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

Q.10 Give an example of a relation.

(i) Which is Symmetric but neither reflexive nor transitive.

Answers (1)
S seema garhwal

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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