Give an example of a relation. Which is Symmetric but neither reflexive nor transitive.
Give an example of a relation. Which is Symmetric but neither reflexive nor transitive.
Let $A=\{5,6,7\}$
Define a relation $R$ on $A$ as $R =\{(5,6),(6,5)\}$
Relation $R$ is not reflexive as $(5,5),\,(6,6),\,(7,7) \notin R$
Now, as $(5,6)\in R$ and also $(6,5) \in R , R$ is symmetric.
$\Rightarrow(5,6),\,(6,5) \in R,$ but $(5,5)\notin R$
$\therefore R$ is not transitive.
Hence, relation $R$ is symmetric but not reflexive or transitive.
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