Which of the following statements are logically equivalent?

1.All poems are artworks.

2.No non-poems are non-artworks.

3.Some poems are artworks.

4.All non-artworks are non-poems.

A1, 3 & 4 only

B1 & 2 only

C3 & 4 only

D1 & 4 only ✓ Correct

Correct answer: (D) 1 & 4 only

Explanation

Statements 1 and 4 are logically equivalent.

Statement 1 is the universal affirmative, 'All poems are artworks'.

Its contrapositive, 'All non-artworks are non-poems', is Statement 4, and the universal affirmative is equivalent to its contrapositive.

Statement 2, 'No non-poems are non-artworks', instead says all non-poems are artworks, which is not the same claim.

Statement 3, 'Some poems are artworks', is only the weaker subaltern, not an equivalent.

Hence contraposition ties the first and the fourth together.

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