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Math Help - Equivilence relations, Reflexivity

  1. #1
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    Equivilence relations, Reflexivity

    Hi all,

    I am given two relations and asked to prove which one is an equivilence relation for integers.

    They are;

    x~ _{1}y if x^{2}+y^{2} is divisible by 5.

    x~ _{2}y if x^{2}-y^{2} is divisible by 4.

    The problem i'm having is finding which one has reflexivity.

    for example, 1^{2}+1^{2}=2 which is not divisble by 5.

    and, k^{2}-k^{2}=0 for all k

    So, is zero divisible by 4?
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  2. #2
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    Re: Equivilence relations, Reflexivity

    Think I've got,

    zero divided by any integer is zero, but since zero is also an integer then it holds.

    Am I right?
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  3. #3
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    Re: Equivilence relations, Reflexivity

    You are right. Zero is divisible by any nonzero integer.
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  4. #4
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    Re: Equivilence relations, Reflexivity

    Quote Originally Posted by Srengam View Post
    Think I've got,
    zero divided by any nonzero integer is zero, but since zero is also an integer then it holds.
    Am I right?
    That is correct.
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