers are both fiction and non-fiction books that have sold well in bookstores.', 5: 'Clock speed is an unreliable benchmark of computer performance.', 6: 'Prosthetic groups are non-polypeptide groups.', 7: 'Households give charity.'}
| 3 |
2,760 |
["Given that the statement 'if many carnivores grab their prey in their mouths, then it is not true that many children have concepts' can be considered false, it can be inferred that most waterbucks have glands.", "When the statement 'if many carnivores grab their prey in their mouths, then it is not true that many children have concepts' can be considered false is true, it follows that the claim that most waterbucks have glands does not correspond with reality.", 'Once we know the claim that many carnivores grab their prey in their mouths has no merit, we also know that chiari syndrome is named after the man who first described it.', 'Those that suggest chiari syndrome is named after the man who first described it are wrong.']
|
Given that the statement 'if many carnivores grab their prey in their mouths, then it is not true that many children have concepts' can be considered false, it can be inferred that most waterbucks have glands. When the statement 'if many carnivores grab their prey in their mouths, then it is not true that many children have concepts' can be considered false is true, it follows that the claim that most waterbucks have glands does not correspond with reality. Once we know the claim that many carnivores grab their prey in their mouths has no merit, we also know that chiari syndrome is named after the man who first described it. Those that suggest chiari syndrome is named after the man who first described it are wrong.
|
It is not true that many children have concepts.
|
It is not true that many children have concepts.
|
TRUE
|
Modus Ponens:
If [1], then (Not [0].). [SC1-1]
[1] [SC2-1]
Therefore, Not [0]..
[SC1-1]
Reductio Ad Absurdum:
If (Not (If [1], then (Not [0].).).), then [2].
If (Not (If [1], then (Not [0].).).), then (Not [2].).
Therefore, If [1], then (Not [0].)..
[SC2-1]
Modus Tonens:
If (Not [1].), then [3].
Not [3].
Therefore, [1].
|
{0: 'Many children have concepts.', 1: 'Many carnivores grab their prey in their mouths.', 2: 'Most waterbucks have glands.', 3: 'Chiari syndrome is named after the man who first described it.'}
| 3 |
2,001 |
["There is good reason to believe that either vaccines save money on both direct and indirect costs of the disease or if elms have (part) tree branches, then time calculated from the moon's position is called ephemeris time and moves at a truly uniform rate.", 'Should it be the case that vaccines save money on both direct and indirect costs of the disease, it follows that either guns can do good, or evil, depending on whose hands they reside or the claim that either diffusion relies on proton secretion or refine sugar includes sugar has no merit.', "One may reasonably assume that if if elms have (part) tree branches, then time calculated from the moon's position is called ephemeris time and moves at a truly uniform rate, then either guns can do good, or evil, depending on whose hands they reside or the claim that either diffusion relies on proton secretion or refine sugar includes sugar has no merit.", 'When guns can do good, or evil, depending on whose hands they reside is true, it follows that if some palm kernels come from oil palm trees, then aisles are located in buildings.', 'It is not true that if some palm kernels come from oil palm trees, then aisles are located in buildings.']
|
There is good reason to believe that either vaccines save money on both direct and indirect costs of the disease or if elms have (part) tree branches, then time calculated from the moon's position is called ephemeris time and moves at a truly uniform rate. Should it be the case that vaccines save money on both direct and indirect costs of the disease, it follows that either guns can do good, or evil, depending on whose hands they reside or the claim that either diffusion relies on proton secretion or refine sugar includes sugar has no merit. One may reasonably assume that if if elms have (part) tree branches, then time calculated from the moon's position is called ephemeris time and moves at a truly uniform rate, then either guns can do good, or evil, depending on whose hands they reside or the claim that either diffusion relies on proton secretion or refine sugar includes sugar has no merit. When guns can do good, or evil, depending on whose hands they reside is true, it follows that if some palm kernels come from oil palm trees, then aisles are located in buildings. It is not true that if some palm kernels come from oil palm trees, then aisles are located in buildings.
|
The claim that either diffusion relies on proton secretion or refine sugar includes sugar has no merit.
|
It is a fact that either diffusion relies on proton secretion or refine sugar includes sugar.
|
FALSE
|
Disjunctive Syllogism:
Either [2] or (Not (Either [0] or [1].).). [SC1-1]
Not [2]. [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Disjunction Elimination:
Either [5] or (If [6], then [7].).
If [5], then (Either [2] or (Not (Either [0] or [1].).).).
If (If [6], then [7].), then (Either [2] or (Not (Either [0] or [1].).).).
Therefore, Either [2] or (Not (Either [0] or [1].).)..
[SC2-1]
Modus Tonens:
If [2], then (If [3], then [4].).
Not (If [3], then [4].).
Therefore, Not [2]..
|
{0: 'Diffusion relies on proton secretion.', 1: 'Refine sugar includes sugar.', 2: 'Guns can do good, or evil, depending on whose hands they reside.', 3: 'Some palm kernels come from oil palm trees.', 4: 'Aisles are located in buildings.', 5: 'Vaccines save money on both direct and indirect costs of the disease.', 6: 'Elms have (part) tree branches.', 7: "Time calculated from the moon's position is called ephemeris time and moves at a truly uniform rate."}
| 3 |
2,823 |
['One may reasonably assume that if if anoles can climb glass walls, then schizophrenia is a disabling disease, then man is the product of chance in a closed system of natural law.', 'Assuming if data collection is a critical part of consumer behavior, then moulds are dishs, we know that man is the product of chance in a closed system of natural law.', 'Should it be the case that the claim that either if anoles can climb glass walls, then schizophrenia is a disabling disease or if data collection is a critical part of consumer behavior, then moulds are dishs has no merit, it follows that influenza is a contagious disease caused by a virus.', 'Given that influenza is a contagious disease caused by a virus, it can be inferred that most armadillos do have teeth.', 'It is not true that most armadillos do have teeth.']
|
One may reasonably assume that if if anoles can climb glass walls, then schizophrenia is a disabling disease, then man is the product of chance in a closed system of natural law. Assuming if data collection is a critical part of consumer behavior, then moulds are dishs, we know that man is the product of chance in a closed system of natural law. Should it be the case that the claim that either if anoles can climb glass walls, then schizophrenia is a disabling disease or if data collection is a critical part of consumer behavior, then moulds are dishs has no merit, it follows that influenza is a contagious disease caused by a virus. Given that influenza is a contagious disease caused by a virus, it can be inferred that most armadillos do have teeth. It is not true that most armadillos do have teeth.
|
Many people rightly believe that man is the product of chance in a closed system of natural law.
|
Men solve problems.
|
Uncertain
|
Disjunction Elimination:
Either (If [1], then [2].) or (If [3], then [4].). [SC1-1]
If (If [1], then [2].), then [0].
If (If [3], then [4].), then [0].
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either (If [1], then [2].) or (If [3], then [4].).).), then [5].
Not [5]. [SC2-2]
Therefore, Either (If [1], then [2].) or (If [3], then [4].)..
[SC2-2]
Modus Tonens:
If [5], then [6].
Not [6].
Therefore, Not [5]..
|
{0: 'Man is the product of chance in a closed system of natural law.', 1: 'Anoles can climb glass walls.', 2: 'Schizophrenia is a disabling disease.', 3: 'Data collection is a critical part of consumer behavior.', 4: 'Moulds are dishs.', 5: 'Influenza is a contagious disease caused by a virus.', 6: 'Most armadillos do have teeth.'}
| 3 |
2,710 |
['Assuming coral snakes live under stones or logs on the forest floor, we know that those that suggest depression can be the result of various factors ranging from hormones to hard times are wrong.', 'The claim that crabs reach full size does not reflect reality.', 'At least one of two things is true: some dogs require more grooming than others, or either crabs reach full size or if coral snakes live under stones or logs on the forest floor, then depression can be the result of various factors ranging from hormones to hard times.', "The statement that 'some dogs require more grooming than others' is incorrect."]
|
Assuming coral snakes live under stones or logs on the forest floor, we know that those that suggest depression can be the result of various factors ranging from hormones to hard times are wrong. The claim that crabs reach full size does not reflect reality. At least one of two things is true: some dogs require more grooming than others, or either crabs reach full size or if coral snakes live under stones or logs on the forest floor, then depression can be the result of various factors ranging from hormones to hard times. The statement that 'some dogs require more grooming than others' is incorrect.
|
The claim that coral snakes live under stones or logs on the forest floor does not correspond with reality.
|
The claim that coral snakes belong and is a genus unique to the northern forms does not reflect reality.
|
Uncertain
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].).
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [0], then [1].). [SC1-2]
Not [2].
Therefore, If [0], then [1]..
[SC1-2]
Disjunctive Syllogism:
Either [3] or (Either [2] or (If [0], then [1].).).
Not [3].
Therefore, Either [2] or (If [0], then [1].)..
|
{0: 'Coral snakes live under stones or logs on the forest floor.', 1: 'Depression can be the result of various factors ranging from hormones to hard times.', 2: 'Crabs reach full size.', 3: 'Some dogs require more grooming than others.'}
| 3 |
2,614 |
['It is fair to say that eye color ranges from gold to copper, the greater depth and brilliance the better.', "The statement 'evangelism is the goal of the apostolic church' can be considered true.", 'At least one of two things is true: if peasants are workers, then cavities are usually brown and somewhat dry, or if a digital voltmeter is a voltmeter, then aerosols are sprays that contain propellants and solvents.', 'Assuming if peasants are workers, then cavities are usually brown and somewhat dry, we know that if evangelism is the goal of the apostolic church, then if eye color ranges from gold to copper, the greater depth and brilliance the better, then woodpeckers use their long, thin beaks to search for insects in tree bark.', 'Given that if a digital voltmeter is a voltmeter, then aerosols are sprays that contain propellants and solvents, it can be inferred that if evangelism is the goal of the apostolic church, then if eye color ranges from gold to copper, the greater depth and brilliance the better, then woodpeckers use their long, thin beaks to search for insects in tree bark.']
|
It is fair to say that eye color ranges from gold to copper, the greater depth and brilliance the better. The statement 'evangelism is the goal of the apostolic church' can be considered true. At least one of two things is true: if peasants are workers, then cavities are usually brown and somewhat dry, or if a digital voltmeter is a voltmeter, then aerosols are sprays that contain propellants and solvents. Assuming if peasants are workers, then cavities are usually brown and somewhat dry, we know that if evangelism is the goal of the apostolic church, then if eye color ranges from gold to copper, the greater depth and brilliance the better, then woodpeckers use their long, thin beaks to search for insects in tree bark. Given that if a digital voltmeter is a voltmeter, then aerosols are sprays that contain propellants and solvents, it can be inferred that if evangelism is the goal of the apostolic church, then if eye color ranges from gold to copper, the greater depth and brilliance the better, then woodpeckers use their long, thin beaks to search for insects in tree bark.
|
The idea that woodpeckers use their long, thin beaks to search for insects in tree bark is true.
|
It is a common misconception that woodpeckers use their long, thin beaks to search for insects in tree bark.
|
FALSE
|
Modus Ponens:
If [1], then [0]. [SC1-1]
[1]
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (If [1], then [0].). [SC1-2]
[2]
Therefore, If [1], then [0]..
[SC1-2]
Disjunction Elimination:
Either (If [3], then [4].) or (If [5], then [6].).
If (If [3], then [4].), then (If [2], then (If [1], then [0].).).
If (If [5], then [6].), then (If [2], then (If [1], then [0].).).
Therefore, If [2], then (If [1], then [0].)..
|
{0: 'Woodpeckers use their long, thin beaks to search for insects in tree bark.', 1: 'Eye color ranges from gold to copper, the greater depth and brilliance the better.', 2: 'Evangelism is the goal of the apostolic church.', 3: 'Peasants are workers.', 4: 'Cavities are usually brown and somewhat dry.', 5: 'A digital voltmeter is a voltmeter.', 6: 'Aerosols are sprays that contain propellants and solvents.'}
| 3 |
2,790 |
['It is rational to believe that either hours have (part) minutes or diploid individuals are unlikely to perform as well in areas where tetraploids are more common.', 'One may reasonably assume that if diploid individuals are unlikely to perform as well in areas where tetraploids are more common, then if most juice contains acid, then many women have trouble.', 'Those that suggest pacinian corpuscles are velocity detectors and sense vibration are wrong.', 'Should it be the case that those that suggest either pacinian corpuscles are velocity detectors and sense vibration or if hours have (part) minutes, then if most juice contains acid, then many women have trouble are wrong, it follows that cement kilns receive liquid hazardous waste to burn as fuel to run their cement processes.', 'Some people mistakenly believe that cement kilns receive liquid hazardous waste to burn as fuel to run their cement processes.']
|
It is rational to believe that either hours have (part) minutes or diploid individuals are unlikely to perform as well in areas where tetraploids are more common. One may reasonably assume that if diploid individuals are unlikely to perform as well in areas where tetraploids are more common, then if most juice contains acid, then many women have trouble. Those that suggest pacinian corpuscles are velocity detectors and sense vibration are wrong. Should it be the case that those that suggest either pacinian corpuscles are velocity detectors and sense vibration or if hours have (part) minutes, then if most juice contains acid, then many women have trouble are wrong, it follows that cement kilns receive liquid hazardous waste to burn as fuel to run their cement processes. Some people mistakenly believe that cement kilns receive liquid hazardous waste to burn as fuel to run their cement processes.
|
On the condition that most juice contains acid, it is definitely the case that many women have trouble.
|
It is not true that if most juice contains acid, then many women have trouble.
|
FALSE
|
Disjunction Elimination:
Either [2] or [3].
If [2], then (If [0], then [1].). [SC2-1]
If [3], then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC2-1]
Disjunctive Syllogism:
Either [4] or (If [2], then (If [0], then [1].).). [SC1-2]
Not [4].
Therefore, If [2], then (If [0], then [1].)..
[SC1-2]
Modus Tonens:
If (Not (Either [4] or (If [2], then (If [0], then [1].).).).), then [5].
Not [5].
Therefore, Either [4] or (If [2], then (If [0], then [1].).)..
|
{0: 'Most juice contains acid.', 1: 'Many women have trouble.', 2: 'Hours have (part) minutes.', 3: 'Diploid individuals are unlikely to perform as well in areas where tetraploids are more common.', 4: 'Pacinian corpuscles are velocity detectors and sense vibration .', 5: 'Cement kilns receive liquid hazardous waste to burn as fuel to run their cement processes.'}
| 3 |
2,408 |
["Once we know the claim that tatting is a type of lace that can be made using a shuttle or a long needle does not reflect reality, we also know that the notion that 'fasteners cover everything from nails to rivets and bolts' is untrue.", 'Assuming those that suggest if the claim that tatting is a type of lace that can be made using a shuttle or a long needle does not reflect reality, then fasteners cover everything from nails to rivets and bolts are wrong, we know that if east wind is wind, then an oak tree is a tree.', "Either kayaks are personal computers or the statement 'if east wind is wind, then an oak tree is a tree' can be considered false.", 'It is not the case that kayaks are personal computers.']
|
Once we know the claim that tatting is a type of lace that can be made using a shuttle or a long needle does not reflect reality, we also know that the notion that 'fasteners cover everything from nails to rivets and bolts' is untrue. Assuming those that suggest if the claim that tatting is a type of lace that can be made using a shuttle or a long needle does not reflect reality, then fasteners cover everything from nails to rivets and bolts are wrong, we know that if east wind is wind, then an oak tree is a tree. Either kayaks are personal computers or the statement 'if east wind is wind, then an oak tree is a tree' can be considered false. It is not the case that kayaks are personal computers.
|
The statement 'tatting is a type of lace that can be made using a shuttle or a long needle' is true.
|
The statement 'tatting is a type of lace that can be made using a shuttle or a long needle' is true.
|
TRUE
|
Reductio Ad Absurdum:
If (Not [0].), then [1]. [SC1-1]
If (Not [0].), then (Not [1].).
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (If (Not [0].), then [1].).), then (If [2], then [3].).
Not (If [2], then [3].). [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Disjunctive Syllogism:
Either [4] or (Not (If [2], then [3].).).
Not [4].
Therefore, Not (If [2], then [3].)..
|
{0: 'Tatting is a type of lace that can be made using a shuttle or a long needle.', 1: 'Fasteners cover everything from nails to rivets and bolts.', 2: 'East wind is wind.', 3: 'An oak tree is a tree.', 4: 'Kayaks are personal computers.'}
| 3 |
2,736 |
["Should it be the case that we know that the claim that if duration is a measure of a security's price sensitivity to changes in interest rates, then heat stroke is the most severe heat condition is false, it follows that ferrets are small animals and blockages are very dangerous.", "So long as ferrets are small animals and blockages are very dangerous, 'enormous currents create upwellings resulting in an abundance of food for marine life' is true.", 'Should it be the case that fires happen when some hot part of the lamp is too close to a meltable or flammable part, it follows that those that suggest enormous currents create upwellings resulting in an abundance of food for marine life are wrong.', 'The statement that states fires happen when some hot part of the lamp is too close to a meltable or flammable part is right.']
|
Should it be the case that we know that the claim that if duration is a measure of a security's price sensitivity to changes in interest rates, then heat stroke is the most severe heat condition is false, it follows that ferrets are small animals and blockages are very dangerous. So long as ferrets are small animals and blockages are very dangerous, 'enormous currents create upwellings resulting in an abundance of food for marine life' is true. Should it be the case that fires happen when some hot part of the lamp is too close to a meltable or flammable part, it follows that those that suggest enormous currents create upwellings resulting in an abundance of food for marine life are wrong. The statement that states fires happen when some hot part of the lamp is too close to a meltable or flammable part is right.
|
Once we know duration is a measure of a security's price sensitivity to changes in interest rates, we also know that heat stroke is the most severe heat condition.
|
Should it be the case that duration is a measure of interest-rate risk of financial assets and liabilities, it follows that heat stroke is the most severe heat condition.
|
Uncertain
|
Modus Tonens:
If (Not (If [0], then [1].).), then [2].
Not [2]. [SC2-1]
Therefore, If [0], then [1]..
[SC2-1]
Modus Tonens:
If [2], then [3].
Not [3]. [SC2-2]
Therefore, Not [2]..
[SC2-2]
Modus Ponens:
If [4], then (Not [3].).
[4]
Therefore, Not [3]..
|
{0: "Duration is a measure of a security's price sensitivity to changes in interest rates.", 1: 'Heat stroke is the most severe heat condition.', 2: 'Ferrets are small animals and blockages are very dangerous.', 3: 'Enormous currents create upwellings resulting in an abundance of food for marine life.', 4: 'Fires happen when some hot part of the lamp is too close to a meltable or flammable part.'}
| 3 |
2,957 |
['Should it be the case that clocks are mechanical devices used to measure or indicate the passage of time, it follows that crabs roam sea.', 'At least one of two things is true: if most species live in groups, then vascular plants provide benefits, or vitamin D is a fat-soluble nutrient essential for the development of strong bones and teeth.', "So long as if most species live in groups, then vascular plants provide benefits, 'clocks are mechanical devices used to measure or indicate the passage of time' is true.", 'One may reasonably assume that if vitamin D is a fat-soluble nutrient essential for the development of strong bones and teeth, then technicians need good organizational skills.', 'It is rational to believe that either a book bag is a bag or if technicians need good organizational skills, then crabs roam sea.', 'The statement, a book bag is a bag, does not hold.']
|
Should it be the case that clocks are mechanical devices used to measure or indicate the passage of time, it follows that crabs roam sea. At least one of two things is true: if most species live in groups, then vascular plants provide benefits, or vitamin D is a fat-soluble nutrient essential for the development of strong bones and teeth. So long as if most species live in groups, then vascular plants provide benefits, 'clocks are mechanical devices used to measure or indicate the passage of time' is true. One may reasonably assume that if vitamin D is a fat-soluble nutrient essential for the development of strong bones and teeth, then technicians need good organizational skills. It is rational to believe that either a book bag is a bag or if technicians need good organizational skills, then crabs roam sea. The statement, a book bag is a bag, does not hold.
|
It is a simple truth that crabs roam sea.
|
It is a simple truth that crabs roam sea.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either (If [4], then [5].) or [6].
If (If [4], then [5].), then [1].
If [6], then [2].
Therefore, Either [1] or [2]..
[SC3-1]
Disjunctive Syllogism:
Either [3] or (If [2], then [0].).
Not [3].
