1F Practice: Deductive Arguments - Counterexamples and invalidity - Logic 5e Student Resources

1. 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

All C are E. All A are E. So, all C are A. Let C= cats, E = mammals, and A = dogs

All E are C. All A are E. So, all C are A. Let C= cats, E = mammals, and A = felines

All C are E. All A are E. So, all C are A. Let C= cats, E = mammals, and A = felines

2. 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

No U are I. No C are I. So, no U are C. Let U = umbrellas, I = icebergs, and C = cats

No U are I. No I are C. So, no U are C. Let U = cats, I = snakes, and C = mammals

No U are I. No C are I. So, no U are C. Let U = cats, I = snakes, and C = mammals

3. 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.

Fidelix was born in 1972. Gil was born in 1988. Thus, Fidelix was born before Gil.

Fidelix was born in 1981. Gil was born in 1980. Thus, Fidelix was born before Gil.

Fidelix was born in 1989. Gil was born in 1990. Thus, Fidelix was born before Gil.

4. 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

All S are F. All S are P. So, all F are P. Let S = puppies, F = dogs, and P = mammals

All F are S. All S are P. So, all F are P. Let S = puppies, F = mammals, and P = dogs

All S are F. All P are F. So, all S are P. Let S = puppies, F = mammals, and P = dogs

5. 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.

No A are P. Some R are P. So some R are A. Let A = dogs, P = cats, R = mammals.

No A are P. Some R are not P. So some R are A. Let A = dogs, P = cats, R = mammals.

No A are P. Some R are P. So some R are A. Let A = cars, P = cats, R = mammals.

6. 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.

No B are C. No D are C. So, no D are B. Let B = beagles, C = collies, and D = dogs.

No B are C. Some D are not C. So, no D are B. Let B = people, C = cats, and D = pets.

No B are C. Some D are C. So, no D are B. Let B = beagles, C = collies, and D = dogs.

7. 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.

Some A are B. All B are C. So, some C are not A. Let A = animals, B = cats, and C = mammals.

Some B are A. All C are B. So, some C are not A. Let A = cats, B = mammals, and C = felines.

Some A are B. All B are C. So, some C are not A. Let A = cats, B = tigers, and C = felines.

8. 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.

All B are A. Some A are C. So, some C are not B. Let A = animals, B = living things, and C = famous things.

All A are B. Some A are not C. So, some C are not B. Let A = dogs, B = animals, and C = beagles.

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.

9. 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.

All A are B. All C are B. So, all A are C. Let A = animals, B = cats, and C = dogs.

All A are B. All C are B. So, all C are A. Let A = cats, B = animals, and C = dogs.

All A are B. All C are B. So, all A are C. Let A = cats, B = animals, and C = dogs.

10. 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.

All A are B. All A are C. So, all C are A. Let A = puppies, B = dogs, and C = mammals.

All A are B. All A are C. So, all B are C. Let A = dogs, B = mammals, and C = puppies.

All A are B. All C are A. So, all A are C. Let A = puppies, B = mammals, and C = dogs.

11. 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.

All A are B. Some C are B. So some C are A. Let A = aardvarks, B = bumblebees, and C = cats.

All A are B. Some B are C. So some C are A. Let A = cats, B = mammals, and C = rodents.

All A are B. Some B are C. So some C are A. Let A = cats, B = mammals, C = wild animals.

12. 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.

All A are B. All A are C. So all C are B. Let A = kittens, B = mammals, and C = cats.

All A are B. All A are C. So all B are C. Let A = girls, B = females, and C = conscious beings.

All A are B. All A are C. So all C are B. Let A = girls, B = females, and C = mammals.

13. 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.

All A are B. Some B are not C. So, some A are not C. Let A = dogs, B = mammals, and C = poodles.

All A are B. Some B are not C. So, some C are not A. Let A = beagles, B = animals, and C = dogs.

All A are B. Some B are not C. So, some A are not C. Let A = beagles, B = animals, and C = dogs.

14. 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.

The Honda costs $61,240. The BMW costs $57,899. So the BMW costs more than the Honda.

The Honda costs $47,799. The BMW costs $61,122. So the BMW costs more than the Honda.

The Honda costs $32,195. The BMW costs $80,269. So the BMW costs more than the Honda.

1F Practice: Deductive Arguments - Counterexamples and invalidity

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