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Give an example of a relation. Which is Symmetric and transitive but not reflexive.

Q.10 Give an example of a relation.

(v) Which is Symmetric and transitive but not reflexive.

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Let there be a relation A in R

A= \left \{ 1,2 \right \}

R=\left \{ (1,2),(2,1),(2,2)\right \}

(1,1)\notin R  So R is not reflexive.

We can see  (1,2)\in R  and  (2,1)\in R 

So it is symmetric.

Let (1,2)\in R     and  (2,1)\in R  

Also  (2,2)\in R

Hence, it is transitive.

Thus, it  Symmetric and transitive but not reflexive.

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