Which of the following statements are logically equivalent? A. Some non-birds…
2024
Which of the following statements are logically equivalent?
A. Some non-birds are mammals.
B. Some birds are not mammals.
C. Some non-mammals are non-birds.
D. Some non-mammals are not non-birds.
Choose the most appropriate answer from the options given below:
Answer: D. B and D Only — ConceptTwo existential categorical statements are logically equivalent only when they assert the same subject–predicate condition. A double negation cancels,…
- A.
A, B and C Only
- B.
A and C Only
- C.
C and D Only
- D.
B and D Only
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept
Two existential categorical statements are logically equivalent only when they assert the same subject–predicate condition. A double negation cancels, so “not non-P” means P.
Application
Represent B as: there exists an x such that Bird(x) and not Mammal(x).
Represent D as: there exists an x such that not Mammal(x) and not-not Bird(x). Removing the double negation gives not Mammal(x) and Bird(x).
The order of terms joined by ‘and’ does not change the condition, so the forms obtained from B and D are identical.
Contrast
A represents Mammal(x) and not Bird(x), so it describes a different region.
C represents not Mammal(x) and not Bird(x), so its bird condition differs.
Cross-check
Both B and D pick out the intersection of birds with non-mammals. Therefore, the logically equivalent statements are B and D only.