- \(\emptyset\)
- \(A\)
- \(B\)
- \(A^c\)
- \(B^c\)
- \(A \cap B\)
- \(A \cup B\)
- \(A \cap B^c\)
- \(B \cap A^c\)
- \(A \cup B^c\)
- \(B \cup A^c\)
- \(A^c \cap B^c\)
- \(A^c \cup B^c\)
- \((A \cap B^c) \cup (B \cap A^c)\)
- \((A \cap B) \cup (A^c \cap B^c)\)
- \(S\)

In this app, \(A\) 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, intersection, and complement. Click on a subset in the list to see the selected subset colored blue in the Venn diagram on the right. Alternately, you can click variously on the four disjoint regions in the picture on the right; clicking on an unselected region selects the region, while clicking on a selected region unselects the region. The subset constructed in this way is checked in the list box on the left.