Question

Let Z be the set of integers. lf A = `{x ∈ Z: 2^((x + 2)(x^2  –  5x  +  6)) = 1}` and B = {x ∈ Z: –3 < 2x – 1 < 9}, then the number of subsets of the set A × B, is ______.

Options

• 2¹⁵

• 2¹⁸

• 2¹²

• 2¹⁰

Answer 1

Let Z be the set of integers. lf A = `{x ∈ Z: 2^((x + 2)(x^2  –  5x  +  6)) = 1}` and B = {x ∈ Z: –3 < 2x – 1 < 9}, then the number of subsets of the set A × B, is `underlinebb(2^15)`.

Explanation:

Let x ∈ A, then

∵ `2^((x + 2)(x^2  –  5x  +  6))` = 1

⇒ (x + 2)(x – 2)(x – 3) = 0

x = –2, 2, 3; A = {–2, 2, 3}; Then, n(A) = 3

Let x ∈ B, then –3 < 2x – 1 < 9

–1 < x < 5 and x ∈ Z

∴ B = {0, 1, 2, 3, 4}

n(B) = 5;

n(A × B) = 3 × 5 = 15

Hence, number of subsets of A × B = 2¹⁵