Question

How many elements has $P\left(A\right)$, if $A=\varnothing$?

Answer 1

Find the number elements in power set of $A$

If a set $A$ has $x$ elements then the power set of $A$ has $2^x$ elements.

If $n\left(A\right)=x$ , then $n\left(P\right(A\left)\right)=2^x$

As $A=\varnothing$ , $n\left(A\right)=0$

$\Rightarrow$$n\left(P\right(A\left)\right)=2^0$

$\Rightarrow$$n\left(P\right(A\left)\right)=1$

Hence, $P\left(A\right)$ has $1$ element.