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Reasoning:
An Introduction to Logic, Sets, and Functions
Elaine Rich, Alan Kaylor Cline
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Contents
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Front Matter
Colophon
Acknowledgements
Preface
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1
Introduction to Logical Thought
Setting the Stage
Statements and Truth Values
What Can Logical Statements Represent?
Valid Arguments and Proofs
2
Boolean Logic
Statements
Truth Table Definitions of Operators
Larger Logical Expressions
Boolean Expressions in Programming
Boolean Queries
English into Logic
Validity, Satisfiability, Contradiction and Counterexamples
More Boolean Operators
Boolean Logic in Circuit Design
3
Boolean Logic Proofs
What Is a Proof?
Boolean Logic Proofs Using Truth Tables
Boolean Identities
Boolean Inference Rules
Natural Deduction I
Natural Deduction II
Soundness and Completeness
4
Predicate Logic
Introduction, Predicates and Quantifiers
More on Using Predicate Logic
Translating to and from Predicate Logic Statements
Validity, Satisfiability, Contradiction and Counterexamples
5
Predicate Logic Proofs
Identities and Inference Rules for Predicate Logic
Creating Predicate Logic Proofs
Soundness/Completeness/Decidability
Appendices
6
Practice Representing Claims in Logic
Some Key Ideas
Converting Formal Claims
Converting Everyday Claims
7
English Into Logic: Issues and Solutions
Getting Off the Ground
We Must Overcome the Perils of English - Ambiguity
We Must Overcome the Perils of English - We Leave Out a Lot and Are Sloppy
Predicate Logic Doesn’t Solve All Our Representation and Reasoning Problems
Dichotomizing the Analog World
Extending the Logical Framework
8
A Richer Catalogue of Reasoning and Proof Techniques
Real Proofs
Direct Proofs
Proof by Contradiction
Proof by Example or Counterexample
Proof by Construction
Divide and Conquer
Invariants
Mathematical Induction I
Mathematical Induction II
Mathematical Induction III
Stronger and Weaker Claims
Empirical Induction
Everyday Reasoning
Appendix
Authored in PreTeXt
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Section
6.3
Converting Everyday Claims
6.3.1
Choosing Appropriate Predicates
