If 'All men are mortal' is true, which of the following can be validly inferred?

1.'No man is mortal' is false

2.'Some men are mortal' is true

3.'Some men are not mortal' is true

4.'Some men are not mortal' is false

5.'Some men are mortal' is false

A1, 2 and 4 only ✓ Correct

B1, 2 and 3 only

C1, 2, 3 and 4 only

D2, 3, 4 and 5 only

Correct answer: (A) 1, 2 and 4 only

Explanation

From the truth of 'All men are mortal', Statements 1, 2 and 4 follow validly.

Its contrary 'No man is mortal' must be false, so Statement 1 holds.

By subalternation 'Some men are mortal' is true, so Statement 2 holds.

Its contradictory 'Some men are not mortal' must be false, so Statement 4, calling it false, holds.

These follow directly from the square of opposition when the universal affirmative is true.

Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.