If the statement 'Some men are cruel' is false, which of the following statement(s) is/are true?

1.All men are cruel

2.No men are cruel

3.Some men are not cruel

A1 and 3

B1 and 2

C2 and 3 ✓ Correct

D3 only

Correct answer: (C) 2 and 3

Explanation

When "Some men are cruel" is false, "No men are cruel" and "Some men are not cruel" are true.

"Some men are cruel" is an I proposition, whose contradictory is the E proposition.

Falsity of the I therefore makes "No men are cruel" true, giving Statement 2.

From this universal negative, subalternation yields the particular negative.

Hence "Some men are not cruel," Statement 3, is also true.

Statement 1, "All men are cruel," is false, since not even one is cruel.

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