If $A$ and $B$ are sets, then $A \cap (B -A)$ is

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

$A \cap C$

Let $P=\{\theta: \sin \theta-\cos \theta=\sqrt{2} \cos \theta\}$ and $Q=\{\theta: \sin \theta+\cos \theta=\sqrt{2} \sin \theta\}$ be two sets. Then

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

$A \cap C$

Is it true that for any sets $\mathrm{A}$ and $\mathrm{B}, P(A) \cup P(B)=P(A \cup B) ?$ Justify your answer.

The shaded region in given figure is-