PrincipleOfInclusionExclusion.md (617B)
1 # Principle of Inclusion-Exclusion 2 3 Ch 8.3 Rosen 4 5 **Definition:** The principle of inclusion-exclusion is a principle used to count the number of elements in the union of a finite number of sets. 6 7 Consider: 8 9 $|A \cup B| = \text{ } ?$ 10 11 We know that all elements of A and all elements of B will be in the union, but there are some elements that may be in both. These are simply elements of $A \cap B$. As such we see: 12 13 $|A \cup B| = |A| + |B| - |A \cap B|$. 14 15 #### Theroem 16 17 I will not write this out, but it should be understood that this can be stated simply as only counting the intersection of sets one time overall.