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Return to Logic 5e Student Resources
1F Practice: Deductive Arguments - Counterexamples and invalidity
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
All computers are electronic devices. All things that require an AC adapter are electronic devices. Therefore, all computers are things that require an AC adapter.
All C are E. All E are A. So, all C are A. Let C= cats, E = mammals, and A = dogs
correct
incorrect
All C are E. All A are E. So, all C are A. Let C= cats, E = mammals, and A = dogs
correct
incorrect
All E are C. All A are E. So, all C are A. Let C= cats, E = mammals, and A = felines
correct
incorrect
All C are E. All A are E. So, all C are A. Let C= cats, E = mammals, and A = felines
correct
incorrect
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not completed
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
No unicorns are immortal creatures. No centaurs are immortal creatures. It follows that no unicorns are centaurs.
No I are U. No C are I. So, no U are C. Let U = cats, I = snakes, and C = mammals
correct
incorrect
No U are I. No C are I. So, no U are C. Let U = umbrellas, I = icebergs, and C = cats
correct
incorrect
No U are I. No I are C. So, no U are C. Let U = cats, I = snakes, and C = mammals
correct
incorrect
No U are I. No C are I. So, no U are C. Let U = cats, I = snakes, and C = mammals
correct
incorrect
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not completed
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
Fidelix was born before 1990. Gil was born before 1991. Thus, Fidelix was born before Gil.
Fidelix was born in 1967. Gil was born in 1977. Thus, Fidelix was born before Gil.
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incorrect
Fidelix was born in 1972. Gil was born in 1988. Thus, Fidelix was born before Gil.
correct
incorrect
Fidelix was born in 1981. Gil was born in 1980. Thus, Fidelix was born before Gil.
correct
incorrect
Fidelix was born in 1989. Gil was born in 1990. Thus, Fidelix was born before Gil.
correct
incorrect
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not completed
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
All strawberries are fruit. All strawberries are plants. It follows that all fruit are plants.
All S are F. All S are P. So, all F are P. Let S = puppies, F = mammals, and P = dogs
correct
incorrect
All S are F. All S are P. So, all F are P. Let S = puppies, F = dogs, and P = mammals
correct
incorrect
All F are S. All S are P. So, all F are P. Let S = puppies, F = mammals, and P = dogs
correct
incorrect
All S are F. All P are F. So, all S are P. Let S = puppies, F = mammals, and P = dogs
correct
incorrect
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not completed
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
No animals are plants. Some protozoans are not plants. Therefore, some protozoans are animals.
No A are P. Some R are not P. So some R are A. Let A = cars, P = cats, R = mammals.
correct
incorrect
No A are P. Some R are P. So some R are A. Let A = dogs, P = cats, R = mammals.
correct
incorrect
No A are P. Some R are not P. So some R are A. Let A = dogs, P = cats, R = mammals.
correct
incorrect
No A are P. Some R are P. So some R are A. Let A = cars, P = cats, R = mammals.
correct
incorrect
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not completed
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
No baseballs are cubes. Some dice are cubes. So no dice are baseballs.
No B are C. Some D are C. So, no D are B. Let B = people, C = cats, and D = pets.
correct
incorrect
No B are C. No D are C. So, no D are B. Let B = beagles, C = collies, and D = dogs.
correct
incorrect
No B are C. Some D are not C. So, no D are B. Let B = people, C = cats, and D = pets.
correct
incorrect
No B are C. Some D are C. So, no D are B. Let B = beagles, C = collies, and D = dogs.
correct
incorrect
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not completed
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
Some rich people are philanthropists. All philanthropists are kind people. So, some kind people are not rich people.
Some A are B. All C are B. So, some C are not A. Let A = animals, B = cats, and C = dogs.
correct
incorrect
Some A are B. All B are C. So, some C are not A. Let A = animals, B = cats, and C = mammals.
correct
incorrect
Some B are A. All C are B. So, some C are not A. Let A = cats, B = mammals, and C = felines.
correct
incorrect
Some A are B. All B are C. So, some C are not A. Let A = cats, B = tigers, and C = felines.
correct
incorrect
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not completed
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
All criminals are lawbreakers. Some criminals are not people who get caught. So, some people who get caught are not lawbreakers.
