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?
If $A=\{3,6,9,12,15,18,21\}, B=\{4,8,12,16,20\},$ $C=\{2,4,6,8,10,12,14,16\}, D=\{5,10,15,20\} ;$ find
$A-C$
If ${N_a} = [an:n \in N\} ,$ then ${N_5} \cap {N_7} = $
If $A=\{3,5,7,9,11\}, B=\{7,9,11,13\}, C=\{11,13,15\}$ and $D=\{15,17\} ;$ find
$A \cap \left( {B \cup D} \right)$
Is it true that for any sets $\mathrm{A}$ and $\mathrm{B}, P(A) \cup P(B)=P(A \cup B) ?$ Justify your answer.