How many elements has P(A), if A = Φ?

We know that if $A$ is a set with $m$ elements i.e., $n(A)=m$, then $n[P(A)]=2^{m}$.

If $A=\Phi$, then $n(A)=0 .$

$\therefore n[\mathrm{P}(\mathrm{A})]=2^{0}=1$

Hence, $P(A)$ has one element.