To the fifth Edition
This new edition continues the evolution of the text as an introduction to the foundation topics of logic, set , relations, and functions, explanations, explanations, examples, and exercises appear thoughout this edition of the text. To help make the introduction to elementary proofs techniques more manageable. We have created separate sections on direct proofs and proofs by contrapositive and contradiction. Many of the "Proofs to Grade" exercises have been reworked to provide more explanation or to present errors that are commonly observed in attempt at proof writing.

Chapter 1 Logic and Proofs
Chapter 2 Set Theory
Chapter 3 Relations
Chapter 4 Functions
Chapter 5 Cardinality
Chapter 6 Concepts of Algebra: Groups
Chapter 7 Concepts of Analysis: Completeness of the Real Numbers