Given: A = {2, 3} and B = {4, 5}
To find: A × B
By the definition of the Cartesian product,
Given two non – empty sets P and Q. The Cartesian product P × Q is the set of all ordered pairs of elements from P and Q, .i.e.
P × Q = {(p, q) : p Є P, q Є Q}
Here, A = {2, 3} and B = {4, 5}. So,
A × B = (2, 3) × (4, 5)
= {(2, 4), (2, 5), (3, 4), (3, 5)}
∴Number of elements of A × B = n = 4
Number of subsets of A × B = 2n
= 24
= 2 × 2 × 2 × 2
= 16
∴, the set A × B has 16 subsets.
