Give an example of a relation. Which is
Symmetric and transitive but not reflexive.

Question

Give an example of a relation. Which is Symmetric and transitive but not reflexive.

Philoid · Accepted Answer

Let A = {-7, -8}

Define a relation R on A as:

R = {(-7, -8), (-8, -7), (-7, -7)}

Relation R is not reflexive as (-8, -8) ∉ R

Relation R is symmetric as (-7, -8) ϵ R and (-8, -7) ϵ R

But it is seen that (-7, -8), (-8, -7) ϵ R.

Also, (-7, -7) ϵ R.

⇒ R is transitive.

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

Give an example of a relation. Which isSymmetric and transitive but not reflexive.