$A$ and $B$ are two subsets of set $S$ = $\{1,2,3,4\}$ such that $A\ \cup \ B$ = $S$ , then number of ordered pair of $(A, B)$ is 

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

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

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

$A \cap B$

If $A  \cap B = B$, then

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?

Let $A$ and $B$ be sets. If $A \cap X=B \cap X=\phi$ and $A \cup X=B \cup X$ for some set $X ,$ show that $A = B$

( Hints $A = A \cap (A \cup X),B = B \cap (B \cup X)$ and use Distributive law )