1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    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
    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook