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Chapter 3-1. Inclusion-Exclusion Principle

Higher category : 【Statistics】 Chapter 3. Probability Space  


1. Intersection and union relationship

2. Inclusion-exclusion principle



1. Intersection and union relationship

⑴ theorem 


drawing

⑵ induction


drawing



2. Inclusion-exclusion principle 

⑴ theorem


drawing

⑵ induction

by the intersection and union relationship, the following equation can be derived 


drawing

as a result, when the equation is established for n = k, it is also established for n = k+1

the intersection and union relationship shows the equation is established for n=2 

in conclusion, the inclusion-exclusion principle is established for all n ∈ ℕ



Input : 2019.06.27 11:33

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