All A are B. Some A are C. So, no C are not B. Let A = dogs, B = animals, and C = beagles.
correct
incorrect
All B are A. Some A are C. So, some C are not B. Let A = animals, B = living things, and C = famous things.
correct
incorrect
All A are B. Some A are not C. So, some C are not B. Let A = dogs, B = animals, and C = beagles.
correct
incorrect
All A are B. Some A are not C. So, some C are not B. Let A = animals, B = living things, and C = famous things.
correct
incorrect
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not completed
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
All testimony under oath is admissible evidence in court. All matters of public record are admissible evidence in court. Therefore, all testimony under oath are matters of public record.
All A are B. All B are C. So, all A are C. Let A = cats, B = animals, and C = dogs.
correct
incorrect
All A are B. All C are B. So, all A are C. Let A = animals, B = cats, and C = dogs.
correct
incorrect
All A are B. All C are B. So, all C are A. Let A = cats, B = animals, and C = dogs.
correct
incorrect
All A are B. All C are B. So, all A are C. Let A = cats, B = animals, and C = dogs.
correct
incorrect
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not completed
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
All vegans are people unafraid to stand on principle. All vegans are independent-minded people. It follows that all people unafraid to stand on principle are independent-minded people.
All A are B. All A are C. So, all B are C. Let A = puppies, B = mammals, and C = dogs.
correct
incorrect
All A are B. All A are C. So, all C are A. Let A = puppies, B = dogs, and C = mammals.
correct
incorrect
All A are B. All A are C. So, all B are C. Let A = dogs, B = mammals, and C = puppies.
correct
incorrect
All A are B. All C are A. So, all A are C. Let A = puppies, B = mammals, and C = dogs.
correct
incorrect
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not completed
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Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
All miracles are highly improbable events. Some highly improbable events are lottery wins. So, some lottery wins are miracles.
All A are B. Some B are C. So some A are C. Let A = aardvarks, B = bumblebees, and C = cats.
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incorrect
All A are B. Some C are B. So some C are A. Let A = aardvarks, B = bumblebees, and C = cats.
correct
incorrect
All A are B. Some B are C. So some C are A. Let A = cats, B = mammals, and C = rodents.
correct
incorrect
All A are B. Some B are C. So some C are A. Let A = cats, B = mammals, C = wild animals.
correct
incorrect
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not completed
.
Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
All professors are people with advanced degrees. All professors are educators. So, all educators are people with advanced degrees.
All A are B. All C are A. So all C are B. Let A = kittens, B = mammals, and C = cats.
correct
incorrect
All A are B. All A are C. So all C are B. Let A = kittens, B = mammals, and C = cats.
correct
incorrect
All A are B. All A are C. So all B are C. Let A = girls, B = females, and C = conscious beings.
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incorrect
All A are B. All A are C. So all C are B. Let A = girls, B = females, and C = mammals.
correct
incorrect
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not completed
.
Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
All scientists are smart people. Some smart people are not stylish people. So, some scientists are not stylish people.
All A are B. Some C are not B. So, some A are not C. Let A = dogs, B = mammals, and C = poodles.
correct
incorrect
All A are B. Some B are not C. So, some A are not C. Let A = dogs, B = mammals, and C = poodles.
correct
incorrect
All A are B. Some B are not C. So, some C are not A. Let A = beagles, B = animals, and C = dogs.
correct
incorrect
All A are B. Some B are not C. So, some A are not C. Let A = beagles, B = animals, and C = dogs.
correct
incorrect
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not completed
.
Choose which argument form correctly models the given argument, and which substitutions create a counterexample that shows the argument is invalid.
The Honda costs over $20,000. The BMW costs over $50,000. Therefore, the BMW costs more than the Honda.
The Honda costs $24,500. The BMW costs $53,199. So the BMW costs more than the Honda.
correct
incorrect
The Honda costs $61,240. The BMW costs $57,899. So the BMW costs more than the Honda.
correct
incorrect
The Honda costs $47,799. The BMW costs $61,122. So the BMW costs more than the Honda.
correct
incorrect
The Honda costs $32,195. The BMW costs $80,269. So the BMW costs more than the Honda.
correct
incorrect
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