If the statement "Some animals are birds" is given as true, which of the…
2023
If the statement "Some animals are birds" is given as true, which of the following statements can be immediately inferred to be false?
Answer: A. No animals are birds. — CONCEPTIn categorical logic, “some A are B” means that at least one member lies in the intersection of sets A and B. Therefore, the intersection A ∩ B is…
- A.
No animals are birds.
- B.
All animals are birds.
- C.
Some animals are not birds.
- D.
All animals cannot fly.
Show answer & explanation
Correct answer: A
CONCEPT
In categorical logic, “some A are B” means that at least one member lies in the intersection of sets A and B. Therefore, the intersection A ∩ B is non-empty.
APPLICATION
Let A be the set of animals and B the set of birds. The given statement says A ∩ B ≠ ∅. The statement “No animals are birds” says A ∩ B = ∅, which cannot hold together with the given statement.
CONTRAST
“All animals are birds” asserts A ⊆ B; the given existential statement neither proves nor disproves this universal claim.
“Some animals are not birds” asserts A \ B ≠ ∅; the given intersection statement does not decide whether such members exist.
“All animals cannot fly” concerns the ability to fly, a property not mentioned in the premise.
Hence, the statement that can be immediately inferred to be false is “No animals are birds.”