If A ⊆ B and B ⊆ C, which statement must be true?

• A. A ⊆ C.
• B. C ⊆ A.
• C. A ∩ C = ∅.
• D. A = C.

Answer: (A)

The statement uses the transitivity of the subset relation: if A is contained in B and B is contained in C, then A must be contained in C. Here’s why: take any element x in A. Since A is a subset of B, x is in B. Since B is a subset of C, x is in C. This holds for every element of A, so all elements of A are in C, meaning A is a subset of C. That makes the statement necessarily true.

For the other possibilities, they aren’t guaranteed by the given information. C being contained in A isn’t required, so elements of C could lie outside A. A and C could share elements, so their intersection need not be empty. And A and C need not be exactly equal; C can have additional elements beyond those in A. A concrete example is A = {1}, B = {1, 2}, C = {1, 2, 3}, where the chain holds and A is indeed contained in C, but the other relations don’t hold.