Source: Extra Practice
If set A has 3 elements and set B = {3, 4, 5}, then find the number of elements in (A × B).
Options
Option A
3
Option B
6
Option C is correct
9
Option D
27
Explanation
The number of elements in the Cartesian product of two sets A and B is given by n(A × B) = n(A) × n(B). Here, n(A) = 3 and B = {3, 4, 5}, so n(B) = 3. Thus, n(A × B) = 3 × 3 = 9. Option 3 is correct. Options 3 and 6 are incorrect counts, and 27 would be the number of elements in A × B × C if n(C) was also 3.