If $A, B$ and $C$ are any three sets, then $A - (B \cap C)$ is equal to

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 $X$ and $Y$ are two sets such that $n( X )=17, n( Y )=23$ and $n( X \cup Y )=38$
find $n( X \cap Y )$

Which of the following pairs of sets are disjoint 

$\{1,2,3,4\}$ and $\{ x:x$ is a natural number and $4\, \le \,x\, \le \,6\} $

If $A=\{3,5,7,9,11\}, B=\{7,9,11,13\}, C=\{11,13,15\}$ and $D=\{15,17\} ;$ find

$\left( {A \cup D} \right) \cap \left( {B \cup C} \right)$

Show that for any sets $\mathrm{A}$ and $\mathrm{B}$, $A=(A \cap B) \cup(A-B)$ and $A \cup(B-A)=(A \cup B).$