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# Let Z be the set of integers.

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 :

1. $2^{18}$

2. $2^{10}$

3. $2^{15}$

4. $2^{12}$

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 $2^{15}$.