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How to prove that R is equivalence relation

  1. Feb 7, 2013 #1
    1. The problem statement, all variables and given/known data
    let X = {1,2,3,..,10} define a relation R on X x X by (a,b)R(c,d) if ad=bc. show that R is an equivalence relation on X x X.


    2. Relevant equations



    3. The attempt at a solution

    I think that the R have to be reflexive (because ad=bc). Eg. one of the subset is (1,1) which satisfy ad=bc, and reflexive. However, I don't know how to prove that R is symmetric, and transitive? thx
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 7, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    R is symmetric if (a,b)R(c,d) if and only if (c,d)R(a,b). Write out what both of those conditions mean in terms of your relation. Same idea for transitive.
     
  4. Feb 8, 2013 #3
    Got it. thx :D
     
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