mathematical concepts

1) discuss “Principle of Mathematical Induction”
Describe in your own words, the “Principle of Mathematical Induction”. Show an example of its usage. Please avoid previously covered examples.
2) discuss the terminology used in “Relations and Functions”.
Using examples, in your words please describe relations and functions and the terminology used in understanding these.

3) through examples, please explain and show your understanding of “Pigeon hole Principle” discussed in section 5.5 of the text.