Question

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

Answer 1

We know that if A is a set with m elements i.e., $n\left(A\right)=m$,

then, $n\left[P\right(A\left)\right]=2^m$.

If $A=\varphi$, then $n\left(A\right)=0$

$\therefore n\left[P\right(A\left)\right]=2^o=1$

Hence, P(A) has one element.