In mathematics, PIE stands for Principle of Inclusion-Exclusion. This principle is used to calculate the probability or count of the union of multiple sets. It helps in determining the total number of elements in the union of sets by including the sizes of individual sets and excluding the sizes of their intersections.
For example, if you have two sets A and B, the Principle of Inclusion-Exclusion states that:
|A ∪ B| = |A| + |B| – |A ∩ B|
Here, |A ∪ B| represents the number of elements in the union of sets A and B, |A| and |B| represent the number of elements in sets A and B respectively, and |A ∩ B| represents the number of elements in the intersection of sets A and B.
This principle can be extended to more than two sets, where you alternately include and exclude the sizes of intersections of the sets.