If all A are B, and some B are C, can we conclude some A are C?

• A. No
• B. Yes
• C. Only if C is a subset of A
• D. Cannot be determined

Answer: (A)

Focus on how subset and existence statements interact. If all A are B, that means every element of A is inside B, but B can have additional elements outside A. If some B are C, there exists at least one element that is both in B and in C. that element could be one of the A elements (which would make some A also in C) or it could be a B element that isn’t in A. Since either scenario is possible, you can’t guarantee that any A is in C based on the given information. For example, take A = {1}, B = {1, 2}, C = {2}; here all A are B and some B are C, but no A is C. Conversely, if C shares an element with A, some A would be C. So the conclusion cannot be determined from these premises.