The relation "congruence modulo $m$" is:

Let $X$ be a non-void set. If $\rho_1$ and $\rho_2$ are transitive relations on $X$, then which of the following is true?

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

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:

Let $A = \{2, 3, 6, 8, 9, 11\}$ and $B = \{1, 4, 5, 10, 15\}$. Let $R$ be a relation on $A \times B$ defined by $(a, b) R (c, d)$ if and only if $3ad - 7bc$ is an even integer. Then the relation $R$ is

Let $A = \{-2, -1, 0, 1, 2, 3, 4\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $2x + y \le 2$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric relations respectively. Then $l + m + n$ is equal to: