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Math Help - Questions about equivalance relations and equivalance classes. . .

  1. #1
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    Questions about equivalance relations and equivalance classes. . .

    http://i54.tinypic.com/1z2q1dl.png

    for the first question, can i assume the non-empty set A has more than one element, and say a = something and b = something to give example.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Questions about equivalance relations and equivalance classes. . .

    Quote Originally Posted by Dakaa View Post
    http://i54.tinypic.com/1z2q1dl.png

    for the first question, can i assume the non-empty set A has more than one element, and say a = something and b = something to give example.
    No, you can't. Choose for example A=\{0\} . A little help: Reflexive For all x\in\mathbb{Z} we have x-x=0 . But 0\in A because being A\neq \emptyset , choosing a\in A we have a-a=0\in A . Conclusion: xRx .

    Try the rest.
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  3. #3
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    Re: Questions about equivalance relations and equivalance classes. . .

    Quote Originally Posted by FernandoRevilla View Post
    No, you can't. Choose for example A=\{0\} . A little help: Reflexive For all x\in\mathbb{Z} we have x-x=0 . But 0\in A because being A\neq \emptyset , choosing a\in A we have a-a=0\in A . Conclusion: xRx .

    Try the rest.
    Yup, did the rest, now moving on to question 2.
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