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Math Help - equivalence relation proof

  1. #1
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    equivalence relation proof

    Hi, I am stuck and need some help.

    Let G be a group. For x,y \in G, x \sim y iff x=y^{\pm 1}. Prove that \sim is an equivalence relation on G.

    Thanks for any help in advance.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: equivalence relation proof

    Quote Originally Posted by shelford View Post
    Let G be a group. For x,y \in G, x \sim y iff x=y^{\pm 1}. Prove that \sim is an equivalence relation on G.
    I suppose you meant x\sim y\Leftrightarrow (x=y)\;\vee \;(x=y^{-1}) . For example : Symmetric: If x\sim y then, x=y or x=y^{-1} . (i) If x=y then y=x i.e. y\sim x (ii) If x=y^{-1} then, taking inverses y=x^{-1} i.e. also y\sim x . Try the Reflexive and Transitive.
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