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Math Help - [SOLVED] Equivalence Relation

  1. #1
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    [SOLVED] Equivalence Relation

    a,b,c\in\mathbb{Z} a\sim b iff. 2|(a+b)

    This is suppose to be an equivalence relation; however, when I did the transitivity, it didn't work out.

    reflexive: a\sim a
    2|(a+a)\rightarrow 2p=2a Yes reflexive.

    symmetric: a\sim b then b\sim a
    2|(a+b) \rightarrow 2n=a+b\rightarrow 2n=b+a\rightarrow 2n|(b+a)

    Thus, b\sim a

    transitive:
    a\sim b, b\sim c, then a\sim c
    a\sim b\rightarrow 2m=a+b
    b\sim c\rightarrow 2r=b+c

    Subtracted the equations:
    2(m-r)=a-c

    Again, I am supposed to conclude transitive what is going wrong here?
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  2. #2
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    So how about a+2b+c=2m+2n\implies a+c=2(m+n-b)?
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