The middle overlaped part is the intersection of S1, S2 and S3.
∣ S 1 U S 2 U S 3 ∣ = ∣ S 1 ∣ + ∣ S 2 ∣ + ∣ S 3 ∣ − ∣ S 1 ∩ S 2 ∣ − ∣ S 2 ∩ S 3 ∣ − ∣ S 3 ∩ S 1 ∣ + ∣ S 1 ∩ S 2 ∩ S 3 ∣ |S1 U S2 U S3| = |S1| + |S2| + |S3| - |S1 ∩ S2| - |S2 ∩ S3| - |S3 ∩ S1| + |S1 ∩ S2 ∩ S3| ∣ S 1 U S 2 U S 3 ∣ = ∣ S 1 ∣ + ∣ S 2 ∣ + ∣ S 3 ∣ − ∣ S 1 ∩ S 2 ∣ − ∣ S 2 ∩ S 3 ∣ − ∣ S 3 ∩ S 1 ∣ + ∣ S 1 ∩ S 2 ∩ S 3 ∣įor visualizing this concept we shall be using the Venn diagram to analyse the visual representation of sets.Īs we see below, the three circles S1, S2 and S3 are all intersected by one another. Mathematically we can defined the principle of Inclusion and Exclusion as below:įor any two finite sets S1 and S2, which are subsets of a Universal set, then (S1-S2), (S2-S1) and (S1 ∩ S2) are the disjoint sets. This fundamental is the basis of the principle of Inclusion and Exclusion which states that to be able to compute the size of the union of multiple sets, we must always start by adding the sizes of these sets separately followed by subtracting the sizes of all the pair intersection of the sets, and then adding back the sizes of the intersection of triples then again subtracting the size of quadruples of the set, and continue up till all the intersections of the sets are covered. When studying combinatorics in mathematics which primarily deals with problems of selection, arrangement, and operation around a finite or discrete system we come across a unique way to access the cardinality of a union set. Inclusion and exclusion criteria increases the likelihood of producing reliable and reproducible results.
This module will explain the important combinatorial principle that is, inclusion-exclusion in the most simplified format with detailed examples.
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