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)

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