Q.How many elements does $P(A)$ have if $A=\phi$?

$A \subseteq B$ means every element of $A$ also lies in $B$; if additionally $A \ne B$, $A$ is a proper subset, $A \subset B$. Every set is a subset of itself, and $\varnothing$ is a subset of every set. Applied to $\mathbb{R}$, subsets of the form "between two numbers" are written as intervals — $(a,b)$, $[a,b]$, $[a,b)$, $(a,b]$ — with square brackets for in …