If A ⊆ B and A ∩ C = ∅, which statement is necessarily true?

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

Answer: (D)

The key idea here is disjointness: A has no elements in common with C. That is exactly what A ∩ C = ∅ means, and that fact is given, so it must be true regardless of how A sits inside B. The fact that A is a subset of B doesn’t change this intersection condition.

The other statements would require additional information not provided. For example, A ⊆ C would force every element of A into C, which isn’t guaranteed and would conflict with A ∩ C = ∅ unless A were empty. B ⊆ C or B ⊆ A imply stronger relationships about B that aren’t given and aren’t necessary.