If A = {3, 4, 5}, B = {5, 6}, and C = {6, 7, 8}, find n[A × (B ∩ C)].
A
5
B
2
C
3
D
4
Correct Option:
C
Explanation
First, B ∩ C = {5, 6} ∩ {6, 7, 8} = {6}. Thus, n(A) = 3 and n(B ∩ C) = 1. The number of elements in a Cartesian product is the product of the cardinalities, so n[A × (B ∩ C)] = 3 × 1 = 3.
