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Proving PoSet of cross product

  1. Dec 2, 2011 #1
    1. The problem statement, all variables and given/known data
    (Z, Q) and (W, S) are two partially ordered sets. There is a relation I on Z x W (Z cross W) that is defined... for all (a, b), (c, d) in Z x W, set (a, b) I (c, d) if and only if aQc and bSd. How does one prove that (Z x W, I) is a partially ordered set?


    2. Relevant equations

    Partially ordered sets are reflexive, anti-symmetric, and transitive.

    3. The attempt at a solution
    (Z, Q) and W, S) are reflexive, anti-symmetric, and transitive
    STUMPED, HELP!!!!!
     
  2. jcsd
  3. Dec 3, 2011 #2

    micromass

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    What do you need to prove for ZxW??
     
  4. Dec 3, 2011 #3
    that is it a partially ordered set
     
  5. Dec 3, 2011 #4

    micromass

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    Yes, and what do you need to prove exactly??
     
  6. Dec 5, 2011 #5
    that (Z x W, I) is reflexive anti-symmetric, and transitive
     
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