Given All A are B and Some B are C, does Some A are C necessarily?

• A. Yes.
• B. No.
• C. Not necessarily.
• D. Only if A equals B.

Answer: (C)

All A are B means A sits inside B. Some B are C means there is at least one element that lies in both B and C. But that particular element doesn’t have to be in A, since A could be a smaller subset of B. So you can’t guarantee any A is also in C.

For example, take A = {1}, B = {1, 2}, C = {2}. All A are B is true, some B are C is true (the element 2 is in both B and C), but some A are C is false because 1 is not in C.

So the statement is not necessarily true. Only in the special case where A and B are the same set would it be guaranteed.