Let $A$ and $B$ be two sets,then $(A \cup B)' \cup (A' \cap B)$ is equal to

If $A = \{ x : x^2 - 5x + 6 = 0 \}, B = \{ 2, 4 \}, C = \{ 4, 5 \}$,then $A \times (B \cap C)$ is

The domain of the function $f(x) = \sqrt{2 - x} - \frac{1}{\sqrt{9 - x^2}}$ is:

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then

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

In a town with a population of $5000$,$3200$ people are egg-eaters,$2500$ are meat-eaters,and $1500$ eat both egg and meat. How many are pure vegetarians?