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Equivalence relations

  1. Feb 20, 2008 #1
    1. The problem statement, all variables and given/known data

    Let S be the set of integers. If a,b[tex]\in[/tex] S, define aRb if ab[tex]\geq[/tex]0. Is R an equivalence relation on S?

    2. Relevant equations



    3. The attempt at a solution

    Def: aRb=bRa [tex]\rightarrow[/tex] ab=ba
    assume that aRb and bRc [tex]\Rightarrow[/tex] aRc
    a=b and b=c
    since a=b, the substitute a in for b to get a=c


    I don't know where to go from here.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 20, 2008 #2

    quasar987

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    You must check 3 things:

    1) That aRa (reflexivity)
    2) That aRb implies bRa (symetry)
    3) That aRb and bRc implies aRc (transitivity)
     
  4. Feb 20, 2008 #3
    So what I have done so far answers the first part of the question?
     
  5. Feb 20, 2008 #4

    quasar987

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    But you haven't explained anything.

    1) Why does aRa for every integer a??
     
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