# Product sets

If *X *and* Y *are sets, then * X *´*
Y* is a new set called a product set. It is defined by:

*X *´*
Y* = {(*x*,*y*) | *x* ∈
*X*, *y* ∈ *Y* }

That is, *X *´*
Y* is the set of tuples formed from elements of *X* and elements
of *Y*. Pictorial examples:

On the left, *X* is a vertical span, and *Y* is a horizontal span.
The product set is the collection of points in the rectangular region formed
by these two spans.

On the right, *X* is a vertical span, and *Y* is a set of discrete
points arranged horizontally. The product set is the collection of points in
the vertical lines.