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If n(A × B) = pq and (A × B) ∩ (A × C) = A × (B ∩ C), then for which choice is the intersection MAXIMISED?
AWhen B and C have no common element
BWhen B and C are disjoint
CWhen B ⊆ C or C ⊆ B
DWhen A is empty
Answer & Solution
Correct answer: C. When B ⊆ C or C ⊆ B
A × (B ∩ C) has |A| × |B ∩ C| elements, which is maximised when B ∩ C is as large as possible — i.e., one of B, C contains the other. Disjoint B, C gives the empty intersection.
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