Question

The number of subsets of the power set of $A$, where $A=\{x:x\in N-3\le |x|<4\}$ will be

Answer 1

$A=\{x:x\in N-3\le |x|<4\}$
But, $|x|\ge 0$ (always)
$\Rightarrow |x|<4\Rightarrow x\in (-4,4)$
Since $x\in N$
$A=\{1,2,3\}$
$\Rightarrow n\left(A\right)=3\Rightarrow n\left(P\right(A\left)\right)=2^3=8$
Now, the number of subsets of power set
$=2^8=256$