Which of the following statements are logically equivalent?

1.No S is P

2.No P is S

3.All S are non-P

4.All P are non-S

5.No S is non-P

A1, 3 & 4 only

B1, 2 & 3 only

C2, 3 & 4 only

D1, 2, 3 & 4 only ✓ Correct

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

Explanation

Statements 1 through 4 all express the same universal negative relation.

'No S is P' converts to 'No P is S,' an equivalent E proposition (Statement 2).

Obverting 'No S is P' gives 'All S are non-P' (Statement 3).

Converting then obverting yields 'All P are non-S,' again equivalent (Statement 4).

Each keeps the class S and class P mutually exclusive, so all four coincide.

The remaining form 'No S is non-P' instead means all S is P, a different relation.

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