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Math Help - Equivalence relations help

  1. #1
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    Equivalence relations help

    Hi there,
    So I've just been given a revision sheet for my upcoming exams and theres just one question I have no idea how to answer.
    So here it is:

    Given the following relation R on the set of non-negative integers, test whether R satisfies each of the properties of an equivalence relation.
    R = {(x, y) : x ≥ y-1}

    Hopefully someone can help me out
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  2. #2
    Super Member girdav's Avatar
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    Re: Equivalence relations help

    Hint: look at the symmetry property.
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  3. #3
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    Re: Equivalence relations help

    more pointedly, clearly (3,1) is in R. is (1,3) in R as well?
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  4. #4
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    Re: Equivalence relations help

    Thanks for trying to help guys, but I still don't really understand.
    I'm just confused over the whole x ≥ y-1 bit I think, because every example my lecturer went through included a mod.
    Thanks anyway though.
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: Equivalence relations help

    Quote Originally Posted by mandarep View Post
    Thanks for trying to help guys, but I still don't really understand.
    What do you not understand? Do you agree the relation is not symmetric thus no equivalence relation?
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  6. #6
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    Re: Equivalence relations help

    Maybe it's the notation that's confusing you. R is a set of all pairs of positive integers that obeys the condition x ≥ y-1. The point (3,1) belongs to R, for R to be an equivalence relation (1,3) should also belong to R. Since it doesn't, we have a counter example that proves R is not an equivalence relation.

    edit: changed "equivalente" to "equivalence". I'm mixing english with portuguese here :P
    Last edited by diegzumillo; May 30th 2012 at 01:17 PM.
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