If all A are B and no B are C, which statement must be true?

• A. Some A are C
• B. No A are C
• C. All C are A
• D. Some B are C

Answer: (B)

When one group is entirely inside another and that outer group doesn’t overlap with a third group, the inner group can’t overlap with that third group either. Here, every A is inside B, and B has no elements in common with C. Therefore, no A can be C, so the statement that no A are C must be true.

Why the other statements don’t hold: Some A are C would require an overlap between A and C, which is impossible given A ⊆ B and B ∩ C is empty. All C are A would only be guaranteed if C had some members; otherwise it can be true vacuously if C is empty, but that isn’t required by the premises. Some B are C would contradict B and C being disjoint.