The **Principle of Inclusion and Exclusion (PIE)** is a way to calculate the number of elements that satisfy at least one of several given properties. If there are two sets, the principle of inclusion and exclusion states

\[ |A \cup B| = |A|+|B| - |A\cap B|.\]

If there are three sets, the principle of inclusion and exclusion states

\[ |A\cup B \cup C| = \\ |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|.\]

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