Discrete Mathematics

Chapter 1

SYMBOLIC LOGIC

1.1 INTRODUCTION TO LOGIC

Logic is essentially the study of arguments. For example, someone may say, suppose A and B are true, can we conclude that C is true? Logic provides rules by which we can conclude that certain things are true given other things are true. Here is a simple example: A tells B that “if it rains, then the grass will get wet. It is raining”; B can then conclude that the grass is wet, if what A has told B is true. Logic provides a mechanism for showing arguments like this to be true or false.

The section starts by showing how to translate English sentences into a logical form, specifically into something called “propositions”. In fact, our study of logic starts with propositional calculus.

Propositional ...