Preface How to Use This Book Chapter 1 Logical Thinking 1.1 Formal Logic 1.1.1 Inquiry Problems 1.1.2 Connectives and Propositions 1.1.3 Truth Tables 1.1.4 Logical Equivalences Exercises 1.1 1.2 Propositional Logic 1.2.1 Tautologies and Contradictions 1.2.2 Derivation Rules 1.2.3 Proof Sequences 1.2.4 Forward-Backward Exercises 1.2 1.3 Predicate Logic 1.3.1 Predicates 1.3.2 Quantifiers 1.3.3 Translation 1.3.4 Negation 1.3.5 Two Common Constructions Exercises 1.3 1.4 Logic in Mathematics 1.4.1 The Role of Definitions in Mathematics 1.4.2 Other Types of Mathematical Statements 1.4.3 Counterexamples 1.4.4 Axiomatic Systems Exercises 1.4 1.5 Methods of Proof 1.5.1 Direct Proofs 1.5.2 Proof by Contraposition 1.5.3 Proof by Contradiction Exercises 1.5 Chapter 2 Relational Thinking 2.1 Graphs 2.1.1 Edges and Vertices 2.1.2 Terminology 2.1.3 Modeling Relationships with Graphs Exercises 2.1 2.2 Sets 2.2.1 Membership and Containment 2.2.2 New Sets from Old 2.2.3 Identities Exercises 2.2 2.3 Functions 2.3.1 Definition and Examples 2.3.2 One-to-One and Onto Functions 2.3.3 New Functions from Old Exercises 2.3 2.4 Relations and Equivalences
2.4.1 Definition and Examples 2.4.2 Graphs of Relations 2.4.3 Relations vs. Functions 2.4.4 Equivalence Relations 2.4.5 Modular Arithmetic Exercises 2.4 2.5 Partial Orderings 2.5.1 Definition and Examples 2.5.2 Hasse Diagrams 2.5.3 Topological Sorting 2.5.4 Isomorphisms 2.5.5 Boolean Algebras* Exercises 2.5 2.6 Graph Theory 2.6.1 Graphs: Formal Definitions …… Chapter 3 Recursive Thinking Chapter 4 Quantitative Thinking Chapter 5 Analytical Thinking Chapter 6 Thinking Through Applications Hints, Answers, and solutions to selected Exercises Selected References Index Index of Symbols
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