Malproposition: Suppose that ~ is a relation on a set A. If ~ is symmetric and transitive, then ~ is reflexive.
Proof: Let x,y belong to A. If x ~ y then y ~ x since ~ is symmetric. Now, x ~ y and y ~ x and since ~ is transitive, we can conclude x ~ x. Therefore ~ is reflexive.
Find the flaw in this reasoning.
(This one I succeeded in doing.)