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## 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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