If A ∩ B = ∅ and A ⊆ C, what can be said about B ∩ C?

• A. Not determinable from given information
• B. A subset of B
• C. Contains all elements of C
• D. Equal to ∅

Answer: (A)

This tests how disjointness with A and A being a subset of C relate to the intersection with C. Since A has no elements in common with B, that alone tells you nothing about B’s overlap with C. The reason is that C includes A plus possibly other elements. B could share some of those extra elements with C, making B ∩ C nonempty, or B might share none of them with C, making B ∩ C empty. Both possibilities are consistent with the given information.

For example, take A = {1}, B = {2}, C = {1, 2}. Here A ∩ B = ∅, A ⊆ C, and B ∩ C = {2}. In another setup, take A = {1}, B = {2}, C = {1}. Then A ∩ B = ∅, A ⊆ C, but B ∩ C = ∅. These show the intersection with C cannot be determined from the given data.