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Math Help - Equivalence Relation Identification

  1. #1
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    Equivalence Relation Identification

    Are the following equivalence relations?

    x~y if x < y NO

    x~y if x <= y NO

    x~y if |x| = |y| YES

    x~y if x =/ y NO

    x~y if xy > 0 NO

    x~y if x|y or y|x YES

    What are the equivalence classes for the ones that are? Thanks!
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  2. #2
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    Quote Originally Posted by jstarks44444 View Post
    Are the following equivalence relations?

    x~y if x < y NO

    x~y if x <= y NO

    x~y if |x| = |y| YES

    x~y if x =/ y NO

    x~y if xy > 0 NO

    x~y if x|y or y|x YES

    What are the equivalence classes for the ones that are? Thanks!
    Do x,y\in\mathbb{Z}\text{?}
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