In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation,it is sufficient,if $R$

Determine whether the following relation is reflexive,symmetric,and transitive:
Relation $R$ in the set $A$ of human beings in a town at a particular time is given by:
$R = \{(x, y) : x \text{ and } y \text{ live in the same locality}\}$

Which of the following is not correct for relation $R$ on the set of real numbers?

Let $A = \{1, 2, 3\}$. The number of relations on $A$ containing $(1, 2)$ and $(2, 3)$ which are reflexive and transitive but not symmetric is . . . . . . .

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

Let $P$ be the relation defined on the set of all real numbers such that $P = \{(a,b) : \sec^2 a - \tan^2 b = 1\}$. Then $P$ is