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

Question

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

Philoid · Accepted Answer

Let A = {3,4,5}

Define a relation R on A as R = {(3,4), (4,3)}

Relation R is not reflexive as (3,3), (4,4) and (5,5) ∉ R.

Now, as (3,4) ϵ R and also (4,3) ϵ R,

R is symmetric.

⇒ (3,4), (4,3) ϵ R, but (3,3) ∉ R

⇒ R is not transitive.

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

Give an example of a relation. Which isSymmetric but neither reflexive nor transitive.