Which of the following statements are logically equivalent?

1.All professors are competent scholars

2.No professors are non-competent scholars

3.No competent scholars are professors

4.All non-competent scholars are non-professors

A2, 3 & 4 only

B1 & 2 only

C2 & 3 only

D1, 2 & 4 only ✓ Correct

Correct answer: (D) 1, 2 & 4 only

Explanation

Statements 1, 2 and 4 are logically equivalent.

Base 1 is the A "All professors are competent scholars".

Its obversion gives 2, "No professors are non-competent scholars".

Its contraposition gives 4, "All non-competent scholars are non-professors".

Statement 3 "No competent scholars are professors" denies overlap and contradicts.

Obversion and contraposition preserve meaning, tying 1, 2 and 4.

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