Question

Let $Z$ be the set of integers. If $A \, = \, \\{ x \in Z : 2^{ (x+2) (x^2 - 5x + 6)} \\}=1$ and $B \, = \, \\{ \, x \in Z: -3 <2x -1 <9 \\}$, then the number of subsets of the set $A \times B$, is :

• A. $2^{18}$
• B. $2^{10}$
• C. $2^{15}$
• D. $2^{12}$

Answer 1

Answer: (C)

$2^{15}$

Answer 2

$A \, = \, \\{ \, x \in z : 2 ^{(x+2)(x^2-5x+6)} \, = \, 1\\}$
$2^{(x+2)(x^2-5x+6)} \, = \, 2^{0} \, \Rightarrow \, x \, = -2,2,3$
$A \, = \, \\{ -2, 2, 3\\}$
$B \, = \, \, {x \in Z : -3 <2x - 1 < 9}$
$A \, \times \, B=3\times15=15$ has $15$ elements so number of subsets
of $A \times B$ is $2^{15}$