Question

Give an example for a relation which is reflexive symmetric but not transitive

Answer 1

➠ AnSwer :-

➝ Let us consider the relation R={(1,1),(2,2),(3,3),(1,3),(3,1),(2,3),(3,2)} on the set A={1,2,3}.

This relation is reflexive since (x,x)∈R, ∀x∈A.

Again this relation is symmetric since (x,y)∈R⇒(y,x)∈R, ∀x,y∈A.

But the relation is not transitive as (2,3)∈R,(3,1)∈R but (2,1) ∈R.