For any two independent events $E_1$ and $E_2$,$P\{(E_1 \cup E_2) \cap (\bar{E}_1 \cap \bar{E}_2)\}$ is

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

If $A = \{1, 2, 3\}$,$B = \{3, 4\}$,and $C = \{4, 5, 6\}$,then find $A \cup (B \cap C)$.

If $A=\{3, 6, 9, 12, 15, 18, 21\}, B=\{4, 8, 12, 16, 20\}, C=\{2, 4, 6, 8, 10, 12, 14, 16\}, D=\{5, 10, 15, 20\};$ find $A-D$.

For any two sets $A$ and $B$, $A-(A-B)$ equals

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