If $A = \{2, 3, 4, 8, 10\}, B = \{3, 4, 5, 10, 12\}, C = \{4, 5, 6, 12, 14\}$ then $(A \cap B) \cup (A \cap C)$ is equal to

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

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

If $A = \{ x:x$ is a natural number $\} ,B = \{ x:x$ is an even natural number $\} $ $C = \{ x:x$ is an odd natural number $\} $ and $D = \{ x:x$ is a prime number $\} ,$ find $B \cap C$

If $\mathrm{R}$ is the set of real numbers and $\mathrm{Q}$ is the set of rational numbers, then what is $\mathrm{R - Q} ?$

$A-(A-B)$ is 

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