Set X contains 3n elements and set Y contains 2n elements, and they have n elements in common. How many elements does (X-Y) \times (Y-X) have?
- A. 5n^2
- B. 4n^2
- C. 3n^2
- D. 2n^2 ✓
Correct Answer: D. 2n^2
Explanation
The number of elements only in X is n(X - Y) = n(X) - n(X \cap Y) = 3n - n = 2n. The number of elements only in Y is n(Y - X) = n(Y) - n(X \cap Y) = 2n - n = n. The number of elements in their Cartesian product is n(X - Y) \times n(Y - X) = 2n \times n = 2n^2.
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