Which of the following statements are logically equivalent? Choose the correct answer from the options given below.

1.Some non-dogs are non-friendly animals.

2.Some dogs are friendly animals.

3.Some friendly animals are dogs.

4.All dogs are friendly animals.

A2, 3 only ✓ Correct

B2, 4 only

C1, 2, 3 only

D1, 4 only

Correct answer: (A) 2, 3 only

Explanation

The two equivalent propositions are "Some dogs are friendly animals" and "Some friendly animals are dogs".

Statement 2 is the particular affirmative I, "Some dogs are friendly animals".

Statement 3 is its converse, "Some friendly animals are dogs".

An I proposition converts validly, keeping the same truth value.

Converse and original assert exactly the same partial overlap of the two classes.

This valid conversion of an I proposition makes Statements 2 and 3 logically equivalent.

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