Therefore, If [2], then [0]..
|
{0: 'Crabs roam sea.', 1: 'Clocks are mechanical devices used to measure or indicate the passage of time.', 2: 'Technicians need good organizational skills.', 3: 'A book bag is a bag.', 4: 'Most species live in groups.', 5: 'Vascular plants provide benefits.', 6: 'Vitamin D is a fat-soluble nutrient essential for the development of strong bones and teeth.'}
| 3 |
2,366 |
['When it is a common misconception that if blood entering the testis is cooled by the venous blood leaving the testis, then geologists study the composition, processes, and history of the Earth is true, it follows that if gas stations are convenience stores, then work is motivated by the goal of money.', 'If it is a common misconception that if blood entering the testis is cooled by the venous blood leaving the testis, then geologists study the composition, processes, and history of the Earth, then it is not true that if gas stations are convenience stores, then work is motivated by the goal of money.', 'It is a fact that either if some social problems contribute to growth, then polarity causes magnetization to have opposite effects or love too happens in a heart beat and travels straight to the soul.', 'On the condition that if some social problems contribute to growth, then polarity causes magnetization to have opposite effects, it is definitely the case that blood entering the testis is cooled by the venous blood leaving the testis.', 'Once we know love too happens in a heart beat and travels straight to the soul, we also know that blood entering the testis is cooled by the venous blood leaving the testis.']
|
When it is a common misconception that if blood entering the testis is cooled by the venous blood leaving the testis, then geologists study the composition, processes, and history of the Earth is true, it follows that if gas stations are convenience stores, then work is motivated by the goal of money. If it is a common misconception that if blood entering the testis is cooled by the venous blood leaving the testis, then geologists study the composition, processes, and history of the Earth, then it is not true that if gas stations are convenience stores, then work is motivated by the goal of money. It is a fact that either if some social problems contribute to growth, then polarity causes magnetization to have opposite effects or love too happens in a heart beat and travels straight to the soul. On the condition that if some social problems contribute to growth, then polarity causes magnetization to have opposite effects, it is definitely the case that blood entering the testis is cooled by the venous blood leaving the testis. Once we know love too happens in a heart beat and travels straight to the soul, we also know that blood entering the testis is cooled by the venous blood leaving the testis.
|
The claim that geologists study the composition, processes, and history of the Earth holds true.
|
We know that the claim that geologists study the composition, processes, and history of the Earth is false.
|
FALSE
|
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 (If [2], then [3].).
If (Not (If [1], then [0].).), then (Not (If [2], then [3].).).
Therefore, If [1], then [0]..
[SC2-1]
Disjunction Elimination:
Either (If [4], then [5].) or [6].
If (If [4], then [5].), then [1].
If [6], then [1].
Therefore, [1].
|
{0: 'Geologists study the composition, processes, and history of the Earth.', 1: 'Blood entering the testis is cooled by the venous blood leaving the testis.', 2: 'Gas stations are convenience stores.', 3: 'Work is motivated by the goal of money.', 4: 'Some social problems contribute to growth.', 5: 'Polarity causes magnetization to have opposite effects.', 6: 'Love too happens in a heart beat and travels straight to the soul.'}
| 3 |
2,918 |
['There is good reason to believe that either zoos keep animals or diseases are located in human bodies.', 'Given that occasional trees produce yellowish-green strobili, it can be inferred that if zoos keep animals, then aphids feeding on developing leaves also can produce leaf curl injuries.', 'The statement that states occasional trees produce yellowish-green strobili is right.', 'If the claim that if diseases are located in human bodies, then aphids feeding on developing leaves also can produce leaf curl injuries does not correspond with reality, then primary care is medical care.', 'If the claim that if diseases are located in human bodies, then aphids feeding on developing leaves also can produce leaf curl injuries does not correspond with reality, then the claim that primary care is medical care does not correspond with reality.']
|
There is good reason to believe that either zoos keep animals or diseases are located in human bodies. Given that occasional trees produce yellowish-green strobili, it can be inferred that if zoos keep animals, then aphids feeding on developing leaves also can produce leaf curl injuries. The statement that states occasional trees produce yellowish-green strobili is right. If the claim that if diseases are located in human bodies, then aphids feeding on developing leaves also can produce leaf curl injuries does not correspond with reality, then primary care is medical care. If the claim that if diseases are located in human bodies, then aphids feeding on developing leaves also can produce leaf curl injuries does not correspond with reality, then the claim that primary care is medical care does not correspond with reality.
|
It is rational to agree that aphids feeding on developing leaves also can produce leaf curl injuries.
|
The statement, aphids feeding on developing leaves also can produce leaf curl injuries, does not hold.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0]. [SC2-1]
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Modus Ponens:
If [3], then (If [1], then [0].).
[3]
Therefore, If [1], then [0]..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [2], then [0].).), then [4].
If (Not (If [2], then [0].).), then (Not [4].).
Therefore, If [2], then [0]..
|
{0: 'Aphids feeding on developing leaves also can produce leaf curl injuries.', 1: 'Zoos keep animals.', 2: 'Diseases are located in human bodies.', 3: 'Occasional trees produce yellowish-green strobili.', 4: 'Primary care is medical care.'}
| 3 |
2,267 |
['If the claim that if it is a common misconception that cellular respiration occurs in the cells of all living things, then either systolic pressure is the first number given in blood pressure readings or caribou avoids regions does not reflect reality, then cattle thrive in groups.', 'The statement, cattle thrive in groups, does not hold.', 'It is rational to believe that either plums have similar storage characteristics and problems as peaches, cherries, and apricots or emotions come from the so-called subconscious mind.', 'Should it be the case that plums have similar storage characteristics and problems as peaches, cherries, and apricots, it follows that if it is a common misconception that cellular respiration occurs in the cells of all living things, then it is not the case that either systolic pressure is the first number given in blood pressure readings or caribou avoids regions.', 'Given that emotions come from the so-called subconscious mind, it can be inferred that if it is a common misconception that cellular respiration occurs in the cells of all living things, then it is not the case that either systolic pressure is the first number given in blood pressure readings or caribou avoids regions.']
|
If the claim that if it is a common misconception that cellular respiration occurs in the cells of all living things, then either systolic pressure is the first number given in blood pressure readings or caribou avoids regions does not reflect reality, then cattle thrive in groups. The statement, cattle thrive in groups, does not hold. It is rational to believe that either plums have similar storage characteristics and problems as peaches, cherries, and apricots or emotions come from the so-called subconscious mind. Should it be the case that plums have similar storage characteristics and problems as peaches, cherries, and apricots, it follows that if it is a common misconception that cellular respiration occurs in the cells of all living things, then it is not the case that either systolic pressure is the first number given in blood pressure readings or caribou avoids regions. Given that emotions come from the so-called subconscious mind, it can be inferred that if it is a common misconception that cellular respiration occurs in the cells of all living things, then it is not the case that either systolic pressure is the first number given in blood pressure readings or caribou avoids regions.
|
The statement 'cellular respiration occurs in the cells of all living things' is true.
|
Cellular respiration begins with the glycolytic pathway.
|
Uncertain
|
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 Tonens:
If (Not (If (Not [0].), then (Either [1] or [2].).).), then [5].
Not [5].
Therefore, If (Not [0].), then (Either [1] or [2].)..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (If (Not [0].), then (Not (Either [1] or [2].).).).
If [4], then (If (Not [0].), then (Not (Either [1] or [2].).).).
Therefore, If (Not [0].), then (Not (Either [1] or [2].).)..
|
{0: 'Cellular respiration occurs in the cells of all living things.', 1: 'Systolic pressure is the first number given in blood pressure readings.', 2: 'Caribou avoids regions.', 3: 'Plums have similar storage characteristics and problems as peaches, cherries, and apricots.', 4: 'Emotions come from the so-called subconscious mind.', 5: 'Cattle thrive in groups.'}
| 3 |
2,230 |
['We know that either orangutans live in a semisolitary social organization that is unique among monkeys and apes or some people think that Guinea pigs are disgusting because they eat their own feces.', 'We know that either operational philosophy is the philosophy of action-directed goals or biometric technology brings computers a step closer to having human capabilities.', 'Once we know operational philosophy is the philosophy of action-directed goals, we also know that if orangutans live in a semisolitary social organization that is unique among monkeys and apes, then some people mistakenly believe that if organic arsenic is usually less harmful than inorganic arsenic, then bryological data indicates the disappearance of a number of moss species.', 'Provided that biometric technology brings computers a step closer to having human capabilities, we know that if orangutans live in a semisolitary social organization that is unique among monkeys and apes, then some people mistakenly believe that if organic arsenic is usually less harmful than inorganic arsenic, then bryological data indicates the disappearance of a number of moss species.', "Given that the statement 'if some people think that Guinea pigs are disgusting because they eat their own feces, then some people mistakenly believe that if organic arsenic is usually less harmful than inorganic arsenic, then bryological data indicates the disappearance of a number of moss species' can be considered false, it can be inferred that either geomagnetic storms are a natural hazard, like hurricanes and tsunamis or honor is an old fashioned word, used in our church maybe most often in the wedding service.", "When the statement 'if some people think that Guinea pigs are disgusting because they eat their own feces, then some people mistakenly believe that if organic arsenic is usually less harmful than inorganic arsenic, then bryological data indicates the disappearance of a number of moss species' can be considered false is true, it follows that the claim that either geomagnetic storms are a natural hazard, like hurricanes and tsunamis or honor is an old fashioned word, used in our church maybe most often in the wedding service has no merit."]
|
We know that either orangutans live in a semisolitary social organization that is unique among monkeys and apes or some people think that Guinea pigs are disgusting because they eat their own feces. We know that either operational philosophy is the philosophy of action-directed goals or biometric technology brings computers a step closer to having human capabilities. Once we know operational philosophy is the philosophy of action-directed goals, we also know that if orangutans live in a semisolitary social organization that is unique among monkeys and apes, then some people mistakenly believe that if organic arsenic is usually less harmful than inorganic arsenic, then bryological data indicates the disappearance of a number of moss species. Provided that biometric technology brings computers a step closer to having human capabilities, we know that if orangutans live in a semisolitary social organization that is unique among monkeys and apes, then some people mistakenly believe that if organic arsenic is usually less harmful than inorganic arsenic, then bryological data indicates the disappearance of a number of moss species. Given that the statement 'if some people think that Guinea pigs are disgusting because they eat their own feces, then some people mistakenly believe that if organic arsenic is usually less harmful than inorganic arsenic, then bryological data indicates the disappearance of a number of moss species' can be considered false, it can be inferred that either geomagnetic storms are a natural hazard, like hurricanes and tsunamis or honor is an old fashioned word, used in our church maybe most often in the wedding service. When the statement 'if some people think that Guinea pigs are disgusting because they eat their own feces, then some people mistakenly believe that if organic arsenic is usually less harmful than inorganic arsenic, then bryological data indicates the disappearance of a number of moss species' can be considered false is true, it follows that the claim that either geomagnetic storms are a natural hazard, like hurricanes and tsunamis or honor is an old fashioned word, used in our church maybe most often in the wedding service has no merit.
|
Some people mistakenly believe that if organic arsenic is usually less harmful than inorganic arsenic, then bryological data indicates the disappearance of a number of moss species.
|
Those that suggest organic arsenic can cause neither cancer, nor DNA damage are wrong.
|
Uncertain
|
Disjunction Elimination:
Either [2] or [3].
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].)..
[SC2-1]
Disjunction Elimination:
Either [6] or [7].
If [6], then (If [2], then (Not (If [0], then [1].).).).
If [7], then (If [2], then (Not (If [0], then [1].).).).
Therefore, If [2], then (Not (If [0], then [1].).)..
[SC3-1]
Reductio Ad Absurdum:
If (Not (If [3], then (Not (If [0], then [1].).).).), then (Either [4] or [5].).
If (Not (If [3], then (Not (If [0], then [1].).).).), then (Not (Either [4] or [5].).).
Therefore, If [3], then (Not (If [0], then [1].).)..
|
{0: 'Organic arsenic is usually less harmful than inorganic arsenic.', 1: 'Bryological data indicates the disappearance of a number of moss species.', 2: 'Orangutans live in a semisolitary social organization that is unique among monkeys and apes.', 3: 'Some people think that Guinea pigs are disgusting because they eat their own feces.', 4: 'Geomagnetic storms are a natural hazard, like hurricanes and tsunamis.', 5: 'Honor is an old fashioned word, used in our church maybe most often in the wedding service.', 6: 'Operational philosophy is the philosophy of action-directed goals.', 7: 'Biometric technology brings computers a step closer to having human capabilities.'}
| 3 |
2,996 |
["The statement 'owls digest meals' can be considered true.", 'depressive disorders come in various forms.', 'Once we know the claim that if depressive disorders come in various forms, then if owls digest meals, then the claim that either earth produces enough food to feed three worlds equal to the Earth or tuberous sclerosis is associated commonly with renal angiomyolipoma is false has no merit, we also know that most sharks feed on prey.', 'The claim that most sharks feed on prey does not correspond with reality.']
|
The statement 'owls digest meals' can be considered true. depressive disorders come in various forms. Once we know the claim that if depressive disorders come in various forms, then if owls digest meals, then the claim that either earth produces enough food to feed three worlds equal to the Earth or tuberous sclerosis is associated commonly with renal angiomyolipoma is false has no merit, we also know that most sharks feed on prey. The claim that most sharks feed on prey does not correspond with reality.
|
The claim that either earth produces enough food to feed three worlds equal to the Earth or tuberous sclerosis is associated commonly with renal angiomyolipoma is false.
|
The claim that either earth produces enough food to feed three worlds equal to the Earth or tuberous sclerosis is associated commonly with renal angiomyolipoma is false.
|
TRUE
|
Modus Ponens:
If [2], then (Not (Either [0] or [1].).). [SC1-1]
[2]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Modus Ponens:
If [3], then (If [2], then (Not (Either [0] or [1].).).). [SC1-2]
[3]
Therefore, If [2], then (Not (Either [0] or [1].).)..
[SC1-2]
Modus Tonens:
If (Not (If [3], then (If [2], then (Not (Either [0] or [1].).).).).), then [4].
Not [4].
Therefore, If [3], then (If [2], then (Not (Either [0] or [1].).).)..
|
{0: 'Earth produces enough food to feed three worlds equal to the Earth.', 1: 'Tuberous sclerosis is associated commonly with renal angiomyolipoma.', 2: 'Owls digest meals.', 3: 'Depressive disorders come in various forms.', 4: 'Most sharks feed on prey.'}
| 3 |
2,635 |
["The statement 'fallow ground is ground which has once been tilled, but has gotten hard and now lies waste' can be considered false.", 'The idea that human beings are just another member of that system which governs all things is true.', 'Given that weakness is usually the first sign of botulism, followed by double vision and difficulty swallowing, it can be inferred that if human beings are just another member of that system which governs all things, then if diseases are caused by bacterial infection, then fallow ground is ground which has once been tilled, but has gotten hard and now lies waste.', 'Many people rightly believe that weakness is usually the first sign of botulism, followed by double vision and difficulty swallowing.']
|
The statement 'fallow ground is ground which has once been tilled, but has gotten hard and now lies waste' can be considered false. The idea that human beings are just another member of that system which governs all things is true. Given that weakness is usually the first sign of botulism, followed by double vision and difficulty swallowing, it can be inferred that if human beings are just another member of that system which governs all things, then if diseases are caused by bacterial infection, then fallow ground is ground which has once been tilled, but has gotten hard and now lies waste. Many people rightly believe that weakness is usually the first sign of botulism, followed by double vision and difficulty swallowing.
|
It is not the case that diseases are caused by bacterial infection.
|
It is the case that diseases are caused by bacterial infection.
|
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]
Therefore, If [2], then (If [0], then [1].)..
|
{0: 'Diseases are caused by bacterial infection.', 1: 'Fallow ground is ground which has once been tilled, but has gotten hard and now lies waste.', 2: 'Human beings are just another member of that system which governs all things.', 3: 'Weakness is usually the first sign of botulism, followed by double vision and difficulty swallowing.'}
| 3 |
2,698 |
['We know that either production occurs in zones or poverty has many causes, and people differ about which are the most important.', 'When production occurs in zones is true, it follows that if physical changes occur in conjunction with a striving for personal identity and autonomy, then wildflower seeds have effects.', 'When poverty has many causes, and people differ about which are the most important is true, it follows that if physical changes occur in conjunction with a striving for personal identity and autonomy, then wildflower seeds have effects.', 'When the claim that physical changes occur in conjunction with a striving for personal identity and autonomy does not correspond with reality is true, it follows that writing is also important when it comes to reading.', 'Provided that the claim that physical changes occur in conjunction with a striving for personal identity and autonomy does not correspond with reality, we know that it is not the case that writing is also important when it comes to reading.']
|
We know that either production occurs in zones or poverty has many causes, and people differ about which are the most important. When production occurs in zones is true, it follows that if physical changes occur in conjunction with a striving for personal identity and autonomy, then wildflower seeds have effects. When poverty has many causes, and people differ about which are the most important is true, it follows that if physical changes occur in conjunction with a striving for personal identity and autonomy, then wildflower seeds have effects. When the claim that physical changes occur in conjunction with a striving for personal identity and autonomy does not correspond with reality is true, it follows that writing is also important when it comes to reading. Provided that the claim that physical changes occur in conjunction with a striving for personal identity and autonomy does not correspond with reality, we know that it is not the case that writing is also important when it comes to reading.
|
The statement 'wildflower seeds have effects' is true.
|
The statement 'wildflower seeds have effects' is true.
|
TRUE
|
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].
If (Not [1].), then (Not [4].).
Therefore, [1].
|
{0: 'Wildflower seeds have effects.', 1: 'Physical changes occur in conjunction with a striving for personal identity and autonomy.', 2: 'Production occurs in zones.', 3: 'Poverty has many causes, and people differ about which are the most important.', 4: 'Writing is also important when it comes to reading.'}
| 3 |
2,251 |
["Provided that the statement 'if we know that the claim that temperature affects the number of seeds that germinate as well as how fast the seeds germinate is false, then sensitization is processes' can be considered false, we know that retroviruses can be effective vectors for introducing recombinant DNA into mammalian cells.", 'The statement, retroviruses can be effective vectors for introducing recombinant DNA into mammalian cells, does not hold.', 'If tests require different skills, then if we know that the claim that temperature affects the number of seeds that germinate as well as how fast the seeds germinate is false, then the claim that sensitization is processes does not correspond with reality.', 'Many people rightly believe that tests require different skills.']
|
Provided that the statement 'if we know that the claim that temperature affects the number of seeds that germinate as well as how fast the seeds germinate is false, then sensitization is processes' can be considered false, we know that retroviruses can be effective vectors for introducing recombinant DNA into mammalian cells. The statement, retroviruses can be effective vectors for introducing recombinant DNA into mammalian cells, does not hold. If tests require different skills, then if we know that the claim that temperature affects the number of seeds that germinate as well as how fast the seeds germinate is false, then the claim that sensitization is processes does not correspond with reality. Many people rightly believe that tests require different skills.
|
The claim that temperature affects the number of seeds that germinate as well as how fast the seeds germinate holds true.
|
We know that the claim that temperature affects the number of seeds that germinate as well as how fast the seeds germinate 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]
Modus Tonens:
If (Not (If (Not [0].), then [1].).), then [3].
Not [3].
Therefore, If (Not [0].), then [1]..
[SC2-1]
Modus Ponens:
If [2], then (If (Not [0].), then (Not [1].).).
[2]
Therefore, If (Not [0].), then (Not [1].)..
|
{0: 'Temperature affects the number of seeds that germinate as well as how fast the seeds germinate.', 1: 'Sensitization is processes.', 2: 'Tests require different skills.', 3: 'Retroviruses can be effective vectors for introducing recombinant DNA into mammalian cells.'}
| 3 |
2,783 |
["On the condition that either lupines add nutrients back into the ecosystem or fern gametophytes produce archegoniums, it is definitely the case that the statement that 'some organisms depend on the decaying litter from a tree for food' is incorrect.", 'The statement that states folic acid is very important during pregnancy is right.', "Whenever it is true that the claim that if folic acid is very important during pregnancy, then either lupines add nutrients back into the ecosystem or fern gametophytes produce archegoniums does not reflect reality, 'any cat is a mammal' is true.", 'Should it be the case that the claim that if folic acid is very important during pregnancy, then either lupines add nutrients back into the ecosystem or fern gametophytes produce archegoniums does not reflect reality, it follows that it is not the case that any cat is a mammal.']
|
On the condition that either lupines add nutrients back into the ecosystem or fern gametophytes produce archegoniums, it is definitely the case that the statement that 'some organisms depend on the decaying litter from a tree for food' is incorrect. The statement that states folic acid is very important during pregnancy is right. Whenever it is true that the claim that if folic acid is very important during pregnancy, then either lupines add nutrients back into the ecosystem or fern gametophytes produce archegoniums does not reflect reality, 'any cat is a mammal' is true. Should it be the case that the claim that if folic acid is very important during pregnancy, then either lupines add nutrients back into the ecosystem or fern gametophytes produce archegoniums does not reflect reality, it follows that it is not the case that any cat is a mammal.
|
The statement that 'some organisms depend on the decaying litter from a tree for food' is incorrect.
|
The statement that 'some organisms depend on the decaying litter from a tree for food' is incorrect.
|
TRUE
|
Modus Ponens:
If (Either [1] or [2].), then (Not [0].).
