Paper 1 · Logical Reasoning
If the statement 'Some men are cruel' is false, which of the following statement(s) is/are true?
- All men are cruel
- No men are cruel
- Some men are not cruel
A1 and 3
B1 and 2
C2 and 3 ✓ Correct
D3 only
Correct answer: (C) 2 and 3 — Statements 2 and 3 are true, so that is the answer.
Explanation
★Statements 2 and 3 are true, so that is the answer.
★'Some men are cruel' is a particular affirmative (I) proposition.
★Its contradictory, 'No men are cruel' (E), must be true when I is false, so statement 2 is true.
★Since no men are cruel, it follows that some men are not cruel (O), so statement 3 is true.
★'All men are cruel' would make some men cruel, so statement 1 is false.
★So the answer is 2 and 3.
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