Show that the relation $R$ in the set $\{1,2,3\}$ given by $R =\{(1,1),\,(2,2),$ $(3,3)$, $(1,2)$, $(2,3)\}$ is reflexive but neither symmetric nor transitive.
Show that the relation $R$ in the set $\{1,2,3\}$ given by $R =\{(1,1),\,(2,2),$ $(3,3)$, $(1,2)$, $(2,3)\}$ is reflexive but neither symmetric nor transitive.
$R$ is reflexive, since $(1,1),\,(2,2)$ and $(3,3)$ lie in $R$. Also, $R$ is not symmetric, as $(1,2)$ $\in R$ but $(2,1)$ $\notin R$. Similarly, $R$ is not transitive, as $(1,2)$ $\in R$ and $(2,3)$ $\in R$ but $(1,3)$ $\notin R$.
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- [JEE MAIN 2023]
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