Contents To the Student xv How to Read a Mathematics Book xvi Exercises xvii To the Instructor xix Audience and Prerequisites xix Topics Covered and Navigating the Sections Xix Sample Course Outlines Special Features xxi What's New in This Second Edition xxiii Acknowledgments XXV This New Edition XXV From the First Edition XXV 1 Fundamentals 1 1 Joy 1 Why?1 The Agony and the Ecstasy 2 Exercise 2 2 Definition 2 Recap 5 Exercises 5 3 Theorem 8 The Nature of Truth 8 If-Then 9 If and Only If 11 And,Or,and Not 12 What Theorems Are Called 13 Vacuous Truth 14 Recap 14 Exercises 15 4 Proof 16 A More Involved Proof 20 Proving If-and-Only-If Theorems 22Contents To the Student xv How to Read a Mathematics Book xvi Exercises xvii To the Instructor xix Audience and Prerequisites xix Topics Covered and Navigating the Sections xix Sample Course Outlines xxi Special Features xxi What's New in This Second Edition xxiii Acknowledgments xxv This New Edition xxv From the First Edition xxv 1 Fundamentals 1 Joy 1 Why? 1 The Agony and the Ecstasy 2 Exercise 2 2 Definition 2 Recap 5 Exercises 5 3 Theorem 8 The Nature of Truth 8 If-Then 9 If and Only If 11 And, Or, and Not 12 What Theorems Are Called 13 Vacuous Truth 14 Recap 14 Exercises 15 4 Proof 16 A More Involved Proof 20 1 Proving If-and-Only-If Theorems 22 v