In this question, three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All necklaces are squares. Some squares are circles. No circle is a ring. Conclusions: I.No square is a ring. II.No ring is a circle. III.Some squares are necklaces.

Correct — B. Rule: a no-X-is-Y statement converts, an all-X-is-Y statement does not.

Conclusion II, no ring is a circle. The third statement says no circle is a ring, and an exclusion holds both ways round, so II follows.

Conclusion III, some squares are necklaces. All necklaces are squares, so the necklaces themselves are squares that are necklaces, and III follows.

Conclusion I, no square is a ring. Rings are barred from the circles, and some squares are circles — but the squares outside that overlap are untouched, so a square could still be a ring. I does not follow.

Two conclusions follow and one does not, which is option (b).

Why the others are wrong

• (a)
  Only conclusions I and III follow. — This accepts conclusion I. No square is a ring overreaches: the statements exclude rings from the circles only, and the squares that are not circles stay unconstrained.
• (c)
  All the conclusions follow. — Conclusion I fails, so a blanket all-follow answer fails with it. II and III are the only two that survive the test.
• (d)
  Only conclusion III follows. — Conclusion III does follow, but so does conclusion II — no circle is a ring converts directly into no ring is a circle.

Three-statement syllogisms turn on two habits. Draw the diagram the statements force, then ask whether a conclusion holds in every diagram you could legally draw, not merely in the first one you drew.

Two conversion rules do most of the work. No A is B converts to no B is A, because an exclusion is symmetric. All A is B does not convert to all B is A, but it does yield some B is A, since the A's are themselves B's that are A's.

Anything merely possible fails. A conclusion follows when no legal diagram contradicts it, and not before.

Key facts

• No A is B converts, so no B is A follows automatically.
• All A is B yields some B is A, which is why all necklaces are squares gives some squares are necklaces.
• Some A is B combined with no B is C does not give no A is C, because only the overlap is excluded.

Common traps

• Reading some squares are circles as though it constrained all squares.
• Rejecting some squares are necklaces as too weak when all necklaces are squares is given.
• Answering that all conclusions follow because two of the three plainly do.

No directly related past PYQ was found.