Preface xiii
1 Logic 11.1 Formal Logic 1
1.2 Basic Logical Strategies 6
1.3 The Direct Argument 10
1.4 More Argument Forms 12
1.5 Proof By Contradiction 15
1.6 Exercises 23
2 Sets 252.1 Set Notation 25
2.2 Predicates 26
2.3 Subsets 28
2.4 Union and Intersection 30
2.5 Exercises 32
3 Venn Diagrams 353.1 Inclusion/Exclusion Principle 35
3.2 Two Circle Venn Diagrams 37
3.3 Three Square Venn Diagrams 42
3.4 Exercises 50
4 Multiplication Principle 554.1 What is the Principle? 55
4.2 Exercises 60
5 Permutations 635.1 Some Special Numbers 64
5.2 Permutations Problems 65
5.3 Exercises 68
6 Combinations 696.1 Some Special Numbers 69
6.2 Combination Problems 70
6.3 Exercises 74
7 Problems Combining Techniques 777.1 Significant Order 77
7.2 Order Not Significant 78
7.3 Exercises 83
8 Arrangement Problems 858.1 Examples of Arrangements 86
8.2 Exercises 91
9 At Least, At Most, and Or 939.1 Counting With Or 93
9.2 At Least, At Most 98
9.3 Exercises 102
10 Complement Counting 10310.1 The Complement Formula 103
10.2 A New View of ?At Least? 105
10.3 Exercises 109
11 Advanced Permutations 11111.1 Venn Diagrams and Permutations 111
11.2 Exercises 120
12 Advanced Combinations 12512.1 Venn Diagrams and Combinations 125
12.2 Exercises 131
13 Poker and Counting 13313.1 Warm Up Problems 133
13.2 Poker Hands 135
13.3 Jacks or Better 141
13.4 Exercises 143
14 Advanced Counting 14514.1 Indistinguishable Objects 145
14.2 Circular Permutations 148
14.3 Bracelets 151
14.4 Exercises 155
15 Algebra and Counting 15715.1 The Binomial Theorem 157
15.2 Identities 160
15.3 Exercises 165
16 Derangements 16716.1 Fixed Point Theorems 168
16.2 His Own Coat 173
16.3 Exercises 174
17 Probability Vocabulary 17517.1 Vocabulary 175
18 Equally Likely Outcomes 18118.1 Exercises 188
19 Probability Trees 18919.1 Tree Diagrams 189
19.2 Exercises 198
20 Independent Events 19920.1 Independence 199
20.2 Logical Consequences of Influence 202
20.3 Exercises 206
21 Sequences and Probability 20921.1 Sequences of Events 209
21.2 Exercises 215
22 Conditional Probability 21722.1 What Does Conditional Mean? 217
22.2 Exercises 223
23 Bayes? Theorem 22523.1 The Theorem 225
23.2 Exercises 230
24 Statistics 23124.1 Introduction 231
24.2 Probability is not Statistics 231
24.3 Conversational Probability 232
24.4 Conditional Statistics 239
24.5 The Mean 241
24.6 Median 242
24.7 Randomness 244
25 Linear Programming 24925.1 Continuous Variables 249
25.2 Discrete Variables 254
25.3 Incorrectly Applied Rules 258
26 Subjective Truth 261Bibliography 267
Index 269
THEODORE G. FATICONI, PhD, is Professor in the Departmentof Mathematics at Fordham University. His professional experienceincludes forty research papers in peer-reviewed journals and fortylectures on his research to colleagues.
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