Let $A = \{ 2,\,4,\,6,\,8\} $. $A$ relation $R$ on $A$ is defined by $R = \{ (2,\,4),\,(4,\,2),\,(4,\,6),\,(6,\,4)\} $. Then $R$ is
Anti-symmetric
Reflexive
Symmetric
Transitive
The number of relations, on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is
The relation $R$ defined in $N$ as $aRb \Leftrightarrow b$ is divisible by $a$ 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)
If $A = \left\{ {1,2,3,......m} \right\},$ then total number of reflexive relations that can be defined from $A \to A$ is
Show that the relation $\mathrm{R}$ in the set $\mathrm{Z}$ of integers given by $\mathrm{R} =\{(\mathrm{a}, \mathrm{b}): 2$ divides $\mathrm{a}-\mathrm{b}\}$ is an equivalence relation.