Which of the following propositions are logically equivalent?

1.No women are arrogant human beings

2.No arrogant human beings are women

3.All women are non-arrogant human beings

4.All non-arrogant human beings are non-women

A1 & 4 only

B1, 2 & 3 only ✓ Correct

C1, 3 & 4 only

D2, 3 & 4 only

Correct answer: (B) 1, 2 & 3 only

Explanation

Statements 1, 2 and 3 all state the same universal negative about women and arrogant human beings.

Statement 1 is the universal negative No women are arrogant human beings.

Statement 2 is its converse, No arrogant human beings are women, valid for an E proposition.

Statement 3 is its obverse, All women are non-arrogant human beings, meaning preserved.

Statement 4 reduces to All women are arrogant human beings, the opposite claim, so it is excluded.

Conversion and obversion are the equivalence-preserving moves on an E proposition.

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