> See also: > - [[Combinatorics]] > - [[Set Theory]] # Inclusion-Exclusion The **inclusion-exclusion principle** is a fundamental principle of combinatorics which provides *a systematic way of accounting for the overlapping elements in different sets*. It states that the size of the union of two or more sets is equal to the sum of their individual sizes minus the size of their possible intersections. ## Set Theory > [!note] **Inclusion-Exclusion of Two Sets** > $|A \cup B| = |A| + |B| - |A \cap B|$ > [!note] **Inclusion-Exclusion of Three Sets** > $|A \cup B \cup C| =$ > $|A| + |B| + |C| - |A \cap B| - |A\cap C| - |B \cap C| + |A \cap B \cap C|$ > [!summary] The Inclusion-Exclusion Principle >