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 :

Question

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 :, 2 12, 2 10, 2 18, 2 15

MARKS App · Accepted Answer

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

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