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 $X = \{4^n - 3n - 1 : n \in N\}$ and $Y = \{9(n - 1) : n \in N\}$,then $X \cap Y =$

If $A = \{1, 2, 3, 4\}$,$B = \{3, 4, 5, 6\}$,$C = \{5, 6, 7, 8\}$,and $D = \{7, 8, 9, 10\}$,find $B \cup C \cup D$.

Let $A = \{a, b, c\}, B = \{b, c, d\}, C = \{a, b, d, e\}$. Then $A \cap (B \cup C)$ is:

The shaded region in the Venn diagram can be represented by which of the following?

Consider the following relations:
$(1) \, A - B = A - (A \cap B)$
$(2) \, A = (A \cap B) \cup (A - B)$
$(3) \, A - (B \cup C) = (A - B) \cup (A - C)$
Which of these is/are correct?