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PrefaceHow to Use This BookChapter 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 1.5Chapter 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 ThinkingChapter 4 Quantitative ThinkingChapter 5 Analytical ThinkingChapter 6 Thinking Through ApplicationsHints, Answers, and solutions to selected ExercisesSelected ReferencesIndexIndex of Symbols