Q.10 Give an example of a relation.

(iii) Which is Reflexive and symmetric but not transitive.

Answers (1)

Let 

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

Define a relation R on A as

R= \left \{ (1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2) \right \}

If   x\in A ,(x,x)\in R i.e.\left \{ (1,1),(2,2),(3,3)\right \} \in R. So it is reflexive.

If  x,y\in A  ,  (x,y)\in R   and  (y,x)\in R i.e.\left \{(1,2),(2,1),(2,3),(3,2) \right \}\in R. So it is symmetric.

(x,y)\in R  and (y,z)\in R  i.e. (1,2)\in R.  and (2,3)\in R 

But (1,3)\notin R So it is not transitive.

Hence, it  is Reflexive and symmetric but not transitive.

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