Addition principle
Counting principle in combinatorics / From Wikipedia, the free encyclopedia
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In combinatorics, the addition principle[1][2] or rule of sum[3][4] is a basic counting principle. Stated simply, it is the intuitive idea that if we have A number of ways of doing something and B number of ways of doing another thing and we can not do both at the same time, then there are ways to choose one of the actions.[3][1] In mathematical terms, the addition principle states that, for disjoint sets A and B, we have ,[2] provided that the intersection of the sets is without any elements.
The rule of sum is a fact about set theory,[5] as can be seen with the previously mentioned equation for the union of disjoint sets A and B being equal to |A| + |B|.[6]
The addition principle can be extended to several sets. If are pairwise disjoint sets, then we have:[1][2]
This statement can be proven from the addition principle by induction on n.[2]