viii CONTENTS CHAPTER 4 Logic and Propositional Calculus 70 4.1 Introduction 70 4.2 Propositions and Compound Statements 4.3 Basic Logical Operations 4.4 Propositions and Truth Tables 4.5 Tautologies and Contradictions 4.6 Logical Equivalence 4.7 Algebra of Propositions 4.8 Conditional and Biconditional Statements 4.9 Arguments 4.10 Propositional Functions,Quantifiers 4.11 Negation of Quantified Statements 012445567936 Solved Problems Supplementary Problems CHAPTER 5 Techniques of Counting 88 5.1 Introduction 5.2 Basic Counting Principles 5.3 Mathematical Functions 5.4 Permutations 5.5 Combinations 5.6 The Pigeonhole Principle 5.7 The Inclusion-Exclusion Principle 5.8 Tree Diagrams 88999459 Solved Problems Supplementary Problems 103 CHAPTER 6 Advanced Counting Techniques,Recursion 107 6.1 Introduction 107 6.2 Combinations with Repetitions 107 6.3 Ordered and Unordered Partitions 108 6.4 Inclusion-Exclusion Principle Revisited 108 6.5 Pigeonhole Principle Revisited 110 6.6 Recurrence Relations 111 6.7 Linear Recurrence Relations with Constant Coefficients 113 6.8 Solving Second-Order Homogeneous Linear Recurrence Relations 114 6.9 Solving General Homogeneous Linear Recurrence Relations 116 Solved Problems 118 Supplementary Problems 121 CHAPTER 7 Probability 123 7.1 Introduction 123 7.2 Sample Space and Events 123 7.3 Finite Probability Spaces 126 7.4 Conditional Probability 127 7.5 Independent Events 129 7.6 Independent Repeated Trials,Binomial Distribution 130 7.7 Random Variables 132viii CONTENTS CHAPTER 4 Logic and Propositional Calculus 70 4.1 Introduction 70 4.2 Propositions and Compound Statements 70 4.3 Basic Logical Operations 71 4.4 Propositions and Truth Tables 72 4.5 Tautologies and Contradictions 74 4.6 Logical Equivalence 74 4.7 Algebra of Propositions 75 4.8 Conditional and Biconditional Statements 75 4.9 Arguments 76 4.10 Propositional Functions, Quantifiers 77 4.11 Negation of Quantified Statements 79 Solved Problems 82 Supplementary Problems 86 CHAPTER 5 Techniques of Counting 88 5.1 Introduction 88 5.2 Basic Counting Principles 88 5.3 Mathematical Functions 89 5.4 Permutations 91 5.5 Combinations 93 5.6 The Pigeonhole Principle 94 5.7 The Inclusion–Exclusion Principle 95 5.8 Tree Diagrams 95 Solved Problems 96 Supplementary Problems 103 CHAPTER 6 Advanced Counting Techniques, Recursion 107 6.1 Introduction 107 6.2 Combinations with Repetitions 107 6.3 Ordered and Unordered Partitions 108 6.4 Inclusion–Exclusion Principle Revisited 108 6.5 Pigeonhole Principle Revisited 110 6.6 Recurrence Relations 111 6.7 Linear Recurrence Relations with Constant Coefficients 113 6.8 Solving Second-Order Homogeneous Linear Recurrence Relations 114 6.9 Solving General Homogeneous Linear Recurrence Relations 116 Solved Problems 118 Supplementary Problems 121 CHAPTER 7 Probability 123 7.1 Introduction 123 7.2 Sample Space and Events 123 7.3 Finite Probability Spaces 126 7.4 Conditional Probability 127 7.5 Independent Events 129 7.6 Independent Repeated Trials, Binomial Distribution 130 7.7 Random Variables 132