Question:
Let $Z$ be the set of integers. If $A=\left\{x \in Z: 2(x+2)\left(x^{2}-5 x+6\right)\right\}=1$ and
$B=\{x \in Z:-3<2 x-1<9\}$, then the number of
subsets of the set $A \times B$, is :
Correct Option: , 3
Solution:
$\mathrm{A}=\left\{\mathrm{x} \in \mathrm{z}: 2^{(\mathrm{x}+2)\left(\mathrm{x}^{2}-5 \mathrm{x}+6\right)}=1\right\}$
$2^{(x+2)\left(x^{2}-5 x+6\right)}=2^{0} \Rightarrow x=-2,2,3$
$A=\{-2,2,3\}$
$B=\{x \in Z:-3<2 x-1<9\}$
$B=\{0,1,2,3,4\}$
$A \times B$ has is 15 elements so number of subsets of $A \times B$ is $2^{15}$.
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