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

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

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

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

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

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

Using that for any sets $\mathrm{A}$ and $\mathrm{B},$

$A \cap(A \cup B)=A$

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

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