Which of the following statements are logically equivalent?

1.All aeroplanes are polluting vehicles

2.No polluting vehicles are aeroplanes

3.All non-polluting vehicles are non-aeroplanes

4.No aeroplanes are non-polluting vehicles

A2 & 3 only

B2 & 4 only

C1 & 4 only

D1, 3 & 4 only ✓ Correct

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

Explanation

Statements 1, 3 and 4 all express the same universal affirmative about aeroplanes.

Statement 1 is the original All aeroplanes are polluting vehicles.

Statement 4 is its obverse, No aeroplanes are non-polluting vehicles, which keeps the meaning.

Statement 3 is its contrapositive, All non-polluting vehicles are non-aeroplanes, also meaning-preserving.

Statement 2 merely converts the A proposition, which is invalid, so it is left out.

Obversion and contraposition are the truth-preserving transformations of an A proposition.

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