Which of the following statements are logically equivalent?

1.No amphibians are mammals

2.All non-mammals are non-amphibians

3.All amphibians are non-mammals

4.No mammals are amphibians

A1, 2 & 3 only

B1, 3 & 4 only ✓ Correct

C1, 2 & 4 only

D1 & 4 only

Correct answer: (B) 1, 3 & 4 only

Explanation

Statements 1, 3 and 4 all express the same universal negative about amphibians and mammals.

Statement 1 is No amphibians are mammals, the universal negative E.

Statement 3 is its obverse, All amphibians are non-mammals, keeping the meaning.

Statement 4 is its converse, No mammals are amphibians, valid for an E proposition.

Statement 2 reduces to All amphibians are mammals, the opposite claim, so it is excluded.

Obversion and conversion are the equivalence-preserving moves on an E proposition.

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