Either [1] or [2]. [SC2-1]
Therefore, Not [0]..
[SC2-1]
Modus Ponens:
If [3], then (Either [1] or [2].). [SC1-2]
[3]
Therefore, Either [1] or [2]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (If [3], then (Either [1] or [2].).).), then [4].
If (Not (If [3], then (Either [1] or [2].).).), then (Not [4].).
Therefore, If [3], then (Either [1] or [2].)..
|
{0: 'Some organisms depend on the decaying litter from a tree for food.', 1: 'Lupines add nutrients back into the ecosystem.', 2: 'Fern gametophytes produce archegoniums.', 3: 'Folic acid is very important during pregnancy.', 4: 'Any cat is a mammal.'}
| 3 |
2,819 |
['Should it be the case that reliable information is provided by other industry organizations, it follows that we know that the claim that traveling causes fear is false.', 'Provided that birds have appetite, we know that we know that the claim that traveling causes fear is false.', 'It is a fact that either animators make up a fairly small population of the people that create an animated film or somatic mutation is a fundamental component of acquired immunity.', 'One may reasonably assume that if somatic mutation is a fundamental component of acquired immunity, then either reliable information is provided by other industry organizations or birds have appetite.', 'We know that at least one of two things is true: some plants contain several such components, or hemolysis ceases when the drug is withdrawn.', 'One may reasonably assume that if some plants contain several such components, then if animators make up a fairly small population of the people that create an animated film, then either reliable information is provided by other industry organizations or birds have appetite.', 'Assuming hemolysis ceases when the drug is withdrawn, we know that if animators make up a fairly small population of the people that create an animated film, then either reliable information is provided by other industry organizations or birds have appetite.']
|
Should it be the case that reliable information is provided by other industry organizations, it follows that we know that the claim that traveling causes fear is false. Provided that birds have appetite, we know that we know that the claim that traveling causes fear is false. It is a fact that either animators make up a fairly small population of the people that create an animated film or somatic mutation is a fundamental component of acquired immunity. One may reasonably assume that if somatic mutation is a fundamental component of acquired immunity, then either reliable information is provided by other industry organizations or birds have appetite. We know that at least one of two things is true: some plants contain several such components, or hemolysis ceases when the drug is withdrawn. One may reasonably assume that if some plants contain several such components, then if animators make up a fairly small population of the people that create an animated film, then either reliable information is provided by other industry organizations or birds have appetite. Assuming hemolysis ceases when the drug is withdrawn, we know that if animators make up a fairly small population of the people that create an animated film, then either reliable information is provided by other industry organizations or birds have appetite.
|
We know that the claim that traveling causes fear is false.
|
The claim that traveling causes fear is true.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].).
If [2], then (Not [0].).
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Either [1] or [2].). [SC2-2]
If [4], then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC2-2]
Disjunction Elimination:
Either [5] or [6].
If [5], then (If [3], then (Either [1] or [2].).).
If [6], then (If [3], then (Either [1] or [2].).).
Therefore, If [3], then (Either [1] or [2].)..
|
{0: 'Traveling causes fear.', 1: 'Reliable information is provided by other industry organizations.', 2: 'Birds have appetite.', 3: 'Animators make up a fairly small population of the people that create an animated film.', 4: 'Somatic mutation is a fundamental component of acquired immunity.', 5: 'Some plants contain several such components.', 6: 'Hemolysis ceases when the drug is withdrawn.'}
| 3 |
2,141 |
['Those that suggest herbal formulations work in a subtle manner that is harmonious with the body s healing processes are wrong.', 'We know that either every object has a mass and a contour or basketball is a game of momentum.', 'On the condition that basketball is a game of momentum, it is definitely the case that either herbal formulations work in a subtle manner that is harmonious with the body s healing processes or immature birds are similar to the female, but have an orange-pink bill instead of black.', 'We know that at least one of two things is true: oil is located in service stations, or trumpets play an important part in Jazz music, and other various popular genres.', 'Given that oil is located in service stations, it can be inferred that if every object has a mass and a contour, then either herbal formulations work in a subtle manner that is harmonious with the body s healing processes or immature birds are similar to the female, but have an orange-pink bill instead of black.', 'If trumpets play an important part in Jazz music, and other various popular genres, then if every object has a mass and a contour, then either herbal formulations work in a subtle manner that is harmonious with the body s healing processes or immature birds are similar to the female, but have an orange-pink bill instead of black.']
|
Those that suggest herbal formulations work in a subtle manner that is harmonious with the body s healing processes are wrong. We know that either every object has a mass and a contour or basketball is a game of momentum. On the condition that basketball is a game of momentum, it is definitely the case that either herbal formulations work in a subtle manner that is harmonious with the body s healing processes or immature birds are similar to the female, but have an orange-pink bill instead of black. We know that at least one of two things is true: oil is located in service stations, or trumpets play an important part in Jazz music, and other various popular genres. Given that oil is located in service stations, it can be inferred that if every object has a mass and a contour, then either herbal formulations work in a subtle manner that is harmonious with the body s healing processes or immature birds are similar to the female, but have an orange-pink bill instead of black. If trumpets play an important part in Jazz music, and other various popular genres, then if every object has a mass and a contour, then either herbal formulations work in a subtle manner that is harmonious with the body s healing processes or immature birds are similar to the female, but have an orange-pink bill instead of black.
|
It is rational to agree that immature birds are similar to the female, but have an orange-pink bill instead of black.
|
The claim that immature birds are similar to the female, but have an orange-pink bill instead of black has no merit.
|
FALSE
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (Either [1] or [0].). [SC2-2]
If [3], then (Either [1] or [0].).
Therefore, Either [1] or [0]..
[SC2-2]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [2], then (Either [1] or [0].).).
If [5], then (If [2], then (Either [1] or [0].).).
Therefore, If [2], then (Either [1] or [0].)..
|
{0: 'Immature birds are similar to the female, but have an orange-pink bill instead of black.', 1: 'Herbal formulations work in a subtle manner that is harmonious with the body s healing processes.', 2: 'Every object has a mass and a contour.', 3: 'Basketball is a game of momentum.', 4: 'Oil is located in service stations.', 5: 'Trumpets play an important part in Jazz music, and other various popular genres.'}
| 3 |
2,316 |
["When the statement that 'risk Management is responsible for loss control, safety and employee benefits' is incorrect is true, it follows that it is a common misconception that food often has a symbolic significance.", "Whenever it is true that some people mistakenly believe that if the statement that 'risk Management is responsible for loss control, safety and employee benefits' is incorrect, then food often has a symbolic significance, 'some people mistakenly believe that some infants calm down to rhythmic motion such as rocking, walking, or riding in a car or stroller' is true.", "We know that either some warm temperature encourages combustion or if some people mistakenly believe that if the statement that 'risk Management is responsible for loss control, safety and employee benefits' is incorrect, then food often has a symbolic significance, then some infants calm down to rhythmic motion such as rocking, walking, or riding in a car or stroller.", 'The statement, some warm temperature encourages combustion, does not hold.']
|
When the statement that 'risk Management is responsible for loss control, safety and employee benefits' is incorrect is true, it follows that it is a common misconception that food often has a symbolic significance. Whenever it is true that some people mistakenly believe that if the statement that 'risk Management is responsible for loss control, safety and employee benefits' is incorrect, then food often has a symbolic significance, 'some people mistakenly believe that some infants calm down to rhythmic motion such as rocking, walking, or riding in a car or stroller' is true. We know that either some warm temperature encourages combustion or if some people mistakenly believe that if the statement that 'risk Management is responsible for loss control, safety and employee benefits' is incorrect, then food often has a symbolic significance, then some infants calm down to rhythmic motion such as rocking, walking, or riding in a car or stroller. The statement, some warm temperature encourages combustion, does not hold.
|
The claim that risk Management is responsible for loss control, safety and employee benefits is true.
|
The claim that risk Management is responsible for loss control, safety and employee benefits is true.
|
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].).
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]..
|
{0: 'Risk Management is responsible for loss control, safety and employee benefits.', 1: 'Food often has a symbolic significance.', 2: 'Some infants calm down to rhythmic motion such as rocking, walking, or riding in a car or stroller.', 3: 'Some warm temperature encourages combustion.'}
| 3 |
2,587 |
['At least one of two things is true: pigs use auditory stimuli extensively as a means of communication in all social activities, or factors create conditions.', 'It is a fact that either bone loss is greater in women or if pigs use auditory stimuli extensively as a means of communication in all social activities, then it is not true that plants require little cultivation, except for weeding during early stages of growth.', "The notion that 'bone loss is greater in women' is untrue.", 'Either one or both of these statements are true: robbery is defined as the theft achieved by either the use of violence or the threat of violence, or libraries are people places.', 'Assuming robbery is defined as the theft achieved by either the use of violence or the threat of violence, we know that if factors create conditions, then it is not true that plants require little cultivation, except for weeding during early stages of growth.', 'Provided that libraries are people places, we know that if factors create conditions, then it is not true that plants require little cultivation, except for weeding during early stages of growth.']
|
At least one of two things is true: pigs use auditory stimuli extensively as a means of communication in all social activities, or factors create conditions. It is a fact that either bone loss is greater in women or if pigs use auditory stimuli extensively as a means of communication in all social activities, then it is not true that plants require little cultivation, except for weeding during early stages of growth. The notion that 'bone loss is greater in women' is untrue. Either one or both of these statements are true: robbery is defined as the theft achieved by either the use of violence or the threat of violence, or libraries are people places. Assuming robbery is defined as the theft achieved by either the use of violence or the threat of violence, we know that if factors create conditions, then it is not true that plants require little cultivation, except for weeding during early stages of growth. Provided that libraries are people places, we know that if factors create conditions, then it is not true that plants require little cultivation, except for weeding during early stages of growth.
|
It is not true that plants require little cultivation, except for weeding during early stages of growth.
|
It is not true that plants require little cultivation, except for weeding during early stages of growth.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then (Not [0].). [SC2-1]
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC2-1]
Disjunctive Syllogism:
Either [3] or (If [1], then (Not [0].).).
Not [3].
Therefore, If [1], then (Not [0].)..
[SC3-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [2], then (Not [0].).).
If [5], then (If [2], then (Not [0].).).
Therefore, If [2], then (Not [0].)..
|
{0: 'Plants require little cultivation, except for weeding during early stages of growth.', 1: 'Pigs use auditory stimuli extensively as a means of communication in all social activities.', 2: 'Factors create conditions.', 3: 'Bone loss is greater in women.', 4: 'Robbery is defined as the theft achieved by either the use of violence or the threat of violence.', 5: 'Libraries are people places.'}
| 3 |
2,331 |
['Either one or both of these statements are true: nits have (part) nuclei, or nourishment is given intravenously or via a tube inserted through the nose and into the stomach.', 'There is good reason to believe that either either some children grow up in nations or epilepsy can have devastating effects on employability or curiosities are emotion.', "Whenever it is true that either some children grow up in nations or epilepsy can have devastating effects on employability, 'if either nits have (part) nuclei or nourishment is given intravenously or via a tube inserted through the nose and into the stomach, then if slicks are the tires used in dry conditions, which means they are used more often, then trapping is most effective when gophers are pushing up new mounds, generally in spring and fall' is true.", 'We know that either animals depend upon plants for survival or if curiosities are emotion, then if either nits have (part) nuclei or nourishment is given intravenously or via a tube inserted through the nose and into the stomach, then if slicks are the tires used in dry conditions, which means they are used more often, then trapping is most effective when gophers are pushing up new mounds, generally in spring and fall.', 'It is not the case that animals depend upon plants for survival.']
|
Either one or both of these statements are true: nits have (part) nuclei, or nourishment is given intravenously or via a tube inserted through the nose and into the stomach. There is good reason to believe that either either some children grow up in nations or epilepsy can have devastating effects on employability or curiosities are emotion. Whenever it is true that either some children grow up in nations or epilepsy can have devastating effects on employability, 'if either nits have (part) nuclei or nourishment is given intravenously or via a tube inserted through the nose and into the stomach, then if slicks are the tires used in dry conditions, which means they are used more often, then trapping is most effective when gophers are pushing up new mounds, generally in spring and fall' is true. We know that either animals depend upon plants for survival or if curiosities are emotion, then if either nits have (part) nuclei or nourishment is given intravenously or via a tube inserted through the nose and into the stomach, then if slicks are the tires used in dry conditions, which means they are used more often, then trapping is most effective when gophers are pushing up new mounds, generally in spring and fall. It is not the case that animals depend upon plants for survival.
|
Given that slicks are the tires used in dry conditions, which means they are used more often, it can be inferred that trapping is most effective when gophers are pushing up new mounds, generally in spring and fall.
|
So long as slicks are used for dry weather, 'trapping is most effective when gophers are pushing up new mounds, generally in spring and fall' is true.
|
Uncertain
|
Modus Ponens:
If (Either [2] or [3].), then (If [0], then [1].). [SC1-1]
Either [2] or [3].
Therefore, If [0], then [1]..
[SC1-1]
Disjunction Elimination:
Either (Either [4] or [5].) or [6].
If (Either [4] or [5].), then (If (Either [2] or [3].), then (If [0], then [1].).).
If [6], then (If (Either [2] or [3].), then (If [0], then [1].).). [SC3-2]
Therefore, If (Either [2] or [3].), then (If [0], then [1].)..
[SC3-2]
Disjunctive Syllogism:
Either [7] or (If [6], then (If (Either [2] or [3].), then (If [0], then [1].).).).
Not [7].
Therefore, If [6], then (If (Either [2] or [3].), then (If [0], then [1].).)..
|
{0: 'Slicks are the tires used in dry conditions, which means they are used more often.', 1: 'Trapping is most effective when gophers are pushing up new mounds, generally in spring and fall.', 2: 'Nits have (part) nuclei.', 3: 'Nourishment is given intravenously or via a tube inserted through the nose and into the stomach.', 4: 'Some children grow up in nations.', 5: 'Epilepsy can have devastating effects on employability.', 6: 'Curiosities are emotion.', 7: 'Animals depend upon plants for survival.'}
| 3 |
2,295 |
["So long as either life insurance is often an important part of an estate plan or poverty is a mentality, 'several medications reduce or eliminate the occurrence of fainting episodes' is true.", 'We know that either epidemiology is integral to medical research or either either life insurance is often an important part of an estate plan or poverty is a mentality or if rainforests provide shelter, then terminator technology predicts markets .', 'It is not true that epidemiology is integral to medical research.', "So long as if rainforests provide shelter, then terminator technology predicts markets , 'jackals respond only to the sounds produced by the members of their family' is true.", 'When jackals respond only to the sounds produced by the members of their family is true, it follows that several medications reduce or eliminate the occurrence of fainting episodes.']
|
So long as either life insurance is often an important part of an estate plan or poverty is a mentality, 'several medications reduce or eliminate the occurrence of fainting episodes' is true. We know that either epidemiology is integral to medical research or either either life insurance is often an important part of an estate plan or poverty is a mentality or if rainforests provide shelter, then terminator technology predicts markets . It is not true that epidemiology is integral to medical research. So long as if rainforests provide shelter, then terminator technology predicts markets , 'jackals respond only to the sounds produced by the members of their family' is true. When jackals respond only to the sounds produced by the members of their family is true, it follows that several medications reduce or eliminate the occurrence of fainting episodes.
|
Many people rightly believe that several medications reduce or eliminate the occurrence of fainting episodes.
|
The statement, several medications reduce or eliminate the occurrence of fainting episodes, does not hold.
|
FALSE
|
Disjunction Elimination:
Either (Either [1] or [2].) or (If [3], then [4].). [SC1-1]
If (Either [1] or [2].), then [0].
If (If [3], then [4].), then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [5] or (Either (Either [1] or [2].) or (If [3], then [4].).).
Not [5].
Therefore, Either (Either [1] or [2].) or (If [3], then [4].)..
[SC3-1]
Hypothetical Syllogism:
If (If [3], then [4].), then [6].
If [6], then [0].
Therefore, If (If [3], then [4].), then [0]..
|
{0: 'Several medications reduce or eliminate the occurrence of fainting episodes.', 1: 'Life insurance is often an important part of an estate plan.', 2: 'Poverty is a mentality.', 3: 'Rainforests provide shelter.', 4: 'Terminator technology predicts markets .', 5: 'Epidemiology is integral to medical research.', 6: 'Jackals respond only to the sounds produced by the members of their family.'}
| 3 |
2,262 |
['If the claim that writing is a somewhat schizophrenic process has no merit, then regulator isa mechanism.', 'On the condition that we know that the claim that if the claim that writing is a somewhat schizophrenic process has no merit, then the claim that regulator isa mechanism is false is false, it is definitely the case that psoriasis can appear in several different forms.', 'When psoriasis can appear in several different forms is true, it follows that diamonds are used for anniversary gifts.', 'Should it be the case that psoriasis can appear in several different forms, it follows that some people mistakenly believe that diamonds are used for anniversary gifts.']
|
If the claim that writing is a somewhat schizophrenic process has no merit, then regulator isa mechanism. On the condition that we know that the claim that if the claim that writing is a somewhat schizophrenic process has no merit, then the claim that regulator isa mechanism is false is false, it is definitely the case that psoriasis can appear in several different forms. When psoriasis can appear in several different forms is true, it follows that diamonds are used for anniversary gifts. Should it be the case that psoriasis can appear in several different forms, it follows that some people mistakenly believe that diamonds are used for anniversary gifts.
|
Many people rightly believe that writing is a somewhat schizophrenic process.
|
We know that the claim that writing is a somewhat schizophrenic process is false.
|
FALSE
|
Reductio Ad Absurdum:
If (Not [0].), then [1].
If (Not [0].), then (Not [1].). [SC2-1]
Therefore, [0].
[SC2-1]
Modus Tonens:
If (Not (If (Not [0].), then (Not [1].).).), then [2].
Not [2]. [SC2-2]
Therefore, If (Not [0].), then (Not [1].)..
[SC2-2]
Reductio Ad Absurdum:
If [2], then [3].
If [2], then (Not [3].).
Therefore, Not [2]..
|
{0: 'Writing is a somewhat schizophrenic process.', 1: 'Regulator isa mechanism.', 2: 'Psoriasis can appear in several different forms.', 3: 'Diamonds are used for anniversary gifts.'}
| 3 |
2,432 |
['We know that at least one of two things is true: sanitation is also an extremely important component to the control of Listeria , or unsaturated fats can actually reduce blood cholesterol.', 'On the condition that sanitation is also an extremely important component to the control of Listeria , it is definitely the case that either photocopies are pictures or the statement, either residual attenuation is the minimum attenuation of a variable Attenuator or natural selection leads to extinction, does not hold.', 'On the condition that unsaturated fats can actually reduce blood cholesterol, it is definitely the case that either photocopies are pictures or the statement, either residual attenuation is the minimum attenuation of a variable Attenuator or natural selection leads to extinction, does not hold.', 'Once we know photocopies are pictures, we also know that sexual assault is a crime.', 'Those that suggest sexual assault is a crime are wrong.']
|
We know that at least one of two things is true: sanitation is also an extremely important component to the control of Listeria , or unsaturated fats can actually reduce blood cholesterol. On the condition that sanitation is also an extremely important component to the control of Listeria , it is definitely the case that either photocopies are pictures or the statement, either residual attenuation is the minimum attenuation of a variable Attenuator or natural selection leads to extinction, does not hold. On the condition that unsaturated fats can actually reduce blood cholesterol, it is definitely the case that either photocopies are pictures or the statement, either residual attenuation is the minimum attenuation of a variable Attenuator or natural selection leads to extinction, does not hold. Once we know photocopies are pictures, we also know that sexual assault is a crime. Those that suggest sexual assault is a crime are wrong.
|
The statement, either residual attenuation is the minimum attenuation of a variable Attenuator or natural selection leads to extinction, does not hold.
|
The claim that some wildebeests have height does not correspond with reality.
|
Uncertain
|
Disjunctive Syllogism:
Either [2] or (Not (Either [0] or [1].).). [SC1-1]
Not [2]. [SC2-1]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Either [2] or (Not (Either [0] or [1].).).).
If [5], then (Either [2] or (Not (Either [0] or [1].).).).
Therefore, Either [2] or (Not (Either [0] or [1].).)..
[SC2-1]
Modus Tonens:
If [2], then [3].
Not [3].
