Let $A$ be a non-empty set of children in a family. The relation $R$ is defined on $A$ as '$x$ is a brother of $y$'. This relation is:

Let $A = \{1, 2, 3, \ldots, 20\}$. Let $R_1$ and $R_2$ be two relations on $A$ such that $R_1 = \{(a, b) : b \text{ is divisible by } a\}$ and $R_2 = \{(a, b) : a \text{ is an integral multiple of } b\}$. Then,the number of elements in $R_1 - R_2$ is equal to . . . . . . .

Let $Z$ be the set of all integers,$A = \{(x, y) \in Z \times Z : (x-2)^{2} + y^{2} \leq 4\}$,$B = \{(x, y) \in Z \times Z : x^{2} + y^{2} \leq 4\}$,and $C = \{(x, y) \in Z \times Z : (x-2)^{2} + (y-2)^{2} \leq 4\}$. If the total number of relations from $A \cap B$ to $A \cap C$ is $2^{p}$,then the value of $p$ is:

The relation $R$ is defined on the set of natural numbers as $\{(a, b) : a = 2b\}$. Then $R^{-1}$ is given by

The number of reflexive relations on a set with $4$ elements is equal to

If $R$ is a relation from set $A$ to set $B$ and $S$ is a relation from set $B$ to set $C$,then the relation $S \circ R$ is: