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

In a group of $70$ people,$37$ like coffee,$52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

If $U = \{a, b, c, d, e, f\}$,$A = \{a, b, c\}$,$B = \{c, d, e, f\}$,and $C = \{c, d, e\}$,find $(A \cup B) \cup C$.

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?

The domain of the function $f(x) = \exp (\sqrt {5x - 3 - 2{x^2}} )$ is

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