# Q.10 Give an example of a relation.(i) Which is Symmetric but neither reflexive nor transitive.

Let

$A = \left \{ 1,2,3 \right \}$

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

$\left ( 1,1 \right ),\left ( 2,2 \right ),(3,3) \notin R$ so it is not reflexive.

$(1,2)\in R$   and  $(2,1)\in R$  so it is symmetric.

$(1,2)\in R \, and\, (2,1)\in R$  but  $(1,1)\notin R$ so it is not transitive.

Hence, symmetric but neither reflexive nor transitive.

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