こんな問題もありました！是非お願いします長いです！

Let X be a non-empty set and 〜　a relation in X. The following purports to be a proof
of the statement that if this relation is symmeric and transitive, then it is necessarily
reflexive : x〜y⇒y〜x; x〜y and y〜x⇒x〜x; therefore x〜x for every x. In view of
Problem 5f, this cannot be a valid proof. What is the flaw in the reasoning?

5f=Give an example of relation which is symmetric and transitive but not reflexive.