Source: Extra Practice
If n(A ∩ B) = 3, find the number of elements common to the sets (A × B) and (B × A).
Options
Option A
3
Option B
6
Option C is correct
9
Option D
0
Explanation
A known property of Cartesian products is that (A × B) ∩ (B × A) = (A ∩ B) × (B ∩ A). If n(A ∩ B) = k, then the number of common elements is k^2. Here k = 3, so 3^2 = 9. Option A is k, not k^2. Option B is 2k. Option D assumes the products are disjoint, which is only true if A and B are disjoint.