Nikos Drakos and Ross Moore's "Cartesian Product of Sets"
Read this page, paying special attention to the proof of proposition 3.3.3 at the end of the page. There is a nice proof of this using characteristic functions, which you will be asked to produce later in the course.
Click http://web.archive.org/web/20160311040106/http://ndp.jct.ac.il/tutorials/discrete/node28.html link to open resource.