Equivalence Principle: A hint on how to start!! Hi, I have no idea where to start. 1. Statement Problem Let X be a non empty set with a equivalence relation ~ on it. Prove that for all x,y[itex]\in[/itex]X, [x]=[y] if and only if x~y. 2. Relevant equations For the Equivalence Relation to exist, it must be transitive, reflexive and symmetric. 3. The attempt at a solution I have no idea where to start. May be, ~ exists means that, x=y. But is self evident. How do I prove the "only If" part as well? Thank You.