Introduction

In this topic we describe methods for constructing proofs. A proof is a valid argument that establishes the truth of a mathematical statement. The methods of proof discussed in this topic have many applications in computer science. These applications include verifying that computer programs are correct, establishing that operating systems are secure, making inferences in artificial intelligence, and so on.

In the first two sections in this of this topic we study methods of proofs such as direct proofs, indirect proofs, exhaustive proofs and proof by cases. We conclude by illustrating the proofs by mathematical induction and strong mathematical induction.