Given totally ordered sets 0..n and 0..m with the ordinary \leq orders, consider the Cartesian product of these sets, with (a, b) \leq (c, d) \Leftrightarrow (a \leq c) \wedge (b \leq d). Draw the Hasse diagram showing the partial order relation.
I'm not really sure where to start with this problem, because the sets we're talking about here are infinite. I guess the root would be the empty set, then 0, etc., but how do you show it for 0..n and 0..m?