Therefore, Not [2]..
|
{0: 'Residual attenuation is the minimum attenuation of a variable Attenuator.', 1: 'Natural selection leads to extinction.', 2: 'Photocopies are pictures.', 3: 'Sexual assault is a crime.', 4: 'Sanitation is also an extremely important component to the control of Listeria .', 5: 'Unsaturated fats can actually reduce blood cholesterol.'}
| 3 |
2,862 |
['The claim that metals are frequently present in active centers of enzymes does not correspond with reality.', 'The claim that famous people come to have a public image is false.', 'It is rational to believe that either premature infants develop kernicterus at lower levels of jaundice than full term infants or either famous people come to have a public image or either metals are frequently present in active centers of enzymes or christian practices add up to a way of life.', 'It is not true that premature infants develop kernicterus at lower levels of jaundice than full term infants.']
|
The claim that metals are frequently present in active centers of enzymes does not correspond with reality. The claim that famous people come to have a public image is false. It is rational to believe that either premature infants develop kernicterus at lower levels of jaundice than full term infants or either famous people come to have a public image or either metals are frequently present in active centers of enzymes or christian practices add up to a way of life. It is not true that premature infants develop kernicterus at lower levels of jaundice than full term infants.
|
The claim that christian practices add up to a way of life holds true.
|
Many Christian practices have their roots in older religions.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Disjunctive Syllogism:
Either [2] or (Either [1] or [0].). [SC1-2]
Not [2].
Therefore, Either [1] or [0]..
[SC1-2]
Disjunctive Syllogism:
Either [3] or (Either [2] or (Either [1] or [0].).).
Not [3].
Therefore, Either [2] or (Either [1] or [0].)..
|
{0: 'Christian practices add up to a way of life.', 1: 'Metals are frequently present in active centers of enzymes.', 2: 'Famous people come to have a public image.', 3: 'Premature infants develop kernicterus at lower levels of jaundice than full term infants.'}
| 3 |
2,582 |
['At least one of two things is true: many schools offer teenage parent programs to help girls complete their education, or food promotes dental health.', 'If many schools offer teenage parent programs to help girls complete their education, then either if most people use a variety of methods during their lifetime, changing as their needs change, then mice inhabit fields or most rodents attract other critters.', 'One may reasonably assume that if food promotes dental health, then either if most people use a variety of methods during their lifetime, changing as their needs change, then mice inhabit fields or most rodents attract other critters.', 'Given that researchers find participation, it can be inferred that the claim that if most people use a variety of methods during their lifetime, changing as their needs change, then mice inhabit fields does not reflect reality.', 'It is reasonable to believe that researchers find participation.']
|
At least one of two things is true: many schools offer teenage parent programs to help girls complete their education, or food promotes dental health. If many schools offer teenage parent programs to help girls complete their education, then either if most people use a variety of methods during their lifetime, changing as their needs change, then mice inhabit fields or most rodents attract other critters. One may reasonably assume that if food promotes dental health, then either if most people use a variety of methods during their lifetime, changing as their needs change, then mice inhabit fields or most rodents attract other critters. Given that researchers find participation, it can be inferred that the claim that if most people use a variety of methods during their lifetime, changing as their needs change, then mice inhabit fields does not reflect reality. It is reasonable to believe that researchers find participation.
|
The statement 'most rodents attract other critters' can be considered true.
|
We know that the claim that most rodents attract other critters is false.
|
FALSE
|
Disjunctive Syllogism:
Either (If [1], then [2].) or [0]. [SC1-1]
Not (If [1], then [2].). [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Either (If [1], then [2].) or [0].).
If [4], then (Either (If [1], then [2].) or [0].).
Therefore, Either (If [1], then [2].) or [0]..
[SC2-1]
Modus Ponens:
If [5], then (Not (If [1], then [2].).).
[5]
Therefore, Not (If [1], then [2].)..
|
{0: 'Most rodents attract other critters.', 1: 'Most people use a variety of methods during their lifetime, changing as their needs change.', 2: 'Mice inhabit fields.', 3: 'Many schools offer teenage parent programs to help girls complete their education.', 4: 'Food promotes dental health.', 5: 'Researchers find participation.'}
| 3 |
2,272 |
['It is a fact that either fornication is carnal union between an unmarried man and an unmarried woman or clouds of ash can disrupt radio communication by scattering or absorbing signals.', 'Assuming fornication is carnal union between an unmarried man and an unmarried woman, we know that if vesicles form along the top of the foot, on the heels and between the claws, then hair is also a symbol of physicality.', 'Once we know clouds of ash can disrupt radio communication by scattering or absorbing signals, we also know that if vesicles form along the top of the foot, on the heels and between the claws, then hair is also a symbol of physicality.', "Whenever it is true that either sulfur acts by competing with oxygen in the blood stream or most cell growth requires nutrients, 'the claim that hair is also a symbol of physicality does not correspond with reality' is true.", 'It is a fact that either sulfur acts by competing with oxygen in the blood stream or most cell growth requires nutrients.']
|
It is a fact that either fornication is carnal union between an unmarried man and an unmarried woman or clouds of ash can disrupt radio communication by scattering or absorbing signals. Assuming fornication is carnal union between an unmarried man and an unmarried woman, we know that if vesicles form along the top of the foot, on the heels and between the claws, then hair is also a symbol of physicality. Once we know clouds of ash can disrupt radio communication by scattering or absorbing signals, we also know that if vesicles form along the top of the foot, on the heels and between the claws, then hair is also a symbol of physicality. Whenever it is true that either sulfur acts by competing with oxygen in the blood stream or most cell growth requires nutrients, 'the claim that hair is also a symbol of physicality does not correspond with reality' is true. It is a fact that either sulfur acts by competing with oxygen in the blood stream or most cell growth requires nutrients.
|
It is a common misconception that vesicles form along the top of the foot, on the heels and between the claws.
|
We know that the claim that vesicles can fuse with the plasma membrane, and release their contents outside the cell is false.
|
Uncertain
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If [0], then [1].).
If [3], then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC2-1]
Modus Ponens:
If (Either [4] or [5].), then (Not [1].).
Either [4] or [5].
Therefore, Not [1]..
|
{0: 'Vesicles form along the top of the foot, on the heels and between the claws.', 1: 'Hair is also a symbol of physicality.', 2: 'Fornication is carnal union between an unmarried man and an unmarried woman.', 3: 'Clouds of ash can disrupt radio communication by scattering or absorbing signals.', 4: 'Sulfur acts by competing with oxygen in the blood stream.', 5: 'Most cell growth requires nutrients.'}
| 3 |
2,270 |
['The claim that many mammals make use of burrows but only a few birds do -e.g has no merit.', 'One may reasonably assume that if the claim that if either animals move limbs or potassium ions are colorless and similar to sodium ions, then many mammals make use of burrows but only a few birds do -e.g does not correspond with reality, then team handball is played with seven players per side, six court players, and one goalkeeper.', 'Given that team handball is played with seven players per side, six court players, and one goalkeeper, it can be inferred that some countries require by law that their citizens serve a term in their armed forces.', 'The statement, some countries require by law that their citizens serve a term in their armed forces, does not hold.']
|
The claim that many mammals make use of burrows but only a few birds do -e.g has no merit. One may reasonably assume that if the claim that if either animals move limbs or potassium ions are colorless and similar to sodium ions, then many mammals make use of burrows but only a few birds do -e.g does not correspond with reality, then team handball is played with seven players per side, six court players, and one goalkeeper. Given that team handball is played with seven players per side, six court players, and one goalkeeper, it can be inferred that some countries require by law that their citizens serve a term in their armed forces. The statement, some countries require by law that their citizens serve a term in their armed forces, does not hold.
|
Some people mistakenly believe that either animals move limbs or potassium ions are colorless and similar to sodium ions.
|
Some people mistakenly believe that either animals move limbs or potassium ions are colorless and similar to sodium ions.
|
TRUE
|
Modus Tonens:
If (Either [0] or [1].), then [2]. [SC1-1]
Not [2].
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Modus Tonens:
If (Not (If (Either [0] or [1].), then [2].).), then [3].
Not [3]. [SC2-2]
Therefore, If (Either [0] or [1].), then [2]..
[SC2-2]
Modus Tonens:
If [3], then [4].
Not [4].
Therefore, Not [3]..
|
{0: 'Animals move limbs.', 1: 'Potassium ions are colorless and similar to sodium ions.', 2: 'Many mammals make use of burrows but only a few birds do -e.g.', 3: 'Team handball is played with seven players per side, six court players, and one goalkeeper.', 4: 'Some countries require by law that their citizens serve a term in their armed forces.'}
| 3 |
2,987 |
['It is a fact that either time is a continual over-dropping of moments, which fall down one upon the other and evaporate or a maverick is a calf.', 'At least one of two things is true: layers protect skin, or if time is a continual over-dropping of moments, which fall down one upon the other and evaporate, then women are four times as likely as men to develop thyroid problems.', 'Some people mistakenly believe that layers protect skin.', 'One may reasonably assume that if the claim that if a maverick is a calf, then women are four times as likely as men to develop thyroid problems does not correspond with reality, then marine invertebrates are moderately diverse.', 'It is not the case that marine invertebrates are moderately diverse.']
|
It is a fact that either time is a continual over-dropping of moments, which fall down one upon the other and evaporate or a maverick is a calf. At least one of two things is true: layers protect skin, or if time is a continual over-dropping of moments, which fall down one upon the other and evaporate, then women are four times as likely as men to develop thyroid problems. Some people mistakenly believe that layers protect skin. One may reasonably assume that if the claim that if a maverick is a calf, then women are four times as likely as men to develop thyroid problems does not correspond with reality, then marine invertebrates are moderately diverse. It is not the case that marine invertebrates are moderately diverse.
|
It is a simple truth that women are four times as likely as men to develop thyroid problems.
|
It is a simple truth that women are four times as likely as men to develop thyroid problems.
|
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 [3] or (If [1], then [0].).
Not [3].
Therefore, If [1], then [0]..
[SC3-1]
Modus Tonens:
If (Not (If [2], then [0].).), then [4].
Not [4].
Therefore, If [2], then [0]..
|
{0: 'Women are four times as likely as men to develop thyroid problems.', 1: 'Time is a continual over-dropping of moments, which fall down one upon the other and evaporate.', 2: 'A maverick is a calf.', 3: 'Layers protect skin.', 4: 'Marine invertebrates are moderately diverse.'}
| 3 |
2,319 |
['On the condition that it is a common misconception that if it is not the case that a premolar is a tooth, then temperature decreases with altitude, it is definitely the case that chamomile tea is made from one ounce of dried flowers to a pint of boiling water.', 'If it is a common misconception that if it is not the case that a premolar is a tooth, then temperature decreases with altitude, then it is not the case that chamomile tea is made from one ounce of dried flowers to a pint of boiling water.', 'Should it be the case that temperature decreases with altitude, it follows that sandbars often form in areas where longshore currents frequently occur.', 'The statement that states sandbars often form in areas where longshore currents frequently occur is false.']
|
On the condition that it is a common misconception that if it is not the case that a premolar is a tooth, then temperature decreases with altitude, it is definitely the case that chamomile tea is made from one ounce of dried flowers to a pint of boiling water. If it is a common misconception that if it is not the case that a premolar is a tooth, then temperature decreases with altitude, then it is not the case that chamomile tea is made from one ounce of dried flowers to a pint of boiling water. Should it be the case that temperature decreases with altitude, it follows that sandbars often form in areas where longshore currents frequently occur. The statement that states sandbars often form in areas where longshore currents frequently occur is false.
|
It is rational to agree that a premolar is a tooth.
|
It is rational to agree that a premolar is a tooth.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (If (Not [0].), then [1].).), then [3].
If (Not (If (Not [0].), then [1].).), then (Not [3].).
Therefore, If (Not [0].), then [1]..
[SC2-1]
Modus Tonens:
If [1], then [2].
Not [2].
Therefore, Not [1]..
|
{0: 'A premolar is a tooth.', 1: 'Temperature decreases with altitude.', 2: 'Sandbars often form in areas where longshore currents frequently occur.', 3: 'Chamomile tea is made from one ounce of dried flowers to a pint of boiling water.'}
| 3 |
2,569 |
['We know that at least one of two things is true: excess is superabundance, or a molter is an animal.', "Should it be the case that excess is superabundance, it follows that the claim that pyrogens stimulate the hypothalamus to raise the body's internal temperature, resulting in a fever is false.", "One may reasonably assume that if the claim that if a molter is an animal, then the claim that pyrogens stimulate the hypothalamus to raise the body's internal temperature, resulting in a fever is false does not reflect reality, then sexual harassment is a form of illegal gender discrimination.", "Whenever it is true that peace is a set of skills, 'those that suggest sexual harassment is a form of illegal gender discrimination are wrong' is true.", 'It is fair to say that peace is a set of skills.']
|
We know that at least one of two things is true: excess is superabundance, or a molter is an animal. Should it be the case that excess is superabundance, it follows that the claim that pyrogens stimulate the hypothalamus to raise the body's internal temperature, resulting in a fever is false. One may reasonably assume that if the claim that if a molter is an animal, then the claim that pyrogens stimulate the hypothalamus to raise the body's internal temperature, resulting in a fever is false does not reflect reality, then sexual harassment is a form of illegal gender discrimination. Whenever it is true that peace is a set of skills, 'those that suggest sexual harassment is a form of illegal gender discrimination are wrong' is true. It is fair to say that peace is a set of skills.
|
The claim that pyrogens stimulate the hypothalamus to raise the body's internal temperature, resulting in a fever is false.
|
We know that the claim that pyrogens are substances is false.
|
Uncertain
|
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].
Not [3]. [SC2-2]
Therefore, If [2], then (Not [0].)..
[SC2-2]
Modus Ponens:
If [4], then (Not [3].).
[4]
Therefore, Not [3]..
|
{0: "Pyrogens stimulate the hypothalamus to raise the body's internal temperature, resulting in a fever.", 1: 'Excess is superabundance.', 2: 'A molter is an animal.', 3: 'Sexual harassment is a form of illegal gender discrimination.', 4: 'Peace is a set of skills.'}
| 3 |
2,643 |
['It is a fact that either murder cases involve violence or crosswalks are located in city streets.', 'On the condition that murder cases involve violence, it is definitely the case that if dental researchers know that all types of sugars can promote tooth decay, then nutritionists offer nutritional assessment and education.', "So long as crosswalks are located in city streets, 'if dental researchers know that all types of sugars can promote tooth decay, then nutritionists offer nutritional assessment and education' is true.", "On the condition that the statement that 'dental researchers know that all types of sugars can promote tooth decay' is incorrect, it is definitely the case that most tenrecs have whiskers.", "Provided that the statement that 'dental researchers know that all types of sugars can promote tooth decay' is incorrect, we know that those that suggest most tenrecs have whiskers are wrong."]
|
It is a fact that either murder cases involve violence or crosswalks are located in city streets. On the condition that murder cases involve violence, it is definitely the case that if dental researchers know that all types of sugars can promote tooth decay, then nutritionists offer nutritional assessment and education. So long as crosswalks are located in city streets, 'if dental researchers know that all types of sugars can promote tooth decay, then nutritionists offer nutritional assessment and education' is true. On the condition that the statement that 'dental researchers know that all types of sugars can promote tooth decay' is incorrect, it is definitely the case that most tenrecs have whiskers. Provided that the statement that 'dental researchers know that all types of sugars can promote tooth decay' is incorrect, we know that those that suggest most tenrecs have whiskers are wrong.
|
It is a simple truth that nutritionists offer nutritional assessment and education.
|
It is a simple truth that nutritionists offer nutritional assessment and education.
|
TRUE
|
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].
If (Not [1].), then (Not [4].).
Therefore, [1].
|
{0: 'Nutritionists offer nutritional assessment and education.', 1: 'Dental researchers know that all types of sugars can promote tooth decay.', 2: 'Murder cases involve violence.', 3: 'Crosswalks are located in city streets.', 4: 'Most tenrecs have whiskers.'}
| 3 |
2,142 |
['Given that it is a common misconception that if either polluted water creates numerous costs to the public and to wildlife or chlorinated compounds don t fluoresce well, then the claim that anaerobic systems are slower than aerobic systems is false, it can be inferred that meteorologists are scientists.', 'The statement, meteorologists are scientists, does not hold.', "At least one of two things is true: aggressive dogs are often a reflection of their owner's character, or muscles are located in jaws.", "Assuming aggressive dogs are often a reflection of their owner's character, we know that either polluted water creates numerous costs to the public and to wildlife or chlorinated compounds don t fluoresce well.", 'Once we know muscles are located in jaws, we also know that either polluted water creates numerous costs to the public and to wildlife or chlorinated compounds don t fluoresce well.']
|
Given that it is a common misconception that if either polluted water creates numerous costs to the public and to wildlife or chlorinated compounds don t fluoresce well, then the claim that anaerobic systems are slower than aerobic systems is false, it can be inferred that meteorologists are scientists. The statement, meteorologists are scientists, does not hold. At least one of two things is true: aggressive dogs are often a reflection of their owner's character, or muscles are located in jaws. Assuming aggressive dogs are often a reflection of their owner's character, we know that either polluted water creates numerous costs to the public and to wildlife or chlorinated compounds don t fluoresce well. Once we know muscles are located in jaws, we also know that either polluted water creates numerous costs to the public and to wildlife or chlorinated compounds don t fluoresce well.
|
The claim that anaerobic systems are slower than aerobic systems is false.
|
The claim that anaerobic systems are slower than aerobic systems is false.
|
TRUE
|
Modus Ponens:
If (Either [1] or [2].), then (Not [0].). [SC1-1]
Either [1] or [2]. [SC2-1]
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (If (Either [1] or [2].), then (Not [0].).).), then [5].
Not [5].
Therefore, If (Either [1] or [2].), then (Not [0].)..
[SC2-1]
Disjunction Elimination:
Either [3] or [4].
If [3], then (Either [1] or [2].).
If [4], then (Either [1] or [2].).
Therefore, Either [1] or [2]..
|
{0: 'Anaerobic systems are slower than aerobic systems.', 1: 'Polluted water creates numerous costs to the public and to wildlife.', 2: 'Chlorinated compounds don t fluoresce well.', 3: "Aggressive dogs are often a reflection of their owner's character.", 4: 'Muscles are located in jaws.', 5: 'Meteorologists are scientists.'}
| 3 |
2,202 |
["Whenever it is true that color is made different by cutting and separating shells, 'some animals like to sleep in logs like snakes, wombats and echidnas' is true.", 'There is good reason to believe that either germanium carries oxygen to the cells or color is made different by cutting and separating shells.', 'Either giraffes have individually distinct patterns or it is not true that germanium carries oxygen to the cells.', 'We know that the claim that giraffes have individually distinct patterns is false.']
|
Whenever it is true that color is made different by cutting and separating shells, 'some animals like to sleep in logs like snakes, wombats and echidnas' is true. There is good reason to believe that either germanium carries oxygen to the cells or color is made different by cutting and separating shells. Either giraffes have individually distinct patterns or it is not true that germanium carries oxygen to the cells. We know that the claim that giraffes have individually distinct patterns is false.
|
It is the case that some animals like to sleep in logs like snakes, wombats and echidnas.
|
Some animals occur in Missouri.
|
Uncertain
|
Modus Ponens:
If [1], then [0].
[1] [SC2-1]
Therefore, [0].
[SC2-1]
Disjunctive Syllogism:
Either [2] or [1].
Not [2]. [SC2-2]
Therefore, [1].
[SC2-2]
Disjunctive Syllogism:
Either [3] or (Not [2].).
Not [3].
Therefore, Not [2]..
|
{0: 'Some animals like to sleep in logs like snakes, wombats and echidnas.', 1: 'Color is made different by cutting and separating shells.', 2: 'Germanium carries oxygen to the cells.', 3: 'Giraffes have individually distinct patterns.'}
| 3 |
2,413 |
["The statement 'temptations are common to humanity' can be considered true.", 'Once we know temptations are common to humanity, we also know that most owls are rather large birds.', 'There is good reason to believe that either organic organizations are low in complexity, formalization, and centralization or if most owls are rather large birds, then we know that the claim that if prostate cancer patients follow diets, then climate change is a natural occurrence is false.', 'It is not true that organic organizations are low in complexity, formalization, and centralization.']
|
The statement 'temptations are common to humanity' can be considered true. Once we know temptations are common to humanity, we also know that most owls are rather large birds. There is good reason to believe that either organic organizations are low in complexity, formalization, and centralization or if most owls are rather large birds, then we know that the claim that if prostate cancer patients follow diets, then climate change is a natural occurrence is false. It is not true that organic organizations are low in complexity, formalization, and centralization.
|
We know that the claim that if prostate cancer patients follow diets, then climate change is a natural occurrence is false.
|
It is not the case that descriptive narration is a way of making visual media more meaningful to people with vision loss.
|
Uncertain
|
Modus Ponens:
If [2], then (Not (If [0], then [1].).). [SC1-1]
[2]
Therefore, Not (If [0], then [1].)..
[SC1-1]
Hypothetical Syllogism:
If [2], then [3].
If [3], then (Not (If [0], then [1].).). [SC2-2]
Therefore, If [2], then (Not (If [0], then [1].).)..
