The relation "congruence modulo $m$" is
Reflexive only
Transitive only
Symmetric only
An equivalence relation
Let $R$ be a relation on the set $N$ of natural numbers defined by $nRm $$\Leftrightarrow$ $n$ is a factor of $m$ (i.e.,$ n|m$). Then $R$ is
Let $R_{1}$ and $R_{2}$ be two relations defined on $R$ by $a R _{1} b \Leftrightarrow a b \geq 0$ and $a R_{2} b \Leftrightarrow a \geq b$, then
Let $R_1$ be a relation defined by $R_1 =\{(a, b) | a \geq b, a, b \in R\}$ . Then $R_1$ is
If $R$ is a relation on the set $N$, defined by $\left\{ {\left( {x,y} \right);3x + 3y = 10} \right\}$
Statement $-1$ : $R$ is symmetric
Statement $-2$ : $R$ is reflexive
Statement $-3$ : $R$ is transitive, then thecorrect sequence of given statements is
(where $T$ means true and $F$ means false)
Let $R$ be a relation from $A = \{2,3,4,5\}$ to $B = \{3,6,7,10\}$ defined by $R = \{(a,b) |$ $a$ divides $b, a \in A, b \in B\}$, then number of elements in $R^{-1}$ will be-