###### Definition4.4.1Duality Principle for Sets

Let \(S\) be any identity involving sets and the operations complement, intersection and union. If \(S*\) is obtained from \(S\) by making the substitutions \(\cup \to \cap\), \(\cap \to \cup\), \(\emptyset \to U\) , and \(U\to \emptyset\), then the statement \(S*\) is also true and it is called the dual of the statement \(S\).