From No A are B and No B are C, can we conclude No A are C?

• A. Yes.
• B. No.
• C. Not necessarily.
• D. Cannot be determined.

Answer: (C)

The idea being tested is whether two separate disjointness statements can force a third disjointness. If A and B have nothing in common, and B and C have nothing in common, that doesn’t automatically say anything about A and C. They could share elements as long as those shared elements aren’t in B, and that’s perfectly consistent with both given statements.

For example, imagine a universe with elements 1, 2, 3. Let A be {1, 2}, B be {3}, and C be {2}. Then A and B don’t overlap, B and C don’t overlap, but A and C do overlap at element 2. In this scenario, saying “No A are C” would be false, even though the two initial statements hold. Hence, you cannot conclude that A and C are disjoint from the given information alone.

So the conclusion is not guaranteed.