Venn Diagram Applet

How many distinct Venn diagrams can be formed using two subsets within a universe S? Are they all exhibited below?

S $\varphi$ A B Ac Bc A $\cap$ B Ac $\cap$ B A $\cap$ Bc Ac $\cap$ Bc A $\cup$ B Ac $\cup$ B A $\cup$ Bc Ac $\cup$ Bc (A $\cap$ B) $\cup$ (Ac $\cap$ Bc) (Ac $\cap$ B) $\cup$ (A $\cap$ Bc)

Description

In this applet, A and B are subsets of a universal set S. The list above gives the 16 different subsets of S that can be constructed from A and B using the basic set operations of union ($\cup$), intersection ($\cap$), and complement (${}^c$). The selected subset is colored red in the Venn diagram on the right.

(From zombie-page http://michaelshepperd.tripod.com/VennDiagramApplet/VennGame.html - I had to modify it to elimate popups, cookies, and other evils.... ael)