Write the set $\{ x : x \text{ is a positive integer and } x^2 < 40 \}$ in the roster form.

In this question,all integers are represented in base $10$. Consider the set $E$ of positive integers $n$ having the property that when any nonzero digit $d \in \{1, 2, \dots, 9\}$ is written to the right of $n$,the resulting number is divisible by $d$. Let $N$ be the smallest element of $E$. The product of the digits of $N$ is:

Examine whether the following statement is true or false:
$\{a\} \in \{a, b, c\}$

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

If $A, B,$ and $C$ are three sets,then $A \cap (B \cup C) =$

Let $a > 0, a \neq 1$. Then,the set $S$ of all positive real numbers $b$ satisfying $(1+a^2)(1+b^2) = 4ab$ is