If sets $A$ and $B$ are defined as follows:
$A = \{(x, y) : y = \frac{1}{x}, 0 \neq x \in R\}$
$B = \{(x, y) : y = -x, x \in R\}$,then

$A$ die is thrown. Describe the following events: $A$: a number less than $7$,$B$: a number greater than $7$. Find $A \cap B$.

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

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