If A is a subset of B and A is a subset of C, what is A ∩ B ∩ C?

• A. B
• B. C
• C. A
• D. Empty set

Answer: (D)

A ∩ B ∩ C equals A in this situation because every element of A is already in B and in C. The intersection includes exactly the elements common to all three sets, and since A sits inside both B and C, nothing from A is excluded. Formally, (A ∩ B) ∩ C = A ∩ C, and since A ⊆ C, A ∩ C = A. So the result is A (which could be empty only in the special case that A is empty).