[SC2-2]
Disjunctive Syllogism:
Either [4] or (If [3], then (Not (If [0], then [1].).).).
Not [4].
Therefore, If [3], then (Not (If [0], then [1].).)..
|
{0: 'Prostate cancer patients follow diets.', 1: 'Climate change is a natural occurrence.', 2: 'Temptations are common to humanity.', 3: 'Most owls are rather large birds.', 4: 'Organic organizations are low in complexity, formalization, and centralization.'}
| 3 |
2,196 |
['Assuming most digestion actually takes place there, rather than in the stomach, we know that the statement that states histograms convey information about percentages by area is false.', 'If corals live mainly where the seas are warm and shallow, then the statement that states histograms convey information about percentages by area is false.', 'When neurons are cells that are specialized for the transmission of information is true, it follows that either most digestion actually takes place there, rather than in the stomach or corals live mainly where the seas are warm and shallow.', 'Given that enkephalins are small proteins, it can be inferred that either most digestion actually takes place there, rather than in the stomach or corals live mainly where the seas are warm and shallow.', 'One may reasonably assume that if it is not the case that either neurons are cells that are specialized for the transmission of information or enkephalins are small proteins, then manatees live on seagrass.', "So long as it is not the case that either neurons are cells that are specialized for the transmission of information or enkephalins are small proteins, 'the claim that manatees live on seagrass does not reflect reality' is true."]
|
Assuming most digestion actually takes place there, rather than in the stomach, we know that the statement that states histograms convey information about percentages by area is false. If corals live mainly where the seas are warm and shallow, then the statement that states histograms convey information about percentages by area is false. When neurons are cells that are specialized for the transmission of information is true, it follows that either most digestion actually takes place there, rather than in the stomach or corals live mainly where the seas are warm and shallow. Given that enkephalins are small proteins, it can be inferred that either most digestion actually takes place there, rather than in the stomach or corals live mainly where the seas are warm and shallow. One may reasonably assume that if it is not the case that either neurons are cells that are specialized for the transmission of information or enkephalins are small proteins, then manatees live on seagrass. So long as it is not the case that either neurons are cells that are specialized for the transmission of information or enkephalins are small proteins, 'the claim that manatees live on seagrass does not reflect reality' is true.
|
The statement that states histograms convey information about percentages by area is false.
|
The statement that states histograms convey information about percentages by area is false.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].).
If [2], then (Not [0].).
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [3] or [4]. [SC1-2]
If [3], then (Either [1] or [2].).
If [4], then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC1-2]
Reductio Ad Absurdum:
If (Not (Either [3] or [4].).), then [5].
If (Not (Either [3] or [4].).), then (Not [5].).
Therefore, Either [3] or [4]..
|
{0: 'Histograms convey information about percentages by area.', 1: 'Most digestion actually takes place there, rather than in the stomach.', 2: 'Corals live mainly where the seas are warm and shallow.', 3: 'Neurons are cells that are specialized for the transmission of information.', 4: 'Enkephalins are small proteins.', 5: 'Manatees live on seagrass.'}
| 3 |
2,264 |
['We know that either altar gear is an area where one can have a great deal of fun and creativity on a shoestring budget or pork contains high quality complete protein with all nine essential amino acids.', 'Once we know altar gear is an area where one can have a great deal of fun and creativity on a shoestring budget, we also know that peregrines are predators.', 'Provided that freedom of expression is the first step to global understanding and peace, we know that if pork contains high quality complete protein with all nine essential amino acids, then peregrines are predators.', 'Once we know it is a common misconception that freedom of expression is the first step to global understanding and peace, we also know that if heated metals tend to oxidize rapidly, then sanctions are the greatest single weapon of mass destruction at work in the world today.', "Assuming it is a common misconception that freedom of expression is the first step to global understanding and peace, we know that the statement 'if heated metals tend to oxidize rapidly, then sanctions are the greatest single weapon of mass destruction at work in the world today' can be considered false."]
|
We know that either altar gear is an area where one can have a great deal of fun and creativity on a shoestring budget or pork contains high quality complete protein with all nine essential amino acids. Once we know altar gear is an area where one can have a great deal of fun and creativity on a shoestring budget, we also know that peregrines are predators. Provided that freedom of expression is the first step to global understanding and peace, we know that if pork contains high quality complete protein with all nine essential amino acids, then peregrines are predators. Once we know it is a common misconception that freedom of expression is the first step to global understanding and peace, we also know that if heated metals tend to oxidize rapidly, then sanctions are the greatest single weapon of mass destruction at work in the world today. Assuming it is a common misconception that freedom of expression is the first step to global understanding and peace, we know that the statement 'if heated metals tend to oxidize rapidly, then sanctions are the greatest single weapon of mass destruction at work in the world today' can be considered false.
|
We can assume that peregrines are predators.
|
We can assume that peregrines are predators.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then [0].
If [2], then [0]. [SC3-1]
Therefore, [0].
[SC3-1]
Modus Ponens:
If [3], then (If [2], then [0].).
[3] [SC2-2]
Therefore, If [2], then [0]..
[SC2-2]
Reductio Ad Absurdum:
If (Not [3].), then (If [4], then [5].).
If (Not [3].), then (Not (If [4], then [5].).).
Therefore, [3].
|
{0: 'Peregrines are predators.', 1: 'Altar gear is an area where one can have a great deal of fun and creativity on a shoestring budget.', 2: 'Pork contains high quality complete protein with all nine essential amino acids.', 3: 'Freedom of expression is the first step to global understanding and peace.', 4: 'Heated metals tend to oxidize rapidly.', 5: 'Sanctions are the greatest single weapon of mass destruction at work in the world today.'}
| 3 |
2,531 |
['Provided that some endosperms contain water, we know that carpels produce female sex cells in ovules inside ovaries.', 'If we know that the claim that if some endosperms contain water, then it is not true that carpels produce female sex cells in ovules inside ovaries is false, then if capacity building is the sum of interest, expertise, and time, then penile cancer is an extremely rare form of cancer.', "Whenever it is true that cesarean section are three to four times more likely for pregnant women with diabetes, 'if we know that the claim that if some endosperms contain water, then it is not true that carpels produce female sex cells in ovules inside ovaries is false, then the statement that states if capacity building is the sum of interest, expertise, and time, then penile cancer is an extremely rare form of cancer is false' is true.", 'We can assume that cesarean section are three to four times more likely for pregnant women with diabetes.']
|
Provided that some endosperms contain water, we know that carpels produce female sex cells in ovules inside ovaries. If we know that the claim that if some endosperms contain water, then it is not true that carpels produce female sex cells in ovules inside ovaries is false, then if capacity building is the sum of interest, expertise, and time, then penile cancer is an extremely rare form of cancer. Whenever it is true that cesarean section are three to four times more likely for pregnant women with diabetes, 'if we know that the claim that if some endosperms contain water, then it is not true that carpels produce female sex cells in ovules inside ovaries is false, then the statement that states if capacity building is the sum of interest, expertise, and time, then penile cancer is an extremely rare form of cancer is false' is true. We can assume that cesarean section are three to four times more likely for pregnant women with diabetes.
|
Those that suggest some endosperms contain water are wrong.
|
The statement 'most endosperms have layers' can be considered false.
|
Uncertain
|
Reductio Ad Absurdum:
If [0], then [1].
If [0], then (Not [1].). [SC2-1]
Therefore, Not [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [0], then (Not [1].).).), then (If [2], then [3].).
If (Not (If [0], then (Not [1].).).), then (Not (If [2], then [3].).). [SC2-2]
Therefore, If [0], then (Not [1].)..
[SC2-2]
Modus Ponens:
If [4], then (If (Not (If [0], then (Not [1].).).), then (Not (If [2], then [3].).).).
[4]
Therefore, If (Not (If [0], then (Not [1].).).), then (Not (If [2], then [3].).)..
|
{0: 'Some endosperms contain water.', 1: 'Carpels produce female sex cells in ovules inside ovaries.', 2: 'Capacity building is the sum of interest, expertise, and time.', 3: 'Penile cancer is an extremely rare form of cancer.', 4: 'Cesarean section are three to four times more likely for pregnant women with diabetes.'}
| 3 |
2,252 |
['We know that either tiger has bright emerald-green eyes or if fall brings cool temperatures, falling leaves, and low stream-water levels, then eye movements, for instance, are one of the most precise movements that animals can make.', "Whenever it is true that tiger has bright emerald-green eyes, 'most physical laws describe behavior' is true.", 'It is a simple truth that marine scientists report levels.', 'Given that it is not true that if marine scientists report levels, then if if fall brings cool temperatures, falling leaves, and low stream-water levels, then eye movements, for instance, are one of the most precise movements that animals can make, then most physical laws describe behavior, it can be inferred that either some traits are the product of many different alleles that occupy a specific gene locus or horses eat prairie grass.', 'It is not true that either some traits are the product of many different alleles that occupy a specific gene locus or horses eat prairie grass.']
|
We know that either tiger has bright emerald-green eyes or if fall brings cool temperatures, falling leaves, and low stream-water levels, then eye movements, for instance, are one of the most precise movements that animals can make. Whenever it is true that tiger has bright emerald-green eyes, 'most physical laws describe behavior' is true. It is a simple truth that marine scientists report levels. Given that it is not true that if marine scientists report levels, then if if fall brings cool temperatures, falling leaves, and low stream-water levels, then eye movements, for instance, are one of the most precise movements that animals can make, then most physical laws describe behavior, it can be inferred that either some traits are the product of many different alleles that occupy a specific gene locus or horses eat prairie grass. It is not true that either some traits are the product of many different alleles that occupy a specific gene locus or horses eat prairie grass.
|
The idea that most physical laws describe behavior is true.
|
Physical law is the law of the material universe.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (If [2], then [3].).
If [1], then [0].
If (If [2], then [3].), then [0]. [SC3-1]
Therefore, [0].
[SC3-1]
Modus Ponens:
If [4], then (If (If [2], then [3].), then [0].). [SC1-2]
[4]
Therefore, If (If [2], then [3].), then [0]..
[SC1-2]
Modus Tonens:
If (Not (If [4], then (If (If [2], then [3].), then [0].).).), then (Either [5] or [6].).
Not (Either [5] or [6].).
Therefore, If [4], then (If (If [2], then [3].), then [0].)..
|
{0: 'Most physical laws describe behavior.', 1: 'Tiger has bright emerald-green eyes.', 2: 'Fall brings cool temperatures, falling leaves, and low stream-water levels.', 3: 'Eye movements, for instance, are one of the most precise movements that animals can make.', 4: 'Marine scientists report levels.', 5: 'Some traits are the product of many different alleles that occupy a specific gene locus.', 6: 'Horses eat prairie grass.'}
| 3 |
2,576 |
['Those that suggest some scientists claim that the robustness of the skull and lower jaws gave a rigid crushing bite are wrong.', 'car maintenance is maintenance.', 'When car maintenance is maintenance is true, it follows that if most waste contains organic pollutants, then some species live in different areas.', 'On the condition that if most waste contains organic pollutants, then some species live in different areas, it is definitely the case that if some people mistakenly believe that if science is part of scientific knowledge, then dogs can disturb or injure wildlife and, in turn, can be injured by other animals, then some scientists claim that the robustness of the skull and lower jaws gave a rigid crushing bite.']
|
Those that suggest some scientists claim that the robustness of the skull and lower jaws gave a rigid crushing bite are wrong. car maintenance is maintenance. When car maintenance is maintenance is true, it follows that if most waste contains organic pollutants, then some species live in different areas. On the condition that if most waste contains organic pollutants, then some species live in different areas, it is definitely the case that if some people mistakenly believe that if science is part of scientific knowledge, then dogs can disturb or injure wildlife and, in turn, can be injured by other animals, then some scientists claim that the robustness of the skull and lower jaws gave a rigid crushing bite.
|
Provided that science is part of scientific knowledge, we know that dogs can disturb or injure wildlife and, in turn, can be injured by other animals
|
If science is part of scientific knowledge, then dogs are a responsibility and are loving creatures that have needs of their own.
|
Uncertain
|
Modus Tonens:
If (Not (If [0], then [1].).), then [2]. [SC1-1]
Not [2].
Therefore, If [0], then [1]..
[SC1-1]
Modus Ponens:
If [3], then (If (Not (If [0], then [1].).), then [2].). [SC1-2]
[3]
Therefore, If (Not (If [0], then [1].).), then [2]..
[SC1-2]
Hypothetical Syllogism:
If [3], then (If [4], then [5].).
If (If [4], then [5].), then (If (Not (If [0], then [1].).), then [2].).
Therefore, If [3], then (If (Not (If [0], then [1].).), then [2].)..
|
{0: 'Science is part of scientific knowledge.', 1: 'Dogs can disturb or injure wildlife and, in turn, can be injured by other animals.', 2: 'Some scientists claim that the robustness of the skull and lower jaws gave a rigid crushing bite.', 3: 'Car maintenance is maintenance.', 4: 'Most waste contains organic pollutants.', 5: 'Some species live in different areas.'}
| 3 |
2,738 |
['We know that at least one of two things is true: differential support means teaching individual children in individual ways, or foot licking in atopics can begin at a very young age, perhaps younger than previously published.', 'Assuming differential support means teaching individual children in individual ways, we know that seals usually hunt for herring during the day.', "So long as seals usually hunt for herring during the day, 'the claim that narwhals feed more regularly in the winter, consuming fish like cod and halibut, shrimp, and squid does not correspond with reality' is true.", 'At least one of two things is true: grain is simply the harvested seed of a plant, or if foot licking in atopics can begin at a very young age, perhaps younger than previously published, then the claim that narwhals feed more regularly in the winter, consuming fish like cod and halibut, shrimp, and squid does not correspond with reality.', 'The claim that grain is simply the harvested seed of a plant does not reflect reality.']
|
We know that at least one of two things is true: differential support means teaching individual children in individual ways, or foot licking in atopics can begin at a very young age, perhaps younger than previously published. Assuming differential support means teaching individual children in individual ways, we know that seals usually hunt for herring during the day. So long as seals usually hunt for herring during the day, 'the claim that narwhals feed more regularly in the winter, consuming fish like cod and halibut, shrimp, and squid does not correspond with reality' is true. At least one of two things is true: grain is simply the harvested seed of a plant, or if foot licking in atopics can begin at a very young age, perhaps younger than previously published, then the claim that narwhals feed more regularly in the winter, consuming fish like cod and halibut, shrimp, and squid does not correspond with reality. The claim that grain is simply the harvested seed of a plant does not reflect reality.
|
The claim that narwhals feed more regularly in the winter, consuming fish like cod and halibut, shrimp, and squid does not correspond with reality.
|
It is a simple truth that narwhals feed more regularly in the winter, consuming fish like cod and halibut, shrimp, and squid.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then (Not [0].). [SC2-1]
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC2-1]
Hypothetical Syllogism:
If [1], then [4].
If [4], then (Not [0].).
Therefore, If [1], then (Not [0].)..
[SC3-1]
Disjunctive Syllogism:
Either [3] or (If [2], then (Not [0].).).
Not [3].
Therefore, If [2], then (Not [0].)..
|
{0: 'Narwhals feed more regularly in the winter, consuming fish like cod and halibut, shrimp, and squid.', 1: 'Differential support means teaching individual children in individual ways.', 2: 'Foot licking in atopics can begin at a very young age, perhaps younger than previously published.', 3: 'Grain is simply the harvested seed of a plant.', 4: 'Seals usually hunt for herring during the day.'}
| 3 |
2,299 |
["Assuming insects excrete waste through an anus, just as most other animals do, we know that the statement that 'birds like water' is incorrect.", 'Should it be the case that we know that the claim that either streams can carry sediment, or alluvium or insects excrete waste through an anus, just as most other animals do is false, it follows that a purifier is apparatus.', 'It is not the case that a purifier is apparatus.', 'There is good reason to believe that either cancer is a process with many steps or most light shows same spectral features.', "So long as cancer is a process with many steps, 'if streams can carry sediment, or alluvium, then the statement that 'birds like water' is incorrect' is true.", "When most light shows same spectral features is true, it follows that if streams can carry sediment, or alluvium, then the statement that 'birds like water' is incorrect."]
|
Assuming insects excrete waste through an anus, just as most other animals do, we know that the statement that 'birds like water' is incorrect. Should it be the case that we know that the claim that either streams can carry sediment, or alluvium or insects excrete waste through an anus, just as most other animals do is false, it follows that a purifier is apparatus. It is not the case that a purifier is apparatus. There is good reason to believe that either cancer is a process with many steps or most light shows same spectral features. So long as cancer is a process with many steps, 'if streams can carry sediment, or alluvium, then the statement that 'birds like water' is incorrect' is true. When most light shows same spectral features is true, it follows that if streams can carry sediment, or alluvium, then the statement that 'birds like water' is incorrect.
|
The statement that 'birds like water' is incorrect.
|
The idea that birds like water is true.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].). [SC2-1]
If [2], then (Not [0].).
Therefore, Not [0]..
[SC1-1]
Modus Tonens:
If (Not (Either [1] or [2].).), then [3].
Not [3].
Therefore, Either [1] or [2]..
[SC2-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [1], then (Not [0].).).
If [5], then (If [1], then (Not [0].).).
Therefore, If [1], then (Not [0].)..
|
{0: 'Birds like water.', 1: 'Streams can carry sediment, or alluvium.', 2: 'Insects excrete waste through an anus, just as most other animals do.', 3: 'A purifier is apparatus.', 4: 'Cancer is a process with many steps.', 5: 'Most light shows same spectral features.'}
| 3 |
2,740 |
['The claim that soybeans vary greatly in both physical appearance and chemical composition does not correspond with reality.', 'Once we know onions also benefit from additional nitrogen, we also know that if the statement, many cancer treatments stop cells dividing and growing, does not hold, then soybeans vary greatly in both physical appearance and chemical composition.', 'Either one or both of these statements are true: some dogs compete for form, or onions also benefit from additional nitrogen.', 'The claim that some dogs compete for form is false.']
|
The claim that soybeans vary greatly in both physical appearance and chemical composition does not correspond with reality. Once we know onions also benefit from additional nitrogen, we also know that if the statement, many cancer treatments stop cells dividing and growing, does not hold, then soybeans vary greatly in both physical appearance and chemical composition. Either one or both of these statements are true: some dogs compete for form, or onions also benefit from additional nitrogen. The claim that some dogs compete for form is false.
|
It is reasonable to believe that many cancer treatments stop cells dividing and growing.
|
It is reasonable to believe that many cancer treatments stop cells dividing and growing.
|
TRUE
|
Modus Tonens:
If (Not [0].), then [1]. [SC1-1]
Not [1].
Therefore, [0].
[SC1-1]
Modus Ponens:
If [2], then (If (Not [0].), then [1].).
[2] [SC2-2]
Therefore, If (Not [0].), then [1]..
[SC2-2]
Disjunctive Syllogism:
Either [3] or [2].
Not [3].
Therefore, [2].
|
{0: 'Many cancer treatments stop cells dividing and growing.', 1: 'Soybeans vary greatly in both physical appearance and chemical composition.', 2: 'Onions also benefit from additional nitrogen.', 3: 'Some dogs compete for form.'}
| 3 |
2,247 |
["So long as crappies are thick in the submerged brush and timber, and suspended over the creek channels, 'it is a common misconception that effects indicate high potential' is true.", 'When either earthquakes trigger nuclear disasters or peanuts are known scientifically as Arachis hypogaea is true, it follows that crappies are thick in the submerged brush and timber, and suspended over the creek channels.', 'Should it be the case that the claim that either earthquakes trigger nuclear disasters or peanuts are known scientifically as Arachis hypogaea does not correspond with reality, it follows that energy use falls only in a stagnant or depressed economy.', 'The claim that energy use falls only in a stagnant or depressed economy has no merit.']
|
So long as crappies are thick in the submerged brush and timber, and suspended over the creek channels, 'it is a common misconception that effects indicate high potential' is true. When either earthquakes trigger nuclear disasters or peanuts are known scientifically as Arachis hypogaea is true, it follows that crappies are thick in the submerged brush and timber, and suspended over the creek channels. Should it be the case that the claim that either earthquakes trigger nuclear disasters or peanuts are known scientifically as Arachis hypogaea does not correspond with reality, it follows that energy use falls only in a stagnant or depressed economy. The claim that energy use falls only in a stagnant or depressed economy has no merit.
|
It is a common misconception that effects indicate high potential.
|
Some people mistakenly believe that effects ensure survival.
|
Uncertain
|
Modus Ponens:
If [1], then (Not [0].).
[1] [SC2-1]
Therefore, Not [0]..
[SC2-1]
Modus Ponens:
If (Either [2] or [3].), then [1].
Either [2] or [3]. [SC2-2]
Therefore, [1].
[SC2-2]
Modus Tonens:
If (Not (Either [2] or [3].).), then [4].
