Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation $R$ in the set $A$ of human beings in a town at a particular time given by

$R =\{(x, y): x$ and $y$ live in the same locality $\}$

Let $R$ and $S$ be two equivalence relations on a set $A$. Then

The relation $R= \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$ on set $A = \{1, 2, 3\}$ is

$R$ is a relation over the set of real numbers and it is given by $nm \ge 0$. Then $R$ is

The void relation on a set $A$ is