If $A = \{1, 2, 3\}$ and $B = \{3, 8\}$,then $(A \cup B) \times (A \cap B)$ is

Let $A = \{x : x \in R, |x| < 1\}$; $B = \{x : x \in R, |x - 1| \ge 1\}$ and $A \cup B = R - D$,then the set $D$ is

Suppose $A_1, A_2, A_3, \dots, A_{30}$ are $30$ sets each having $5$ elements and $B_1, B_2, \dots, B_n$ are $n$ sets each with $3$ elements. Let $\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^n B_j = S$ and each element of $S$ belongs to exactly $10$ of the $A_i$'s and exactly $9$ of the $B_j$'s. Then $n$ is equal to:

Let $A = \{ \theta : \sin \theta = \tan \theta \}$ and $B = \{ \theta : \cos \theta = 1 \}$ be two sets. Then

In a class,$50$ students play cricket,$20$ students play football and $10$ play both cricket and football. How many students play at least one of these two games?

If $A = \{a, d\}, B = \{b, c, e\}$ and $C = \{b, c, f\},$ then $A \times (B - C) =$