Question

3. Prove that the relation R in the set {1,2,3} given by R= {(1, 2), (2, 1), (2,3)} is symmetric but neither reflexive nor transitive.

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Answer 1

Answer:

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Step-by-step explanation:

Set ={1,2,3}

R={(1,2)(2,1)}

If relation is reflexive.

then (a,a) ϵ R for all a ϵ {1,2,3}

as (1,1) ∈

/

R

so , R is not reflexive

If relation is symmetric

then (a, b) & (b, a) ϵ R

Here (1,2) & (2,1) ϵ R

So, R is symmetric

If relation is transitive

then (a ,b) ϵ R & (b,c) ϵ r → (a,c) ϵR

Here (1, 2) & (2, 1) ϵ R but (1,1) ∈

So, R is not transitive.