Give an example of a relation. Which is Symmetric but neither reflexive nor transitive.

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1.Relation and Function

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Give an example of a relation. Which is Symmetric but neither reflexive nor transitive.

Option A

Option B

Option C

Option D

Solution

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.

Standard 12

Mathematics

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