Identify the following propositions which are logically equivalent. Choose the correct answer from the options given below.

1.Some books are novels.

2.Some books are not non-novels.

3.Some novels are not non-books.

4.Some novels are books.

A3, 4 only

B1, 4 only

C1, 3 only

D1, 2, 3, 4 ✓ Correct

Correct answer: (D) 1, 2, 3, 4

Explanation

All four propositions carry the same information, "some books are novels", through valid immediate inferences.

Statement 1 is the original particular affirmative, "Some books are novels".

Statement 2 is its obverse, "Some books are not non-novels", which keeps the meaning.

Statement 4 is its converse, "Some novels are books", valid for an I proposition.

Statement 3 is the obverse of that converse, "Some novels are not non-books".

Since obversion and conversion of an I proposition preserve truth, the four are logically equivalent.

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