1. ## Proving Theorem Help

Hey I need help with this problem

Let R be an equivalence relation on S. For any 2 members x and y of S, define x y provided that x and y belong to the same member of S/R. Then x y if and only if xRy

I am hoping some one can guide me step by step to figure out this proof since I do not know how to even start this thanks.

2. ## Re: Proving Theorem Help

As far as I know, the notation S/R is not universally accepted when S is a just set and not, for example, a group or a ring. Nevertheless, my guess is that you don't know where to start because you don't know the definition of S/R used in your source.

3. ## Re: Proving Theorem Help

Originally Posted by gfbrd
Let R be an equivalence relation on S. For any 2 members x and y of S, define x y provided that x and y belong to the same member of S/R. Then x y if and only if xRy.
As far as I know, if we start with equivalence relation, $\mathcal{R}$, on $S$ then $S/\mathcal{R}$ is the collection of equivalence classes. It is a standard exercise to show that collection partitions the set $S$ and any partition determines an equivalence relation. That should be a theorem in your textbook.

4. ## Re: Proving Theorem Help

yea I didn't understood the definition before but after understanding it now, I figured it out.
Thanks a lot for your help