If all A are B, and some B are C, which statement must be true?

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

Answer: (C)

All A are B means A sits inside B. The fact that some B are C tells you there exists at least one element that is both in B and in C. Since A is contained in B, that B–C element could be inside A or outside A; the premises don’t guarantee any overlap between A and C. What is guaranteed by the information given is exactly that some B is also C. The other statements require additional connections between A and C that aren’t forced by these premises, so they aren’t must-be-true.