Not [4].
Therefore, Either [2] or [3]..
|
{0: 'Effects indicate high potential.', 1: 'Crappies are thick in the submerged brush and timber, and suspended over the creek channels.', 2: 'Earthquakes trigger nuclear disasters.', 3: 'Peanuts are known scientifically as Arachis hypogaea.', 4: 'Energy use falls only in a stagnant or depressed economy.'}
| 3 |
2,926 |
['Given that interfaith dialogue can lead to diplomacy which ends wars, it can be inferred that the claim that substance abuse includes drugs, medicines and alcohols does not reflect reality.', 'Should it be the case that mouths have tongues, it follows that the claim that substance abuse includes drugs, medicines and alcohols does not reflect reality.', 'If genetic engineering is a young, and in many ways poorly understood, technology, then interfaith dialogue can lead to diplomacy which ends wars.', 'When economic information is grouped by geographical regions is true, it follows that mouths have tongues.', 'There is good reason to believe that either some growth hormones used in meat production are human carcinogens or either site refers to the actual physical position and conditions of a place or some allergic individuals go into shocks.', 'Assuming some growth hormones used in meat production are human carcinogens, we know that either genetic engineering is a young, and in many ways poorly understood, technology or economic information is grouped by geographical regions.', 'Given that either site refers to the actual physical position and conditions of a place or some allergic individuals go into shocks, it can be inferred that either genetic engineering is a young, and in many ways poorly understood, technology or economic information is grouped by geographical regions.']
|
Given that interfaith dialogue can lead to diplomacy which ends wars, it can be inferred that the claim that substance abuse includes drugs, medicines and alcohols does not reflect reality. Should it be the case that mouths have tongues, it follows that the claim that substance abuse includes drugs, medicines and alcohols does not reflect reality. If genetic engineering is a young, and in many ways poorly understood, technology, then interfaith dialogue can lead to diplomacy which ends wars. When economic information is grouped by geographical regions is true, it follows that mouths have tongues. There is good reason to believe that either some growth hormones used in meat production are human carcinogens or either site refers to the actual physical position and conditions of a place or some allergic individuals go into shocks. Assuming some growth hormones used in meat production are human carcinogens, we know that either genetic engineering is a young, and in many ways poorly understood, technology or economic information is grouped by geographical regions. Given that either site refers to the actual physical position and conditions of a place or some allergic individuals go into shocks, it can be inferred that either genetic engineering is a young, and in many ways poorly understood, technology or economic information is grouped by geographical regions.
|
The claim that substance abuse includes drugs, medicines and alcohols does not reflect reality.
|
The claim that substance abuse includes drugs, medicines and alcohols does not reflect reality.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].).
If [2], then (Not [0].).
Therefore, Not [0]..
[SC1-1]
Constructive Dilemma:
Either [3] or [4]. [SC1-2]
If [3], then [1].
If [4], then [2].
Therefore, Either [1] or [2]..
[SC1-2]
Disjunction Elimination:
Either [5] or (Either [6] or [7].).
If [5], then (Either [3] or [4].).
If (Either [6] or [7].), then (Either [3] or [4].).
Therefore, Either [3] or [4]..
|
{0: 'Substance abuse includes drugs, medicines and alcohols.', 1: 'Interfaith dialogue can lead to diplomacy which ends wars.', 2: 'Mouths have tongues.', 3: 'Genetic engineering is a young, and in many ways poorly understood, technology.', 4: 'Economic information is grouped by geographical regions.', 5: 'Some growth hormones used in meat production are human carcinogens.', 6: 'Site refers to the actual physical position and conditions of a place.', 7: 'Some allergic individuals go into shocks.'}
| 3 |
2,412 |
['Either one or both of these statements are true: official languages are Swahili and English, or if trees provide sources, then salt helps to aid digestion.', 'When official languages are Swahili and English is true, it follows that if hind legs are important for a grasshopper to hop, then black wildebeests reach sexual maturity.', 'Given that if hind legs are important for a grasshopper to hop, then black wildebeests reach sexual maturity, it can be inferred that pandas are the second most threatened species in the world.', 'When gambian has (part) cells is true, it follows that if if trees provide sources, then salt helps to aid digestion, then pandas are the second most threatened species in the world.', 'It is true that gambian has (part) cells.']
|
Either one or both of these statements are true: official languages are Swahili and English, or if trees provide sources, then salt helps to aid digestion. When official languages are Swahili and English is true, it follows that if hind legs are important for a grasshopper to hop, then black wildebeests reach sexual maturity. Given that if hind legs are important for a grasshopper to hop, then black wildebeests reach sexual maturity, it can be inferred that pandas are the second most threatened species in the world. When gambian has (part) cells is true, it follows that if if trees provide sources, then salt helps to aid digestion, then pandas are the second most threatened species in the world. It is true that gambian has (part) cells.
|
The idea that pandas are the second most threatened species in the world is true.
|
Most pandas have teeth.
|
Uncertain
|
Disjunction Elimination:
Either [1] or (If [2], then [3].).
If [1], then [0]. [SC2-1]
If (If [2], then [3].), then [0]. [SC3-1]
Therefore, [0].
[SC2-1]
Hypothetical Syllogism:
If [1], then (If [5], then [6].).
If (If [5], then [6].), then [0].
Therefore, If [1], then [0]..
[SC3-1]
Modus Ponens:
If [4], then (If (If [2], then [3].), then [0].).
[4]
Therefore, If (If [2], then [3].), then [0]..
|
{0: 'Pandas are the second most threatened species in the world.', 1: 'Official languages are Swahili and English.', 2: 'Trees provide sources.', 3: 'Salt helps to aid digestion.', 4: 'Gambian has (part) cells.', 5: 'Hind legs are important for a grasshopper to hop.', 6: 'Black wildebeests reach sexual maturity.'}
| 3 |
2,389 |
["Whenever it is true that it is a common misconception that either agriculture is dependent on a plentiful supply of quality water or unfertilized eggs go through cleavage divisions, sometimes to blastula, 'a pleura is animal tissue' is true.", "Whenever it is true that a pleura is animal tissue, 'daughters have responses' is true.", 'Should it be the case that it is a common misconception that either agriculture is dependent on a plentiful supply of quality water or unfertilized eggs go through cleavage divisions, sometimes to blastula, it follows that gaurs have (part) cell membranes.', 'Assuming gaurs have (part) cell membranes, we know that those that suggest daughters have responses are wrong.']
|
Whenever it is true that it is a common misconception that either agriculture is dependent on a plentiful supply of quality water or unfertilized eggs go through cleavage divisions, sometimes to blastula, 'a pleura is animal tissue' is true. Whenever it is true that a pleura is animal tissue, 'daughters have responses' is true. Should it be the case that it is a common misconception that either agriculture is dependent on a plentiful supply of quality water or unfertilized eggs go through cleavage divisions, sometimes to blastula, it follows that gaurs have (part) cell membranes. Assuming gaurs have (part) cell membranes, we know that those that suggest daughters have responses are wrong.
|
Either one or both of these statements are true: agriculture is dependent on a plentiful supply of quality water, or unfertilized eggs go through cleavage divisions, sometimes to blastula.
|
It is rational to believe that either agriculture is a significant sector of the economy or unfertilized eggs are identifiable under the microscope by their elongated shape.
|
Uncertain
|
Reductio Ad Absurdum:
If (Not (Either [0] or [1].).), then [2]. [SC1-1]
If (Not (Either [0] or [1].).), then (Not [2].). [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Hypothetical Syllogism:
If (Not (Either [0] or [1].).), then [4].
If [4], then [2].
Therefore, If (Not (Either [0] or [1].).), then [2]..
[SC2-1]
Hypothetical Syllogism:
If (Not (Either [0] or [1].).), then [3].
If [3], then (Not [2].).
Therefore, If (Not (Either [0] or [1].).), then (Not [2].)..
|
{0: 'Agriculture is dependent on a plentiful supply of quality water.', 1: 'Unfertilized eggs go through cleavage divisions, sometimes to blastula.', 2: 'Daughters have responses.', 3: 'Gaurs have (part) cell membranes.', 4: 'A pleura is animal tissue.'}
| 3 |
2,796 |
["So long as accidents are often the foundation for discoveries in research, 'it is not the case that witches certainly can hold their beliefs and practices in private' is true.", 'We know that at least one of two things is true: most plants thrive in subtropical regions, or if accidents are often the foundation for discoveries in research, then witches certainly can hold their beliefs and practices in private.', "When either sulfur is used to make garden soil more acid or some specialists study antler deer growth is true, it follows that the statement 'most plants thrive in subtropical regions' can be considered false.", 'Either sulfur is used to make garden soil more acid or some specialists study antler deer growth.']
|
So long as accidents are often the foundation for discoveries in research, 'it is not the case that witches certainly can hold their beliefs and practices in private' is true. We know that at least one of two things is true: most plants thrive in subtropical regions, or if accidents are often the foundation for discoveries in research, then witches certainly can hold their beliefs and practices in private. When either sulfur is used to make garden soil more acid or some specialists study antler deer growth is true, it follows that the statement 'most plants thrive in subtropical regions' can be considered false. Either sulfur is used to make garden soil more acid or some specialists study antler deer growth.
|
Some people mistakenly believe that accidents are often the foundation for discoveries in research.
|
Those that suggest accidents are often the foundation for discoveries in research are right.
|
FALSE
|
Reductio Ad Absurdum:
If [0], then [1]. [SC1-1]
If [0], then (Not [1].).
Therefore, Not [0]..
[SC1-1]
Disjunctive Syllogism:
Either [2] or (If [0], then [1].).
Not [2]. [SC2-2]
Therefore, If [0], then [1]..
[SC2-2]
Modus Ponens:
If (Either [3] or [4].), then (Not [2].).
Either [3] or [4].
Therefore, Not [2]..
|
{0: 'Accidents are often the foundation for discoveries in research.', 1: 'Witches certainly can hold their beliefs and practices in private.', 2: 'Most plants thrive in subtropical regions.', 3: 'Sulfur is used to make garden soil more acid.', 4: 'Some specialists study antler deer growth.'}
| 3 |
2,601 |
['The claim that jungle is woods is false.', 'Provided that china is a third world country, we know that jungle is woods.', 'Provided that aphids spread virus and cause distorted growth, we know that if either nutrient availability is dependent upon soil pH levels or bookcases are furniture, then china is a third world country.', "The statement 'aphids spread virus and cause distorted growth' can be considered true."]
|
The claim that jungle is woods is false. Provided that china is a third world country, we know that jungle is woods. Provided that aphids spread virus and cause distorted growth, we know that if either nutrient availability is dependent upon soil pH levels or bookcases are furniture, then china is a third world country. The statement 'aphids spread virus and cause distorted growth' can be considered true.
|
It is not the case that either nutrient availability is dependent upon soil pH levels or bookcases are furniture.
|
It is not the case that either nutrient availability is dependent upon soil pH levels or bookcases are furniture.
|
TRUE
|
Modus Tonens:
If (Either [0] or [1].), then [2]. [SC1-1]
Not [2].
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Hypothetical Syllogism:
If (Either [0] or [1].), then [3]. [SC1-2]
If [3], then [2].
Therefore, If (Either [0] or [1].), then [2]..
[SC1-2]
Modus Ponens:
If [4], then (If (Either [0] or [1].), then [3].).
[4]
Therefore, If (Either [0] or [1].), then [3]..
|
{0: 'Nutrient availability is dependent upon soil pH levels.', 1: 'Bookcases are furniture.', 2: 'Jungle is woods.', 3: 'China is a third world country.', 4: 'Aphids spread virus and cause distorted growth.'}
| 3 |
2,654 |
['Assuming it is not the case that laws require urban water agencies, we know that canes weakened by galls are more subject to winter injury.', 'Some people mistakenly believe that bluebottles are the most common cause of jellyfish stings in Australia.', 'We know that at least one of two things is true: an elbow is a diarthrosis, or civets are the source for one of the oldest components of perfume known.', 'Once we know an elbow is a diarthrosis, we also know that bluebottles are the most common cause of jellyfish stings in Australia.', "Provided that civets are the source for one of the oldest components of perfume known, we know that if it is not the case that laws require urban water agencies, then the notion that 'canes weakened by galls are more subject to winter injury' is untrue."]
|
Assuming it is not the case that laws require urban water agencies, we know that canes weakened by galls are more subject to winter injury. Some people mistakenly believe that bluebottles are the most common cause of jellyfish stings in Australia. We know that at least one of two things is true: an elbow is a diarthrosis, or civets are the source for one of the oldest components of perfume known. Once we know an elbow is a diarthrosis, we also know that bluebottles are the most common cause of jellyfish stings in Australia. Provided that civets are the source for one of the oldest components of perfume known, we know that if it is not the case that laws require urban water agencies, then the notion that 'canes weakened by galls are more subject to winter injury' is untrue.
|
Those that suggest laws require urban water agencies are right.
|
Those that suggest laws require urban water agencies are right.
|
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]
Constructive Dilemma:
Either [3] or [4].
If [3], then [2].
If [4], then (If (Not [0].), then (Not [1].).).
Therefore, Either [2] or (If (Not [0].), then (Not [1].).)..
|
{0: 'Laws require urban water agencies.', 1: 'Canes weakened by galls are more subject to winter injury.', 2: 'Bluebottles are the most common cause of jellyfish stings in Australia.', 3: 'An elbow is a diarthrosis.', 4: 'Civets are the source for one of the oldest components of perfume known.'}
| 3 |
2,261 |
['If the claim that either fog also occurs when the air is cooled below a critical temperature called the dew point or prehistories are time periods does not correspond with reality, then carnivores feed on live prey.', "The notion that 'carnivores feed on live prey' is untrue.", 'When fog also occurs when the air is cooled below a critical temperature called the dew point is true, it follows that diesel engines are more fuel-efficient than petrol ones, and diesel fuel has a lower fire risk.', 'On the condition that fog also occurs when the air is cooled below a critical temperature called the dew point, it is definitely the case that the claim that diesel engines are more fuel-efficient than petrol ones, and diesel fuel has a lower fire risk has no merit.']
|
If the claim that either fog also occurs when the air is cooled below a critical temperature called the dew point or prehistories are time periods does not correspond with reality, then carnivores feed on live prey. The notion that 'carnivores feed on live prey' is untrue. When fog also occurs when the air is cooled below a critical temperature called the dew point is true, it follows that diesel engines are more fuel-efficient than petrol ones, and diesel fuel has a lower fire risk. On the condition that fog also occurs when the air is cooled below a critical temperature called the dew point, it is definitely the case that the claim that diesel engines are more fuel-efficient than petrol ones, and diesel fuel has a lower fire risk has no merit.
|
The claim that prehistories are time periods is true.
|
It is a common misconception that prehistories are time periods.
|
FALSE
|
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].
If [1], then (Not [2].).
Therefore, Not [1]..
|
{0: 'Prehistories are time periods.', 1: 'Fog also occurs when the air is cooled below a critical temperature called the dew point.', 2: 'Diesel engines are more fuel-efficient than petrol ones, and diesel fuel has a lower fire risk.', 3: 'Carnivores feed on live prey.'}
| 3 |
2,456 |
['Either noses have (part) ground substances or sensors are used in everyday objects .', 'When noses have (part) ground substances is true, it follows that either manuals have information or multimedia has many different meanings to many different people.', 'On the condition that sensors are used in everyday objects , it is definitely the case that either manuals have information or multimedia has many different meanings to many different people.', "At least one of two things is true: either history comes alive when children see the human side that is reflected in biographies or most gene therapy extends life, or the statement 'manuals have information' can be considered false.", 'The claim that either history comes alive when children see the human side that is reflected in biographies or most gene therapy extends life has no merit.']
|
Either noses have (part) ground substances or sensors are used in everyday objects . When noses have (part) ground substances is true, it follows that either manuals have information or multimedia has many different meanings to many different people. On the condition that sensors are used in everyday objects , it is definitely the case that either manuals have information or multimedia has many different meanings to many different people. At least one of two things is true: either history comes alive when children see the human side that is reflected in biographies or most gene therapy extends life, or the statement 'manuals have information' can be considered false. The claim that either history comes alive when children see the human side that is reflected in biographies or most gene therapy extends life has no merit.
|
It is fair to say that multimedia has many different meanings to many different people.
|
Multimedia is the use of technology to better communicate information.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (Either [1] or [0].).
If [5], then (Either [1] or [0].).
Therefore, Either [1] or [0]..
[SC2-1]
Disjunctive Syllogism:
Either (Either [2] or [3].) or (Not [1].).
Not (Either [2] or [3].).
Therefore, Not [1]..
|
{0: 'Multimedia has many different meanings to many different people.', 1: 'Manuals have information.', 2: 'History comes alive when children see the human side that is reflected in biographies.', 3: 'Most gene therapy extends life.', 4: 'Noses have (part) ground substances.', 5: 'Sensors are used in everyday objects .'}
| 3 |
2,386 |
['There is good reason to believe that either either some animals eat seaweed or average high temperature decreases during seasons or globalization is, in fact, a very old process, in some sense as old as human civilization itself.', "Whenever it is true that either some animals eat seaweed or average high temperature decreases during seasons, 'rain usually washes a lot of pollen out of the air - counts go down' is true.", "So long as globalization is, in fact, a very old process, in some sense as old as human civilization itself, 'narcotics kill sensitivity to pain and reduce unwanted feelings of anger, irritability, and anxiety' is true.", "It is a fact that either summer is the time to learn and develop or if self reliance is nothing more than doing all possible to carry one's own burdens, then most jackrabbits have eyes.", "So long as summer is the time to learn and develop, 'we know that the claim that rain usually washes a lot of pollen out of the air - counts go down is false' is true.", "Provided that if self reliance is nothing more than doing all possible to carry one's own burdens, then most jackrabbits have eyes, we know that we know that the claim that rain usually washes a lot of pollen out of the air - counts go down is false."]
|
There is good reason to believe that either either some animals eat seaweed or average high temperature decreases during seasons or globalization is, in fact, a very old process, in some sense as old as human civilization itself. Whenever it is true that either some animals eat seaweed or average high temperature decreases during seasons, 'rain usually washes a lot of pollen out of the air - counts go down' is true. So long as globalization is, in fact, a very old process, in some sense as old as human civilization itself, 'narcotics kill sensitivity to pain and reduce unwanted feelings of anger, irritability, and anxiety' is true. It is a fact that either summer is the time to learn and develop or if self reliance is nothing more than doing all possible to carry one's own burdens, then most jackrabbits have eyes. So long as summer is the time to learn and develop, 'we know that the claim that rain usually washes a lot of pollen out of the air - counts go down is false' is true. Provided that if self reliance is nothing more than doing all possible to carry one's own burdens, then most jackrabbits have eyes, we know that we know that the claim that rain usually washes a lot of pollen out of the air - counts go down is false.
|
Many people rightly believe that narcotics kill sensitivity to pain and reduce unwanted feelings of anger, irritability, and anxiety.
|
Narcotics are excellent pain relievers and create a feeling of euphoria and a sense of well being.
|
Uncertain
|
Disjunctive Syllogism:
Either [1] or [0]. [SC1-1]
Not [1]. [SC2-1]
Therefore, [0].
[SC1-1]
Constructive Dilemma:
Either (Either [2] or [3].) or [4].
If (Either [2] or [3].), then [1].
If [4], then [0].
Therefore, Either [1] or [0]..
[SC2-1]
Disjunction Elimination:
Either [5] or (If [6], then [7].).
If [5], then (Not [1].).
If (If [6], then [7].), then (Not [1].).
