Which of the following propositions are logically equivalent?

1.Some men are arrogant human beings

2.Some non-arrogant human beings are not non-men

3.Some men are not non-arrogant human beings

4.Some arrogant human beings are men

A2 & 4 only

B1 & 3 only

C1, 2 & 3 only

D1, 3 & 4 only ✓ Correct

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

Explanation

Statements 1, 3 and 4 all state the same particular affirmative content.

Statement 1 is Some men are arrogant human beings, an I proposition.

Statement 3 is its obverse, Some men are not non-arrogant human beings, logically equal.

Statement 4 is its converse, Some arrogant human beings are men, valid for I.

Statement 2 shifts terms invalidly and is not equivalent.

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