Which of the following two propositions can neither be both true together nor both false together? Choose the correct answer from the options given below.

1.All squares are rectangles

2.Some squares are rectangles

3.No squares are rectangles

4.Some squares are not rectangles

A1 and 2 only

B2 and 3 only ✓ Correct

C1 and 3 only

D1, 2 and 4 only

Correct answer: (B) 2 and 3 only

Explanation

Statements 2 and 3 form a contradictory pair, so they can neither both be true nor both be false.

Statement 2 is the I proposition 'Some squares are rectangles'.

Statement 3 is the E proposition 'No squares are rectangles'.

I and E are contradictories in the square of opposition.

Exactly one of a contradictory pair is true and the other false, with no middle ground.

This total opposition rules out both joint truth and joint falsity.

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