Definition 4.4.1. Duality 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 \(\cup \to \cap\text{,}\) \(\cap \to \cup\text{,}\) \(\emptyset \to U\) , and \(U\to \emptyset\text{,}\) then the statement \(S^*\) is also true and it is called the dual of the statement \(S\text{.}\)