Find the cardinal number of the following set $\{x: x\}$ is a natural number $\leq 30$ and is divisible by $7$ or $\{11\}$

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

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:

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

The domain of the function $f(x) = \frac{1}{1 + e^x}$ is

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements are true?