The relation "congruence modulo $m$" is:

Let $A = \{-2, -1, 0, 1, 2, 3\}$. Let $R$ be a relation on $A$ defined by $x R y$ if and only if $y = \max \{x, 1\}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added to $R$ to make it reflexive and symmetric,respectively. Then $l + m + n$ is equal to

Let $R$ be a relation from $Q$ to $Q$ defined by $R = \{(a, b) : a, b \in Q \text{ and } a - b \in Z \}$. Show that $(a, a) \in R$ for all $a \in Q$.

$A$ relation $R$ on the set of natural numbers is defined as $\{(a, b) : |a - b| = 3\}$. Then $R$ is:

Let $H$ be the set of all houses in a village where each house is faced in one of the directions,East,West,North,South. Let $R = \{ (x,y) | (x,y) \in H \times H \text{ and } x, y \text{ are faced in same direction} \}$. Then the relation $R$ is

The void relation on a set $A$ is