Not Important - Inclusion and Exclusion Proof by Induction

# Not Important - Inclusion and Exclusion Proof by Induction...

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Proof of the inclusion-exclusion principle using mathematical induction Cornell ORIE 3500, Summer 2011 Note: this is a slight modifcation oF the document at http://www.math.lsa.umich.edu/~baik/Teaching/inclusion-exclusion.pdf 1 Mathematical induction Suppose that we want to prove a sequence oF statements A ( n ) , n = 1 , 2 . . . . ±or example, A ( n ) represents the statement that “the sum oF 1 , 2 , . . . , n is n ( n +1) 2 ”. Mathematical induction is a way to prove A ( n ) For all n in the Following two steps: (a) ±irst prove A (1). (b) Assuming that A ( n ) is true, we prove that A ( n + 1) is true. Since A (1) is proven to be true by step (a), step (b) shows that A (2) is true. Hence again by step (b), A (3) is true. Hence by (b) again, A (4) is true, and so on. Thus A ( n ) is true For all n. Try to prove that “the sum oF 1 , 2 , . . . , n is n ( n +1) 2 ” using mathematical induction.

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## This note was uploaded on 12/09/2011 for the course IMSE 0301 taught by Professor Song during the Spring '11 term at HKU.

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Not Important - Inclusion and Exclusion Proof by Induction...

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