If All A are B and No A are C, which of the following correctly describes A ∩ C?

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Multiple Choice

If All A are B and No A are C, which of the following correctly describes A ∩ C?

This question tests how subset and disjointness statements affect an intersection. If every A is inside B, that means A is a subset of B. If no A is inside C, then A shares no elements with C. When a set has nothing in common with another, their intersection contains no elements. So A ∩ C is empty. Saying the intersection has elements would contradict the fact that no A are C, and saying it equals A would mean every A lies in C, which also contradicts the disjointness. Since the two given statements together force there to be no shared elements, the intersection is the empty set.

This question tests how subset and disjointness statements affect an intersection. If every A is inside B, that means A is a subset of B. If no A is inside C, then A shares no elements with C. When a set has nothing in common with another, their intersection contains no elements. So A ∩ C is empty.

Saying the intersection has elements would contradict the fact that no A are C, and saying it equals A would mean every A lies in C, which also contradicts the disjointness. Since the two given statements together force there to be no shared elements, the intersection is the empty set.

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