Which of the following statements are logically equivalent?

A. All professors are competent scholars.

B. No professors are non-competent scholars.

C. No competent scholars are professors.

D. All non-competent scholars are non-professors.

Choose the correct answer from the options given below:

Question

Question

This question was previously asked in

UGC NET Paper 1: Held on 13th Mar 2023 Shift 1

Answer 1

Key Points

Statements A and B are logically equivalent because they both say that there is no overlap between the set of professors and the set of non-competent scholars.
Statements B and D are logically equivalent because they both say that if a person is a non-competent scholar, then they cannot be a professor.
Statement C is not logically equivalent to any of the other statements because it says that there is no overlap between the set of competent scholars and the set of professors. However, it is possible for a person to be a competent scholar and not be a professor.

Therefore, the correct answer is 4, A, B and D only.

Here is a table that summarizes the logical equivalence of the four statements:

Statement	Logically equivalent to
A: All professors are competent scholars.	B: No professors are non-competent scholars.
B: No professors are non-competent scholars.	A: All professors are competent scholars.
C: No competent scholars are professors.
D: All non-competent scholars are non-professors.	B: No professors are non-competent scholars.