Q

# 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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