The set $A = \{ x: x \in R, x^2 = 16 \text{ and } 2x = 6 \}$ equals

If $n$ is an integer,the domain of the function $\sqrt{\sin 2x}$ is

If $n(U) = 600$,$n(A) = 100$,$n(B) = 200$,and $n(A \cap B) = 50$,then $n(\bar{A} \cap \bar{B})$ is (where $U$ is the universal set and $A$ and $B$ are subsets of $U$).

Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{2, 3, 6, 7\}$. Then the number of elements in $(A \times B) \cap (B \times A)$ is

Which of the following sets is finite?

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?