A and B are two sets having 3 elements in common. If n(A) = 5, n(B) = 4, then what is n(A × B) equal to?

Concept:

Let A and B be two sets. Number of elements in A is given as n(A) and number of elements in B is given as n(B), then the number of elements in n(A × B) = n(A) × n(B)

Calculation:

Given: n(A) = 5, n(B) = 4 and A and B have 3 elements in common.

To find: n(A × B)

n(A × B) = n(A)n(B)

= 5 × 4

= 20

Alternate Solution:

Let A = {a, b, 1, 2, 3} and B = {1, 2, 3, 4}

A × B = {(a,1), (b,1), (1,1), (2,1), (3,1), (a,2), (b,2), (1,2), (2,2), (3,2), (a,3), (b,3), (1,3), (2,3), (3,3), (a,4), (b,4), (1,4), (2,4), (3,4)}

n(A × B) = 20