Let
and
with
and
Let the ordering on A and B be
and
respectively and let an ordering on
be given by
We need to determine when
where
and
The elements of A times B can be ordered with respect to the sets A and B.
In fact, finite sets can be ordered in many different ways. Elements ofcan be arranged in 12! different ways, and this is equal to the number of ways in which elements ofcan be ordered.