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Discrete Mathematics and Combinatorics by T. Sengadir

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Chapter 5

Mathematical Induction, Principle of Inclusion and Exclusion, and Pigeon-hole Principle

Learning Objectives

On completing this chapter, you should be able to:

  • state the principle of mathematical induction

  • prove formulas that are valid for all n ∈ ℕ by using the principle of mathematical induction

  • state the principle of inclusion and exclusion

  • solve counting problems using the principle of inclusion and exclusion

  • state and prove the result on the number of functions from a finite set onto another finite set

  • state the pigeon-hole principle

  • solve simple counting problems using the pigeon-hole principle

Mathematical induction is a technique, which is used in proving statements that are valid for all nN. We are familiar with the ...

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