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Partial order relations

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data
    Are these two relations reflexive, antisymmetric, transitive?

    1. (w,x)<=(y,z) iff w+x <= y+z

    2. (w,x)<=(y,z) iff w+x <= y+z AND w<y

    2. Relevant equations



    3. The attempt at a solution

    1. reflexive - yes; antisymmetric - no; transitive - yes;

    2. reflexive - yes; antisymmetric - yes; transitive - yes;
     
  2. jcsd
  3. Dec 1, 2011 #2

    lanedance

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    would you say the second is reflexive?
     
  4. Dec 1, 2011 #3
    With the way I wrote it no. But I actually made a typo, it should be w+x <= y+z AND w<=y. So I'd say yes
     
  5. Dec 1, 2011 #4

    lanedance

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    ok, would that change anything else?
     
  6. Dec 1, 2011 #5
    No, I think #2 would still be antisymmetric and transitive
     
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