CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
If A = {1, 2} and B = {2, 3}, what is n[(A × B) ∩ (B × A)]?
The intersection has exactly one element, the pair (2,2). Listing A × B and B × A shows only (2,2) appears in both, which agrees with the result (A∩B) × (B∩A) = {2} × {2}.
- A0
- B1Correct
- C2
- D4
Explanation
A × B = {(1,2),(1,3),(2,2),(2,3)}. B × A = {(2,1),(2,2),(3,1),(3,2)}. The only common pair is (2,2), so the count is 1. Using (A∩B)×(B∩A) = {2}×{2} confirms this.
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