Which of the following statements are logically equivalent?

1.No philosophers are underpaid scholars

2.All philosophers are non-underpaid scholars

3.No underpaid scholars are philosophers

4.All non-underpaid scholars are non-philosophers

A1, 2 & 3 only ✓ Correct

B3 & 4 only

C2 & 4 only

D1, 2 & 4 only

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

Explanation

Statements 1, 2 and 3 all say the same thing about philosophers and underpaid scholars.

Statement 1 is the universal negative No philosophers are underpaid scholars.

Statement 2 is its obverse, All philosophers are non-underpaid scholars, meaning preserved.

Statement 3 is its converse, No underpaid scholars are philosophers, valid for an E proposition.

Statement 4 reduces to All philosophers are underpaid, the opposite claim, so it is excluded.

Obversion and conversion both preserve the truth of an E proposition.

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