Let $A$ be the non-void set of the children in a family. The relation '$x$ is a brother of $y$' on $A$ is

Let $R$ be the relation in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3)\}$. Choose the correct answer.

Among the relations $S = \{(a, b) : a, b \in R - \{0\}, 2 + \frac{a}{b} > 0\}$ and $T = \{(a, b) : a, b \in R, a^2 - b^2 \in Z\}$,which of the following is true?

$R = \{(\pi, \pi), (\pi^2, \pi^2), (\pi^3, \pi^3), (\pi, \pi^2), (\pi^2, \pi^3)\}$ is defined on the set $A = \{\pi, \pi^2, \pi^3\}$. Then $R$ is . . . . . . .

Let $R$ be a relation on a set $A$ such that $R = R^{-1}$. Then $R$ is:

Let $R$ be a relation on $N \times N$ defined by $(a, b) R (c, d)$ if and only if $ad(b-c) = bc(a-d)$. Then $R$ is