离散数学 英文版PDF电子书下载

1．Propositional Logic 1

1.1 Propositions and Connectives 2

1.2 Propositional WFF and Assignment 10

1.3 Propositional Equivalences 15

1.4 Disjunctive Normal Form 23

1.5 Functionally Complete Set of Logical Connectives 32

1.6 Rules of Inference 34

2．Predicate Logic 43

2.1 Predicates and Quantifiers 44

2.2 Well-Formed Formulas in Predicate Logic 53

2.3 Equivalent Formulas 60

2.4 Prenex Normal Form 67

2.5 Inference Rules in Predicate Calculus 71

3．Set Theory 80

3.1 Sets 80

3.2 Set Operations 85

3.3 Inclusion-Exclusion 92

4．Relations 98

4.1 Cartesian Products and Relations 98

4.2 Properties of Relations 103

4.3 Representing Relations 109

4.4 Closure of Relations 117

4.5 Equivalence Relations 129

4.6 Partial Orderings 136

5．Graphs 151

5.1 Graph Terminology 152

5.2 Representing Graphs and Graph Isomorphism 159

5.3 Subgraphs 167

5.4 Euler and Hamilton Paths 176

5.5 The Shortest-Path Problem 191

5.6 Planar Graphs 195

6．Trees 202

6.1 Basic Concepts 202

6.2 Roots and Orderings 205

6.3 Spanning Trees 214

7．Boolean Algebras 224

7.1 Basic Concepts 225

7.2 Boolean Functions 229

7.3 Logic Gates 232

7.4 Minimization of Circuits 234

Reference 242