Introduction

Mathematics is a subject built on precision, and that precision comes from proof. A proof, in turn, is only as good as the reasoning behind it — and the formal study of correct reasoning is what we call logic. The very word "logic" traces back to the Greek term logos, meaning "reason." It was the Greek philosopher Aristotle who first turned reasoning into a systematic discipline, laying the foundations of classical logic. Centuries later, the English mathematician George Boole (1815–1864) reshaped logic into a mathematical framework — what we now call symbolic or Boolean logic — and it is this mathematical form of logic that this chapter develops.

We normally communicate our thoughts through language, and language is built out of sentences. But not every sentence is useful for logical reasoning — many sentences are questions, commands, or exclamations that cannot be judged true or false. Logic instead works with a special, restricted class of sentences called statements, and the rest of this chapter is devoted to understanding what a statement is, how statements combine, and how their truth or falsity can be tracked and computed.