All A are B; No B are C. What is necessarily true about A and C?

• A. A and C share some members
• B. No A are C
• C. All A are C
• D. Some C are A

Answer: (B)

Understanding how set relationships translate to what must be true is key here. “All A are B” means A is entirely inside B (A ⊆ B). “No B are C” means B has no elements in common with C (B ∩ C = ∅).

Since A is a subset of B and B has no elements in C, A cannot have any elements in C either. Put another way, there’s no overlap between A and C. So the only necessarily true statement is that no A are C.

Because A lies within B and B doesn’t touch C, any claim that some A are C, or that all A are C, or that A and C share elements, would contradict the given conditions.