Statements: All dancers are artists. No artist is lazy. Conclusions: I. No dancer is lazy. II. Some lazy are dancers.

Correct — A.
Rule: All A are B + No B is C ⇒ No A is C.

Every dancer is inside the artists' circle, and the lazy circle does not touch the artists. So it cannot touch the dancers: No dancer is lazy, and conclusion I follows.

Conclusion II, some lazy are dancers, would put a lazy person among the dancers, which I rules out. II fails, so the answer is option (a), Only I follows.

Why the others are wrong

• (b)
  Only II follows — Conclusion II says some lazy people are dancers. The statements put every dancer among the artists and no artist among the lazy, so II is ruled out, not merely unproven.
• (c)
  Both I and II follow — Both cannot follow: I says no dancer is lazy and II says some lazy are dancers. The two contradict each other, and the statements back I.
• (d)
  Neither I nor II follows — Neither is wrong because conclusion I is forced by the statements. Every dancer is an artist and no artist is lazy, which leaves no room for a lazy dancer.

A two-statement syllogism links a first group to a third through a middle term. Here the middle term is artists: dancers lie wholly inside it, and the lazy lie wholly outside it.

That chain gives a certain universal negative: no dancer is lazy. Draw dancers inside artists and lazy as a separate circle, then test each conclusion against the drawing, not against what sounds plausible.

Key facts

• All A are B and No B is C together give No A is C.
• No A is C converts to No C is A.
• Some C are A contradicts No A is C, so the two cannot both be true.

Common traps

• Reading II as the converse of I. The converse is No lazy person is a dancer, the opposite of II.
• Accepting both conclusions because each links the same two groups.

No directly related past PYQ was found.