Relations

Question

Proof that a relation which is symmetric and transitive, need not be reflexive relation.

Answer 1

Prove it by contradiction.

let consider that if relation $R$ is symmetric and transitive then it must be reflexive. 

Now consider $R$ as an empty relation. Now Empty relation is symmetric and transitive but not reflexive. Read here. 

Hence our assumption is wrong. 

Hence A relation which is symmetric and transitive, need not be reflexive.