Proving PoSet of cross product

[PennState666]

Homework Statement

(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?

Homework Equations

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

The Attempt at a Solution

(Z, Q) and W, S) are reflexive, anti-symmetric, and transitive
STUMPED, HELP!

 

[micromass]

What do you need to prove for ZxW??

 

[PennState666]

that is it a partially ordered set

 

[micromass]

Yes, and what do you need to prove exactly??

 

[PennState666]

that (Z x W, I) is reflexive anti-symmetric, and transitive