If $S$ and $T$ are two sets such that $S$ has $21$ elements, $T$ has $32$ elements, and $S$ $\cap \,T$ has $11$ elements, how many elements does $S\, \cup$ $T$ have?

For any sets $\mathrm{A}$ and $\mathrm{B}$, show that

$P(A \cap B)=P(A) \cap P(B).$

If $X=\{a, b, c, d\}$ and $Y=\{f, b, d, g\},$ find

$Y-X$

If $A$ and $B$ are not disjoint sets, then $n(A \cup B)$ is equal to

Find the union of each of the following pairs of sets :

$A=\{1,2,3\}, B=\varnothing$