Which of the following propositions are logically equivalent?

A. No women are arrogant human beings.

B. No arrogant human beings are women.

C. All women are non-arrogant human beings.

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

Choose the correct answer from the options given below:

The correct answer is A, B and C only.
Key PointsProposition A states that no women are arrogant human beings, which can be rephrased as "All women are non-arrogant human beings" (by converting the negative statement to an equivalent positive statement).

Proposition B states that no arrogant human beings are women, which can be rephrased as "All non-women are non-arrogant human beings" (by converting the negative statement to an equivalent positive statement and reversing the subject and predicate).

Proposition C states that all women are non-arrogant human beings, which is equivalent to proposition A (by using the conversion rule mentioned above).

Proposition D states that all non-arrogant human beings are non-women, which is not equivalent to any of the other propositions. It is the contrapositive of the converse of proposition A.

Therefore, the logically equivalent propositions are A, B, and C
Additional InformationA logical argument is a process of creating a new statement from the existing statements. It comes to a conclusion from a set of premises by means of logical implications via logical inference.