If $A=\{1,2,3\}, B=\{2,3,4\}, C=\{1,3,4\}$ and $D=\{2,4,5\},$ then $(A \times B) \cap (C \times D) =$

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 $U$).

If $A = \{1, 2, 4\}, B = \{2, 4, 5\}, C = \{2, 5\},$ then $(A - B) \times (B - C)$ is

In a class of $140$ students numbered $1$ to $140$,all even-numbered students opted for the Mathematics course,those whose number is divisible by $3$ opted for the Physics course,and those whose number is divisible by $5$ opted for the Chemistry course. The number of students who did not opt for any of the three courses is:

The domain of the function $\sqrt{\log(x^2 - 6x + 6)}$ is

Given two finite sets $A$ and $B$ such that $n(A) = 2$ and $n(B) = 3$. Then,the total number of relations from $A$ to $B$ is: