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Math Help - Proving Theorem Help

  1. #1
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    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.
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  2. #2
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    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.
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  3. #3
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    Re: Proving Theorem Help

    Quote Originally Posted by gfbrd View Post
    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.
    Thanks from gfbrd
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  4. #4
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    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
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