I have seen a similar problem (on equivalence classes) posted by you, before. Unfortunately I fail to understand the language. Can you tell me the definition of ""??the kernel relation of a mapping

I will be able to help you, if you do so...

Pick any element , then by hypothesis such that . But since the relation is symmetric we get .Let R be a relation on a set S such that R is symmetric and transitive and for each x c- S there is an element y c- S ( those are supposed to be the E rounded) such that x R y. Prove that R is an equivalence relation in other words prove that it is reflexive.

So and .... what do you think transitivity will do?