Introduction

What This Section Establishes

This introductory section sets the stage for the appendix: it recalls the logical building blocks you already know from earlier classes and previews a systematic study of how to prove mathematical statements.

The Logical Toolkit You Already Have

• Statement: a sentence that is either true or false, but not both.
• Compound statement: a statement formed by joining two or more simple statements using connectives like "and", "or", "if...then", "if and only if".
• Negation: the opposite of a statement; the negation of $p$ is "not $p$", written $\sim p$.
• Converse: for a conditional "if $p$ then $q$" ($p \Rightarrow q$), its converse is "if $q$ then $p$" ($q \Rightarrow p$).
• Contrapositive: for $p \Rightarrow q$, its contrapositive is "if not $q$ then not $p$" ($\sim q \Rightarrow \sim p$).
• Axiom: a statement accepted as true without proof.
• Conjecture: a statement believed true but not yet proved.
• Theorem: a statement proved true using logical reasoning.
• Deductive reasoning: drawing a specific conclusion from general premises or axioms.

The Goal of This Appendix …