Let Z be the set of integers. If A = x ∈ Z   : 2 x + 2 x 2 - 5 x + 6 = 1 and B = x ∈ Z    : -   3 <   2 x - 1 < 9 , then the number of subsets of the set A × B , is :

Step-by-step solution

Given 2 x + 2 x - 2 x - 3 = 1 = 2 0 ⇒ x = - 2 ,   2 ,   3 . ∴ n A = 3 Again, - 3 < 2 x - 1 < 9 ⇒ - 1 < x < 5 ⇒ x = 0 ,   1 ,   2 ,   3 ,   4 ∴ n B = 5 ∴ n   A × B = 3 × 5 = 15 ∴ Number of subset of A × B = 2 15