Introduction

The rules of logic give precise meaning to mathematical statements. These rules are used to distinguish between valid and invalid mathematical arguments. Thus it is of course very important to start our study of discrete mathematics with an introduction to mathematical logic.

Besides the importance of logic in understanding mathematical proofs, logic has numerous applications to computer sciences. These rules are used in the design of computer circuits, the construction of computer programs, the verification of the correctness of programs, and in many other ways.

This topic consists of three sections. In the first section we introduce the notion of a proposition, the negation of a proposition, and the truth values of compound propositions. We prove the equivalence of some important laws of logic. In the second section of this chapter we study quantifiers and nested quantifiers. In the third section we study rules of inferences and we explain how to use rules of inferences to prove validity of arguments.