Which of the following statements are logically equivalent?

1.No P is S

2.Some S are non-P

3.Some non-P are not non-S

4.Some S are not P

A1 & 3 only

B3 & 4 only

C2, 3 & 4 only ✓ Correct

D1, 2, 3 & 4

Correct answer: (C) 2, 3 & 4 only

Explanation

Some S are non-P, Some non-P are not non-S and Some S are not P all express the same particular negative.

Obverting Some S are not P gives Some S are non-P, so Statement 4 equals Statement 2.

Statement 3, Some non-P are not non-S, obverts to Some non-P are S, which converts to Some S are non-P.

So Statements 2, 3 and 4 all reduce to one another and are equivalent.

Statement 1, No P is S, is universal and stands apart from these particulars.

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