Give an example of a relation. Which is Reflexive and symmetric but not transitive.
Give an example of a relation. Which is Reflexive and symmetric but not transitive.
Let $A=\{4,6,8\}$
Define a relation $R$ on $A$ as
$A=\{(4,4),\,(6,6),\,(8,8),\,(4,6),\,(6,4),\,(6,8),\,(8,6)\}$
Relation $R$ is reflexive since for every $a \in A,\,(a, \,a) \in R$
i.e., $\{(4,4),(6,6),(8,8)\}\in R$
Relation $R$ is symmetric since $(a, \,b) \in R \Rightarrow(b, a) \in R$ for all $a, \,b \in R$
Relation $R$ is not transitive since $(4,6),(6,8) \in R,$ but $(4,8)\notin R$
Hence, relation $R$ is reflexive and symmetric but not transitive.
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