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Equivalence relation ?

  1. Jan 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine whether the given relation is an equivalence relation on the set. Describe the partition arising from each equivalence relation:

    xRy in ℝ if x≥y

    2. Relevant equations

    Reflexive: for all x in X, x~x
    Symmetric: for all x,y in X, if x~y, then y~x
    Transitive: for all x,y,z in X, if x~y, and y~z, then x~z

    3. The attempt at a solution

    I showed that it's reflexive, because x≥x

    I'm kind of confused in regards to how to show that it's symmetric and transitive (if it is)?

    Any help is appreciated, thanks.
     
  2. jcsd
  3. Jan 17, 2012 #2
    The first thing i would do it's to try some value of x y and z to see if the property holds.
     
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