# Give an example of a relation. Which isReflexive and symmetric but not transitive.

Let us take A = {2,4,6}

Define a relation R on A as:

A = {(2,2), (4,4), (6,6), (2,4), (4,2), (4,6), (6,4)}

Relation of R is reflexive as for every a ϵ A,

(a,a) ϵ R

(2,2), (4,4), (6,6) ϵ R,

Relation R is symmetric as (a,b) ϵ R

(b,a) ϵ R for all a ,b ϵ R

And Relation R is not transitive as (2,4), (4,6) ϵ R,

but (2,6) R

Therefore, relation R is reflexive and symmetric but not transitive.

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