Therefore, Not [1]..
|
{0: 'Narcotics kill sensitivity to pain and reduce unwanted feelings of anger, irritability, and anxiety.', 1: 'Rain usually washes a lot of pollen out of the air - counts go down.', 2: 'Some animals eat seaweed.', 3: 'Average high temperature decreases during seasons.', 4: 'Globalization is, in fact, a very old process, in some sense as old as human civilization itself.', 5: 'Summer is the time to learn and develop.', 6: "Self reliance is nothing more than doing all possible to carry one's own burdens.", 7: 'Most jackrabbits have eyes.'}
| 3 |
2,982 |
["Should it be the case that young animals learning to hunt have to take what they can get, it follows that the statement 'either agriculture is protected by tariffs or a mountain laurel is a bush' can be considered false.", "Whenever it is true that human beings possess a capability far beyond animals, 'either young animals learning to hunt have to take what they can get or if suffrage is based on the principle of one person, one vote, then modern novels have no connection between crime and retribution' is true.", 'It is the case that human beings possess a capability far beyond animals.', 'Assuming if suffrage is based on the principle of one person, one vote, then modern novels have no connection between crime and retribution, we know that either women are more likely than men to take sleeping pills, and their use increases with age or abnormal fibrinogen is produced, leading to clotting problems in some individuals.', "When either women are more likely than men to take sleeping pills, and their use increases with age or abnormal fibrinogen is produced, leading to clotting problems in some individuals is true, it follows that the statement 'either agriculture is protected by tariffs or a mountain laurel is a bush' can be considered false."]
|
Should it be the case that young animals learning to hunt have to take what they can get, it follows that the statement 'either agriculture is protected by tariffs or a mountain laurel is a bush' can be considered false. Whenever it is true that human beings possess a capability far beyond animals, 'either young animals learning to hunt have to take what they can get or if suffrage is based on the principle of one person, one vote, then modern novels have no connection between crime and retribution' is true. It is the case that human beings possess a capability far beyond animals. Assuming if suffrage is based on the principle of one person, one vote, then modern novels have no connection between crime and retribution, we know that either women are more likely than men to take sleeping pills, and their use increases with age or abnormal fibrinogen is produced, leading to clotting problems in some individuals. When either women are more likely than men to take sleeping pills, and their use increases with age or abnormal fibrinogen is produced, leading to clotting problems in some individuals is true, it follows that the statement 'either agriculture is protected by tariffs or a mountain laurel is a bush' can be considered false.
|
The statement 'either agriculture is protected by tariffs or a mountain laurel is a bush' can be considered false.
|
We know that at least one of two things is true: agriculture is protected by tariffs, or a mountain laurel is a bush.
|
FALSE
|
Disjunction Elimination:
Either [2] or (If [3], then [4].). [SC1-1]
If [2], then (Not (Either [0] or [1].).).
If (If [3], then [4].), then (Not (Either [0] or [1].).). [SC3-1]
Therefore, Not (Either [0] or [1].)..
[SC1-1]
Modus Ponens:
If [5], then (Either [2] or (If [3], then [4].).).
[5]
Therefore, Either [2] or (If [3], then [4].)..
[SC3-1]
Hypothetical Syllogism:
If (If [3], then [4].), then (Either [6] or [7].).
If (Either [6] or [7].), then (Not (Either [0] or [1].).).
Therefore, If (If [3], then [4].), then (Not (Either [0] or [1].).)..
|
{0: 'Agriculture is protected by tariffs.', 1: 'A mountain laurel is a bush.', 2: 'Young animals learning to hunt have to take what they can get.', 3: 'Suffrage is based on the principle of one person, one vote.', 4: 'Modern novels have no connection between crime and retribution.', 5: 'Human beings possess a capability far beyond animals.', 6: 'Women are more likely than men to take sleeping pills, and their use increases with age.', 7: 'Abnormal fibrinogen is produced, leading to clotting problems in some individuals.'}
| 3 |
2,909 |
['At least one of two things is true: dramatic play helps children experiment with and understand social roles, or if fishing is a recreational sport or hobby that can be enjoyed by many people, for many years to come, then mifepristone is approved for use in Sweden.', 'One may reasonably assume that if dramatic play helps children experiment with and understand social roles, then either eukaryotic chromosomes occur in the cell in greater numbers than prokaryotic chromosomes or either most agates occur in cavities of eruptive rocks or ancient lavas or all scorpions are nocturnal and generally venture from their shelters at night to forage for prey.', 'Given that if fishing is a recreational sport or hobby that can be enjoyed by many people, for many years to come, then mifepristone is approved for use in Sweden, it can be inferred that either eukaryotic chromosomes occur in the cell in greater numbers than prokaryotic chromosomes or either most agates occur in cavities of eruptive rocks or ancient lavas or all scorpions are nocturnal and generally venture from their shelters at night to forage for prey.', "Whenever it is true that eukaryotic chromosomes occur in the cell in greater numbers than prokaryotic chromosomes, 'men run a greater overall risk for developing high blood pressure than women' is true.", 'The claim that men run a greater overall risk for developing high blood pressure than women does not reflect reality.']
|
At least one of two things is true: dramatic play helps children experiment with and understand social roles, or if fishing is a recreational sport or hobby that can be enjoyed by many people, for many years to come, then mifepristone is approved for use in Sweden. One may reasonably assume that if dramatic play helps children experiment with and understand social roles, then either eukaryotic chromosomes occur in the cell in greater numbers than prokaryotic chromosomes or either most agates occur in cavities of eruptive rocks or ancient lavas or all scorpions are nocturnal and generally venture from their shelters at night to forage for prey. Given that if fishing is a recreational sport or hobby that can be enjoyed by many people, for many years to come, then mifepristone is approved for use in Sweden, it can be inferred that either eukaryotic chromosomes occur in the cell in greater numbers than prokaryotic chromosomes or either most agates occur in cavities of eruptive rocks or ancient lavas or all scorpions are nocturnal and generally venture from their shelters at night to forage for prey. Whenever it is true that eukaryotic chromosomes occur in the cell in greater numbers than prokaryotic chromosomes, 'men run a greater overall risk for developing high blood pressure than women' is true. The claim that men run a greater overall risk for developing high blood pressure than women does not reflect reality.
|
At least one of two things is true: most agates occur in cavities of eruptive rocks or ancient lavas, or all scorpions are nocturnal and generally venture from their shelters at night to forage for prey.
|
The claim that either most agates occur in cavities of eruptive rocks or ancient lavas or all scorpions are nocturnal and generally venture from their shelters at night to forage for prey does not correspond with reality.
|
FALSE
|
Disjunctive Syllogism:
Either [2] or (Either [0] or [1].). [SC1-1]
Not [2]. [SC2-1]
Therefore, Either [0] or [1]..
[SC1-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then (Either [2] or (Either [0] or [1].).).
If (If [4], then [5].), then (Either [2] or (Either [0] or [1].).).
Therefore, Either [2] or (Either [0] or [1].)..
[SC2-1]
Modus Tonens:
If [2], then [6].
Not [6].
Therefore, Not [2]..
|
{0: 'Most agates occur in cavities of eruptive rocks or ancient lavas.', 1: 'All scorpions are nocturnal and generally venture from their shelters at night to forage for prey.', 2: 'Eukaryotic chromosomes occur in the cell in greater numbers than prokaryotic chromosomes.', 3: 'Dramatic play helps children experiment with and understand social roles.', 4: 'Fishing is a recreational sport or hobby that can be enjoyed by many people, for many years to come.', 5: 'Mifepristone is approved for use in Sweden.', 6: 'Men run a greater overall risk for developing high blood pressure than women.'}
| 3 |
2,693 |
['It is rational to believe that either actions take effects or most trees have wood.', 'One may reasonably assume that if actions take effects, then we know that the claim that some infection is caused by mold is false.', 'Either combative fighting is a Class D felony or if most trees have wood, then we know that the claim that some infection is caused by mold is false.', 'When combative fighting is a Class D felony is true, it follows that life processes at molecular level.', "So long as combative fighting is a Class D felony, 'the statement 'life processes at molecular level' can be considered false' is true."]
|
It is rational to believe that either actions take effects or most trees have wood. One may reasonably assume that if actions take effects, then we know that the claim that some infection is caused by mold is false. Either combative fighting is a Class D felony or if most trees have wood, then we know that the claim that some infection is caused by mold is false. When combative fighting is a Class D felony is true, it follows that life processes at molecular level. So long as combative fighting is a Class D felony, 'the statement 'life processes at molecular level' can be considered false' is true.
|
We know that the claim that some infection is caused by mold is false.
|
We know that the claim that some infection is caused by mold is false.
|
TRUE
|
Disjunction Elimination:
Either [1] or [2].
If [1], then (Not [0].).
If [2], then (Not [0].). [SC3-1]
Therefore, Not [0]..
[SC3-1]
Disjunctive Syllogism:
Either [3] or (If [2], then (Not [0].).).
Not [3]. [SC2-2]
Therefore, If [2], then (Not [0].)..
[SC2-2]
Reductio Ad Absurdum:
If [3], then [4].
If [3], then (Not [4].).
Therefore, Not [3]..
|
{0: 'Some infection is caused by mold.', 1: 'Actions take effects.', 2: 'Most trees have wood.', 3: 'Combative fighting is a Class D felony.', 4: 'Life processes at molecular level.'}
| 3 |
2,236 |
['Should it be the case that people drink for a number of reasons, many of which are associated with depression, it follows that moles are common.', 'Given that it is not true that either alligators eat meat or people drink for a number of reasons, many of which are associated with depression, it can be inferred that sparrows are passerines.', "The statement 'sparrows are passerines' can be considered false.", "So long as unattended children increase risk of fire play, 'if alligators eat meat, then moles are common' is true.", 'The claim that unattended children increase risk of fire play holds true.']
|
Should it be the case that people drink for a number of reasons, many of which are associated with depression, it follows that moles are common. Given that it is not true that either alligators eat meat or people drink for a number of reasons, many of which are associated with depression, it can be inferred that sparrows are passerines. The statement 'sparrows are passerines' can be considered false. So long as unattended children increase risk of fire play, 'if alligators eat meat, then moles are common' is true. The claim that unattended children increase risk of fire play holds true.
|
It is fair to say that moles are common.
|
Those that suggest moles are common are wrong.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then [0]. [SC2-1]
If [2], then [0].
Therefore, [0].
[SC1-1]
Modus Tonens:
If (Not (Either [1] or [2].).), then [3].
Not [3].
Therefore, Either [1] or [2]..
[SC2-1]
Modus Ponens:
If [4], then (If [1], then [0].).
[4]
Therefore, If [1], then [0]..
|
{0: 'Moles are common.', 1: 'Alligators eat meat.', 2: 'People drink for a number of reasons, many of which are associated with depression.', 3: 'Sparrows are passerines.', 4: 'Unattended children increase risk of fire play.'}
| 3 |
2,501 |
['On the condition that addiction is a disease of the body, mind and spirit, it is definitely the case that either damp wood causes creosote to build up, which can result in a chimney fire or canned vegetables are located in pantries.', 'Should it be the case that either damp wood causes creosote to build up, which can result in a chimney fire or canned vegetables are located in pantries, it follows that the statement that states gingers have green leaves is false.', 'When we know that the claim that if either damp wood causes creosote to build up, which can result in a chimney fire or canned vegetables are located in pantries, then gingers have green leaves is false is true, it follows that smokes are of various kinds, each one significant of a particular object.', "The statement that 'smokes are of various kinds, each one significant of a particular object' is incorrect."]
|
On the condition that addiction is a disease of the body, mind and spirit, it is definitely the case that either damp wood causes creosote to build up, which can result in a chimney fire or canned vegetables are located in pantries. Should it be the case that either damp wood causes creosote to build up, which can result in a chimney fire or canned vegetables are located in pantries, it follows that the statement that states gingers have green leaves is false. When we know that the claim that if either damp wood causes creosote to build up, which can result in a chimney fire or canned vegetables are located in pantries, then gingers have green leaves is false is true, it follows that smokes are of various kinds, each one significant of a particular object. The statement that 'smokes are of various kinds, each one significant of a particular object' is incorrect.
|
Those that suggest addiction is a disease of the body, mind and spirit are wrong.
|
We can assume that addiction is a disease of the body, mind and spirit.
|
FALSE
|
Modus Tonens:
If [0], then (Either [1] or [2].).
Not (Either [1] or [2].). [SC2-1]
Therefore, Not [0]..
[SC2-1]
Reductio Ad Absurdum:
If (Either [1] or [2].), then [3]. [SC1-2]
If (Either [1] or [2].), then (Not [3].).
Therefore, Not (Either [1] or [2].)..
[SC1-2]
Modus Tonens:
If (Not (If (Either [1] or [2].), then [3].).), then [4].
Not [4].
Therefore, If (Either [1] or [2].), then [3]..
|
{0: 'Addiction is a disease of the body, mind and spirit.', 1: 'Damp wood causes creosote to build up, which can result in a chimney fire.', 2: 'Canned vegetables are located in pantries.', 3: 'Gingers have green leaves.', 4: 'Smokes are of various kinds, each one significant of a particular object.'}
| 3 |
2,497 |
["Whenever it is true that most evergreens prefer full sun but can often get by with a little shade, 'either cardiac arrhythmias are often present or a smuggler is a criminal' is true.", 'Either one or both of these statements are true: cottontail rabbits live up to years, or either most evergreens prefer full sun but can often get by with a little shade or fusion only takes place at very high temperatures and pressures.', 'The statement that states cottontail rabbits live up to years is false.', 'On the condition that fusion only takes place at very high temperatures and pressures, it is definitely the case that cognitive development is a slow gradual process of change.', 'If cognitive development is a slow gradual process of change, then either cardiac arrhythmias are often present or a smuggler is a criminal.']
|
Whenever it is true that most evergreens prefer full sun but can often get by with a little shade, 'either cardiac arrhythmias are often present or a smuggler is a criminal' is true. Either one or both of these statements are true: cottontail rabbits live up to years, or either most evergreens prefer full sun but can often get by with a little shade or fusion only takes place at very high temperatures and pressures. The statement that states cottontail rabbits live up to years is false. On the condition that fusion only takes place at very high temperatures and pressures, it is definitely the case that cognitive development is a slow gradual process of change. If cognitive development is a slow gradual process of change, then either cardiac arrhythmias are often present or a smuggler is a criminal.
|
Either one or both of these statements are true: cardiac arrhythmias are often present, or a smuggler is a criminal.
|
Either one or both of these statements are true: cardiac arrhythmia is a term that denotes a disturbance of the heart rhythm, or smugglers are criminals.
|
Uncertain
|
Disjunction Elimination:
Either [2] or [3]. [SC1-1]
If [2], then (Either [0] or [1].).
If [3], then (Either [0] or [1].). [SC3-1]
Therefore, Either [0] or [1]..
[SC1-1]
Disjunctive Syllogism:
Either [5] or (Either [2] or [3].).
Not [5].
Therefore, Either [2] or [3]..
[SC3-1]
Hypothetical Syllogism:
If [3], then [4].
If [4], then (Either [0] or [1].).
Therefore, If [3], then (Either [0] or [1].)..
|
{0: 'Cardiac arrhythmias are often present.', 1: 'A smuggler is a criminal.', 2: 'Most evergreens prefer full sun but can often get by with a little shade.', 3: 'Fusion only takes place at very high temperatures and pressures.', 4: 'Cognitive development is a slow gradual process of change.', 5: 'Cottontail rabbits live up to years.'}
| 3 |
2,874 |
['We know that at least one of two things is true: tourism is the world s largest industry, or chickens are egg-laying birds.', "It is rational to believe that either if contrition is the opposite of carnal indifference to one's sins, then belief systems can be sacred or secular or if tourism is the world s largest industry, then either most western countries have laws that protect homosexuals from violence and discrimination or statistics provide quantitative information about people, processes, events, and ideas.", "We know that the claim that if contrition is the opposite of carnal indifference to one's sins, then belief systems can be sacred or secular is false.", 'Either modern insects are likely remains found in amber or organists are musicians.', 'One may reasonably assume that if modern insects are likely remains found in amber, then if chickens are egg-laying birds, then either most western countries have laws that protect homosexuals from violence and discrimination or statistics provide quantitative information about people, processes, events, and ideas.', 'One may reasonably assume that if organists are musicians, then if chickens are egg-laying birds, then either most western countries have laws that protect homosexuals from violence and discrimination or statistics provide quantitative information about people, processes, events, and ideas.']
|
We know that at least one of two things is true: tourism is the world s largest industry, or chickens are egg-laying birds. It is rational to believe that either if contrition is the opposite of carnal indifference to one's sins, then belief systems can be sacred or secular or if tourism is the world s largest industry, then either most western countries have laws that protect homosexuals from violence and discrimination or statistics provide quantitative information about people, processes, events, and ideas. We know that the claim that if contrition is the opposite of carnal indifference to one's sins, then belief systems can be sacred or secular is false. Either modern insects are likely remains found in amber or organists are musicians. One may reasonably assume that if modern insects are likely remains found in amber, then if chickens are egg-laying birds, then either most western countries have laws that protect homosexuals from violence and discrimination or statistics provide quantitative information about people, processes, events, and ideas. One may reasonably assume that if organists are musicians, then if chickens are egg-laying birds, then either most western countries have laws that protect homosexuals from violence and discrimination or statistics provide quantitative information about people, processes, events, and ideas.
|
Either most western countries have laws that protect homosexuals from violence and discrimination or statistics provide quantitative information about people, processes, events, and ideas.
|
It is rational to believe that either most Western countries use alphabets containing far fewer characters or statistics Provides statistics and information on education in the U.S. and elsewhere.
|
Uncertain
|
Disjunction Elimination:
Either [2] or [3].
If [2], then (Either [0] or [1].). [SC2-1]
If [3], then (Either [0] or [1].). [SC3-1]
Therefore, Either [0] or [1]..
[SC2-1]
Disjunctive Syllogism:
Either (If [6], then [7].) or (If [2], then (Either [0] or [1].).).
Not (If [6], then [7].).
Therefore, If [2], then (Either [0] or [1].)..
[SC3-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [3], then (Either [0] or [1].).).
If [5], then (If [3], then (Either [0] or [1].).).
Therefore, If [3], then (Either [0] or [1].)..
|
{0: 'Most western countries have laws that protect homosexuals from violence and discrimination .', 1: 'Statistics provide quantitative information about people, processes, events, and ideas.', 2: 'Tourism is the world s largest industry.', 3: 'Chickens are egg-laying birds.', 4: 'Modern insects are likely remains found in amber.', 5: 'Organists are musicians.', 6: "Contrition is the opposite of carnal indifference to one's sins.", 7: 'Belief systems can be sacred or secular.'}
| 3 |
2,452 |
['There is good reason to believe that either if back isa body part, then centrosomes consist of a pair of centrioles and are found near the nuclear envelope in animal cells or most small mammals have impact.', 'Given that most small mammals have impact, it can be inferred that some dinoflagellates have roles.', 'One may reasonably assume that if if back isa body part, then centrosomes consist of a pair of centrioles and are found near the nuclear envelope in animal cells, then products are produced by muscle breakdowns.', 'Either one or both of these statements are true: most dolphins interact with humans, or if products are produced by muscle breakdowns, then some dinoflagellates have roles.', 'It is not the case that most dolphins interact with humans.']
|
There is good reason to believe that either if back isa body part, then centrosomes consist of a pair of centrioles and are found near the nuclear envelope in animal cells or most small mammals have impact. Given that most small mammals have impact, it can be inferred that some dinoflagellates have roles. One may reasonably assume that if if back isa body part, then centrosomes consist of a pair of centrioles and are found near the nuclear envelope in animal cells, then products are produced by muscle breakdowns. Either one or both of these statements are true: most dolphins interact with humans, or if products are produced by muscle breakdowns, then some dinoflagellates have roles. It is not the case that most dolphins interact with humans.
|
The statement 'some dinoflagellates have roles' is true.
|
The statement 'some dinoflagellates have roles' is true.
|
TRUE
|
Disjunction Elimination:
Either (If [1], then [2].) or [3].
If (If [1], then [2].), then [0]. [SC2-1]
If [3], then [0].
Therefore, [0].
[SC2-1]
Hypothetical Syllogism:
If (If [1], then [2].), then [4].
If [4], then [0]. [SC2-2]
Therefore, If (If [1], then [2].), then [0]..
[SC2-2]
Disjunctive Syllogism:
Either [5] or (If [4], then [0].).
Not [5].
Therefore, If [4], then [0]..
|
{0: 'Some dinoflagellates have roles.', 1: 'Back isa body part.', 2: 'Centrosomes consist of a pair of centrioles and are found near the nuclear envelope in animal cells.', 3: 'Most small mammals have impact.', 4: 'Products are produced by muscle breakdowns.', 5: 'Most dolphins interact with humans.'}
| 3 |
2,494 |
['Should it be the case that the statement, either isolated islands are famous for their endemic plants and animals or most damsels are aggressive, does not hold, it follows that biodiversity increases stability.', 'Some people mistakenly believe that biodiversity increases stability.', "Should it be the case that predators have alternative strategies, it follows that the statement that 'isolated islands are famous for their endemic plants and animals' is incorrect.", 'Those that suggest predators have alternative strategies are right.']
|
Should it be the case that the statement, either isolated islands are famous for their endemic plants and animals or most damsels are aggressive, does not hold, it follows that biodiversity increases stability. Some people mistakenly believe that biodiversity increases stability. Should it be the case that predators have alternative strategies, it follows that the statement that 'isolated islands are famous for their endemic plants and animals' is incorrect. Those that suggest predators have alternative strategies are right.
|
Many people rightly believe that most damsels are aggressive.
|
Many people rightly believe that most damsels are aggressive.
|
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 [2].
Not [2].
Therefore, Either [1] or [0]..
[SC2-1]
Modus Ponens:
If [3], then (Not [1].).
