Read the following statement carefully and identify the conclusion that follows. Statement: No woman is lazy. Some men are lazy. Conclusions: I. No man is a woman. II. Some lazy people are men.

Correct — B.
Rule: Some A are B → Some B are A.

II: some men are lazy, so some lazy people are men ✓

I: no woman is lazy, so the lazy men are not women. That proves some men are not women and says nothing about the men who are not lazy, so No man is a woman does not follow ✗

Only II follows → option (b).

Why the others are wrong

• (a)
  Only I follows — Only I takes an everyday truth for a proof. The statements show only that lazy men are not women, and II, Some men are lazy turned round, does follow.
• (c)
  Both I and II follow — Both would need I to follow. The statements prove only that lazy men are not women and say nothing about other men, so No man is a woman is not proved.
• (d)
  Neither I nor II follows — Neither misses II. Some men are lazy turns round into Some lazy people are men, and a Some A are B statement always turns round this way.

In a syllogism a conclusion follows only if the statements force it. What you know about the world does not count.

Draw it: the woman circle and the lazy circle do not touch, and the men circle overlaps the lazy circle.

Nothing stops the men circle from also reaching the woman circle outside the lazy area, so No man is a woman is possible but not certain.

Key facts

• Some A are B converts to Some B are A.
• No A is B with Some C are B gives Some C are not A.
• A conclusion follows only if every diagram of the statements makes it true.

Common traps

• Accepting No man is a woman because it is true in real life
• Rejecting II because the statement reads 'Some men are lazy', not 'Some lazy people are men'

No directly related past PYQ was found.