[3]
Therefore, Not [1]..
|
{0: 'Most damsels are aggressive.', 1: 'Isolated islands are famous for their endemic plants and animals.', 2: 'Biodiversity increases stability.', 3: 'Predators have alternative strategies.'}
| 3 |
2,923 |
['When rabbits are very emotional animals and cry when they lose a mate is true, it follows that mosquitoes are the source of the virus, infecting birds and people.', 'Either all digital systems are clocked, meaning clock pulses cause everything to happen or either rabbits are very emotional animals and cry when they lose a mate or sediment is the stuff that is transported by wind, water or ice to a site of deposition.', 'The statement that states all digital systems are clocked, meaning clock pulses cause everything to happen is false.', 'At least one of two things is true: some dogs work with teachers, or nilgai isa antelope.', 'Assuming some dogs work with teachers, we know that if sediment is the stuff that is transported by wind, water or ice to a site of deposition, then mosquitoes are the source of the virus, infecting birds and people.', 'If nilgai isa antelope, then if sediment is the stuff that is transported by wind, water or ice to a site of deposition, then mosquitoes are the source of the virus, infecting birds and people.']
|
When rabbits are very emotional animals and cry when they lose a mate is true, it follows that mosquitoes are the source of the virus, infecting birds and people. Either all digital systems are clocked, meaning clock pulses cause everything to happen or either rabbits are very emotional animals and cry when they lose a mate or sediment is the stuff that is transported by wind, water or ice to a site of deposition. The statement that states all digital systems are clocked, meaning clock pulses cause everything to happen is false. At least one of two things is true: some dogs work with teachers, or nilgai isa antelope. Assuming some dogs work with teachers, we know that if sediment is the stuff that is transported by wind, water or ice to a site of deposition, then mosquitoes are the source of the virus, infecting birds and people. If nilgai isa antelope, then if sediment is the stuff that is transported by wind, water or ice to a site of deposition, then mosquitoes are the source of the virus, infecting birds and people.
|
It is the case that mosquitoes are the source of the virus, infecting birds and people.
|
It is the case that mosquitoes are the source of the virus, infecting birds and people.
|
TRUE
|
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 [3] or (Either [1] or [2].).
Not [3].
Therefore, Either [1] or [2]..
[SC3-1]
Disjunction Elimination:
Either [4] or [5].
If [4], then (If [2], then [0].).
If [5], then (If [2], then [0].).
Therefore, If [2], then [0]..
|
{0: 'Mosquitoes are the source of the virus, infecting birds and people.', 1: 'Rabbits are very emotional animals and cry when they lose a mate.', 2: 'Sediment is the stuff that is transported by wind, water or ice to a site of deposition.', 3: 'All digital systems are clocked, meaning clock pulses cause everything to happen.', 4: 'Some dogs work with teachers.', 5: 'Nilgai isa antelope.'}
| 3 |
2,279 |
["So long as polymorphism uses date and time of infection, 'sound waves travel slower in bubbly water than in either water or air' is true.", 'Given that sound waves travel slower in bubbly water than in either water or air, it can be inferred that lilies are sweet-smelling, delicate flowers symbolizing purity.', 'It is a fact that either monoclonal antibodies are mouse antibodies which are piggy-backed by radioactivity or young plants undergo systemic infection resulting in stunting and leaf streaking.', "Provided that monoclonal antibodies are mouse antibodies which are piggy-backed by radioactivity, we know that if polymorphism uses date and time of infection, then the statement that 'lilies are sweet-smelling, delicate flowers symbolizing purity' is incorrect.", "Provided that young plants undergo systemic infection resulting in stunting and leaf streaking, we know that if polymorphism uses date and time of infection, then the statement that 'lilies are sweet-smelling, delicate flowers symbolizing purity' is incorrect."]
|
So long as polymorphism uses date and time of infection, 'sound waves travel slower in bubbly water than in either water or air' is true. Given that sound waves travel slower in bubbly water than in either water or air, it can be inferred that lilies are sweet-smelling, delicate flowers symbolizing purity. It is a fact that either monoclonal antibodies are mouse antibodies which are piggy-backed by radioactivity or young plants undergo systemic infection resulting in stunting and leaf streaking. Provided that monoclonal antibodies are mouse antibodies which are piggy-backed by radioactivity, we know that if polymorphism uses date and time of infection, then the statement that 'lilies are sweet-smelling, delicate flowers symbolizing purity' is incorrect. Provided that young plants undergo systemic infection resulting in stunting and leaf streaking, we know that if polymorphism uses date and time of infection, then the statement that 'lilies are sweet-smelling, delicate flowers symbolizing purity' is incorrect.
|
It is not true that polymorphism uses date and time of infection.
|
It is not true that polymorphism uses date and time of infection.
|
TRUE
|
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 [4].
If [4], then [1].
Therefore, If [0], then [1]..
[SC2-1]
Disjunction Elimination:
Either [2] or [3].
If [2], then (If [0], then (Not [1].).).
If [3], then (If [0], then (Not [1].).).
Therefore, If [0], then (Not [1].)..
|
{0: 'Polymorphism uses date and time of infection.', 1: 'Lilies are sweet-smelling, delicate flowers symbolizing purity.', 2: 'Monoclonal antibodies are mouse antibodies which are piggy-backed by radioactivity.', 3: 'Young plants undergo systemic infection resulting in stunting and leaf streaking.', 4: 'Sound waves travel slower in bubbly water than in either water or air.'}
| 3 |
2,638 |
['Given that universities are institutions, it can be inferred that it is not the case that owners know death.', 'If arrogance is ignorance, then it is not the case that owners know death.', 'It is a fact that either larvae transform into pupas or if elephants are amazingly strong and can hold or pull a lot of mass altogether, then anthrax spores are apparently one of the top choices of weapons for biological warfare.', 'Once we know if elephants are amazingly strong and can hold or pull a lot of mass altogether, then anthrax spores are apparently one of the top choices of weapons for biological warfare, we also know that either universities are institutions or arrogance is ignorance.', 'One may reasonably assume that if medications used for stabilizing mood include lithium, depakene and tegretol, then if larvae transform into pupas, then either universities are institutions or arrogance is ignorance.', 'It is fair to say that medications used for stabilizing mood include lithium, depakene and tegretol.']
|
Given that universities are institutions, it can be inferred that it is not the case that owners know death. If arrogance is ignorance, then it is not the case that owners know death. It is a fact that either larvae transform into pupas or if elephants are amazingly strong and can hold or pull a lot of mass altogether, then anthrax spores are apparently one of the top choices of weapons for biological warfare. Once we know if elephants are amazingly strong and can hold or pull a lot of mass altogether, then anthrax spores are apparently one of the top choices of weapons for biological warfare, we also know that either universities are institutions or arrogance is ignorance. One may reasonably assume that if medications used for stabilizing mood include lithium, depakene and tegretol, then if larvae transform into pupas, then either universities are institutions or arrogance is ignorance. It is fair to say that medications used for stabilizing mood include lithium, depakene and tegretol.
|
It is not the case that owners know death.
|
It is fair to say that owners know death.
|
FALSE
|
Disjunction Elimination:
Either [1] or [2]. [SC1-1]
If [1], then (Not [0].).
If [2], then (Not [0].).
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either [3] or (If [4], then [5].).
If [3], then (Either [1] or [2].). [SC2-2]
If (If [4], then [5].), then (Either [1] or [2].).
Therefore, Either [1] or [2]..
[SC2-2]
Modus Ponens:
If [6], then (If [3], then (Either [1] or [2].).).
[6]
Therefore, If [3], then (Either [1] or [2].)..
|
{0: 'Owners know death.', 1: 'Universities are institutions.', 2: 'Arrogance is ignorance.', 3: 'Larvae transform into pupas.', 4: 'Elephants are amazingly strong and can hold or pull a lot of mass altogether.', 5: 'Anthrax spores are apparently one of the top choices of weapons for biological warfare.', 6: 'Medications used for stabilizing mood include lithium, depakene and tegretol.'}
| 3 |
2,485 |
['It is a fact that either volcanoes are a source of significant chemical energy, both as heat, and elements or predators require water.', "If the notion that 'if volcanoes are a source of significant chemical energy, both as heat, and elements, then if corporations are the kinds of entities that like to keep their communications private, then copyrights protect the thoughts and ideas of authors, composers and artists' is untrue, then some talons are part of orioles.", "When the notion that 'if volcanoes are a source of significant chemical energy, both as heat, and elements, then if corporations are the kinds of entities that like to keep their communications private, then copyrights protect the thoughts and ideas of authors, composers and artists' is untrue is true, it follows that the notion that 'some talons are part of orioles' is untrue.", 'When predators require water is true, it follows that environmental conditions have more influence on watering than any other factor.', "So long as environmental conditions have more influence on watering than any other factor, 'if corporations are the kinds of entities that like to keep their communications private, then copyrights protect the thoughts and ideas of authors, composers and artists' is true."]
|
It is a fact that either volcanoes are a source of significant chemical energy, both as heat, and elements or predators require water. If the notion that 'if volcanoes are a source of significant chemical energy, both as heat, and elements, then if corporations are the kinds of entities that like to keep their communications private, then copyrights protect the thoughts and ideas of authors, composers and artists' is untrue, then some talons are part of orioles. When the notion that 'if volcanoes are a source of significant chemical energy, both as heat, and elements, then if corporations are the kinds of entities that like to keep their communications private, then copyrights protect the thoughts and ideas of authors, composers and artists' is untrue is true, it follows that the notion that 'some talons are part of orioles' is untrue. When predators require water is true, it follows that environmental conditions have more influence on watering than any other factor. So long as environmental conditions have more influence on watering than any other factor, 'if corporations are the kinds of entities that like to keep their communications private, then copyrights protect the thoughts and ideas of authors, composers and artists' is true.
|
Once we know corporations are the kinds of entities that like to keep their communications private, we also know that copyrights protect the thoughts and ideas of authors, composers and artists.
|
Whenever it is true that corporations are the kinds of entities that like to keep their communications private, 'copyrights protect the expression of ideas' is true.
|
Uncertain
|
Disjunction Elimination:
Either [2] or [3].
If [2], then (If [0], then [1].). [SC2-1]
If [3], then (If [0], then [1].). [SC3-1]
Therefore, If [0], then [1]..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If [2], then (If [0], then [1].).).), then [5].
If (Not (If [2], then (If [0], then [1].).).), then (Not [5].).
Therefore, If [2], then (If [0], then [1].)..
[SC3-1]
Hypothetical Syllogism:
If [3], then [4].
If [4], then (If [0], then [1].).
Therefore, If [3], then (If [0], then [1].)..
|
{0: 'Corporations are the kinds of entities that like to keep their communications private.', 1: 'Copyrights protect the thoughts and ideas of authors, composers and artists.', 2: 'Volcanoes are a source of significant chemical energy, both as heat, and elements.', 3: 'Predators require water.', 4: 'Environmental conditions have more influence on watering than any other factor.', 5: 'Some talons are part of orioles.'}
| 3 |
2,568 |
['It is a common misconception that either friction causes a skateboard to stop rolling or affected people have white hair, colorless skin, red irises, and vision defects.', 'Once we know melody is music, we also know that either either friction causes a skateboard to stop rolling or affected people have white hair, colorless skin, red irises, and vision defects or the claim that most diets prevent cancer has no merit.', 'When it is not the case that melody is music is true, it follows that price includes cost of material, cost of labour and profit or loss on sale.', 'The claim that price includes cost of material, cost of labour and profit or loss on sale has no merit.']
|
It is a common misconception that either friction causes a skateboard to stop rolling or affected people have white hair, colorless skin, red irises, and vision defects. Once we know melody is music, we also know that either either friction causes a skateboard to stop rolling or affected people have white hair, colorless skin, red irises, and vision defects or the claim that most diets prevent cancer has no merit. When it is not the case that melody is music is true, it follows that price includes cost of material, cost of labour and profit or loss on sale. The claim that price includes cost of material, cost of labour and profit or loss on sale has no merit.
|
The claim that most diets prevent cancer has no merit.
|
The claim that diets limit intake does not reflect reality.
|
Uncertain
|
Disjunctive Syllogism:
Either (Either [1] or [2].) or (Not [0].). [SC1-1]
Not (Either [1] or [2].).
Therefore, Not [0]..
[SC1-1]
Modus Ponens:
If [3], then (Either (Either [1] or [2].) or (Not [0].).).
[3] [SC2-2]
Therefore, Either (Either [1] or [2].) or (Not [0].)..
[SC2-2]
Modus Tonens:
If (Not [3].), then [4].
Not [4].
Therefore, [3].
|
{0: 'Most diets prevent cancer.', 1: 'Friction causes a skateboard to stop rolling.', 2: 'Affected people have white hair, colorless skin, red irises, and vision defects.', 3: 'Melody is music.', 4: 'Price includes cost of material, cost of labour and profit or loss on sale.'}
| 3 |
2,108 |
['Those that suggest drug addiction is habituation are wrong.', 'Provided that either most sunlight reflects intensity or variety is the degree of genetic variation within a species, we know that if some bacteria infect insects, then drug addiction is habituation.', 'On the condition that clouds reduce visibility, it is definitely the case that if some bacteria infect insects, then drug addiction is habituation.', 'One may reasonably assume that if if light is created by lamps, then cuckoos are common in Bhutan and the Asian highlands but are difficult to approach, then either either most sunlight reflects intensity or variety is the degree of genetic variation within a species or clouds reduce visibility.', 'On the condition that light is created by lamps, it is definitely the case that cuckoos are common in Bhutan and the Asian highlands but are difficult to approach.']
|
Those that suggest drug addiction is habituation are wrong. Provided that either most sunlight reflects intensity or variety is the degree of genetic variation within a species, we know that if some bacteria infect insects, then drug addiction is habituation. On the condition that clouds reduce visibility, it is definitely the case that if some bacteria infect insects, then drug addiction is habituation. One may reasonably assume that if if light is created by lamps, then cuckoos are common in Bhutan and the Asian highlands but are difficult to approach, then either either most sunlight reflects intensity or variety is the degree of genetic variation within a species or clouds reduce visibility. On the condition that light is created by lamps, it is definitely the case that cuckoos are common in Bhutan and the Asian highlands but are difficult to approach.
|
It is not the case that some bacteria infect insects.
|
It is not the case that some bacteria infect insects.
|
TRUE
|
Modus Tonens:
If [0], then [1]. [SC1-1]
Not [1].
Therefore, Not [0]..
[SC1-1]
Disjunction Elimination:
Either (Either [2] or [3].) or [4]. [SC1-2]
If (Either [2] or [3].), then (If [0], then [1].).
If [4], then (If [0], then [1].).
Therefore, If [0], then [1]..
[SC1-2]
Modus Ponens:
If (If [5], then [6].), then (Either (Either [2] or [3].) or [4].).
If [5], then [6].
Therefore, Either (Either [2] or [3].) or [4]..
|
{0: 'Some bacteria infect insects.', 1: 'Drug addiction is habituation.', 2: 'Most sunlight reflects intensity.', 3: 'Variety is the degree of genetic variation within a species.', 4: 'Clouds reduce visibility.', 5: 'Light is created by lamps.', 6: 'Cuckoos are common in Bhutan and the Asian highlands but are difficult to approach.'}
| 3 |
2,367 |
["So long as if problems need care, then ischemia is a common cause of non-healing wounds, 'overweight people lack loving relationships and have relationships with food instead' is true.", 'One may reasonably assume that if the claim that either if problems need care, then ischemia is a common cause of non-healing wounds or drug use leads to an increase in health care costs has no merit, then stable isotopes can reveal directions, pathways and rates of waterflow in and out of reservoirs.', 'Once we know the claim that either if problems need care, then ischemia is a common cause of non-healing wounds or drug use leads to an increase in health care costs has no merit, we also know that those that suggest stable isotopes can reveal directions, pathways and rates of waterflow in and out of reservoirs are wrong.', "At least one of two things is true: tea rituals are a way to express one's appreciation of the natural world, or if drug use leads to an increase in health care costs, then overweight people lack loving relationships and have relationships with food instead.", "It is not true that tea rituals are a way to express one's appreciation of the natural world."]
|
So long as if problems need care, then ischemia is a common cause of non-healing wounds, 'overweight people lack loving relationships and have relationships with food instead' is true. One may reasonably assume that if the claim that either if problems need care, then ischemia is a common cause of non-healing wounds or drug use leads to an increase in health care costs has no merit, then stable isotopes can reveal directions, pathways and rates of waterflow in and out of reservoirs. Once we know the claim that either if problems need care, then ischemia is a common cause of non-healing wounds or drug use leads to an increase in health care costs has no merit, we also know that those that suggest stable isotopes can reveal directions, pathways and rates of waterflow in and out of reservoirs are wrong. At least one of two things is true: tea rituals are a way to express one's appreciation of the natural world, or if drug use leads to an increase in health care costs, then overweight people lack loving relationships and have relationships with food instead. It is not true that tea rituals are a way to express one's appreciation of the natural world.
|
Many people rightly believe that overweight people lack loving relationships and have relationships with food instead.
|
Many people rightly believe that overweight people lack loving relationships and have relationships with food instead.
|
TRUE
|
Disjunction Elimination:
Either (If [1], then [2].) or [3]. [SC1-1]
If (If [1], then [2].), then [0].
If [3], then [0]. [SC3-1]
Therefore, [0].
[SC1-1]
Reductio Ad Absurdum:
If (Not (Either (If [1], then [2].) or [3].).), then [5].
If (Not (Either (If [1], then [2].) or [3].).), then (Not [5].).
Therefore, Either (If [1], then [2].) or [3]..
[SC3-1]
Disjunctive Syllogism:
Either [4] or (If [3], then [0].).
Not [4].
Therefore, If [3], then [0]..
|
{0: 'Overweight people lack loving relationships and have relationships with food instead.', 1: 'Problems need care.', 2: 'Ischemia is a common cause of non-healing wounds.', 3: 'Drug use leads to an increase in health care costs.', 4: "Tea rituals are a way to express one's appreciation of the natural world.", 5: 'Stable isotopes can reveal directions, pathways and rates of waterflow in and out of reservoirs.'}
| 3 |
2,644 |
["Once we know the notion that 'if it is a common misconception that if a perm is a wave, then some people show cats, then either breast cancers have the same clinical characteristics in elderly women as in younger women or polar bears adapt to environments' is untrue, we also know that horse hairs are coarse hairs, of course.", 'The statement that states horse hairs are coarse hairs, of course is false.', "So long as the claim that if it is a common misconception that if a perm is a wave, then some people show cats, then the statement, either breast cancers have the same clinical characteristics in elderly women as in younger women or polar bears adapt to environments, does not hold does not reflect reality, 'pickups have (part) petrol gages' is true.", "Whenever it is true that the claim that if it is a common misconception that if a perm is a wave, then some people show cats, then the statement, either breast cancers have the same clinical characteristics in elderly women as in younger women or polar bears adapt to environments, does not hold does not reflect reality, 'the claim that pickups have (part) petrol gages does not correspond with reality' is true."]
|
Once we know the notion that 'if it is a common misconception that if a perm is a wave, then some people show cats, then either breast cancers have the same clinical characteristics in elderly women as in younger women or polar bears adapt to environments' is untrue, we also know that horse hairs are coarse hairs, of course. The statement that states horse hairs are coarse hairs, of course is false. So long as the claim that if it is a common misconception that if a perm is a wave, then some people show cats, then the statement, either breast cancers have the same clinical characteristics in elderly women as in younger women or polar bears adapt to environments, does not hold does not reflect reality, 'pickups have (part) petrol gages' is true. Whenever it is true that the claim that if it is a common misconception that if a perm is a wave, then some people show cats, then the statement, either breast cancers have the same clinical characteristics in elderly women as in younger women or polar bears adapt to environments, does not hold does not reflect reality, 'the claim that pickups have (part) petrol gages does not correspond with reality' is true.
|
On the condition that a perm is a wave, it is definitely the case that some people show cats.
|
On the condition that a perm is a wave, it is definitely the case that some people show cats.
|
TRUE
|
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].).). [SC2-1]
Therefore, If [0], then [1]..
[SC1-1]
Modus Tonens:
If (Not (If (Not (If [0], then [1].).), then (Either [2] or [3].).).), then [5].
Not [5].
Therefore, If (Not (If [0], then [1].).), then (Either [2] or [3].)..
[SC2-1]
Reductio Ad Absurdum:
If (Not (If (Not (If [0], then [1].).), then (Not (Either [2] or [3].).).).), then [4].
If (Not (If (Not (If [0], then [1].).), then (Not (Either [2] or [3].).).).), then (Not [4].).
Therefore, If (Not (If [0], then [1].).), then (Not (Either [2] or [3].).)..
|
{0: 'A perm is a wave.', 1: 'Some people show cats.', 2: 'Breast cancers have the same clinical characteristics in elderly women as in younger women.', 3: 'Polar bears adapt to environments.', 4: 'Pickups have (part) petrol gages.', 5: 'Horse hairs are coarse hairs, of course.'}
| 3 |
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