Book of Proof - Amazon S3

Contents
Preface
Introduction
vii
viii
I
Fundamentals
1. Sets 3
1.1. Introduction to Sets 3
1.2. The Cartesian Product 8
1.3. Subsets 11
1.4. Power Sets 14
1.5. Union, Intersection, Difference 17
1.6. Complement 19
1.7. Venn Diagrams 21
1.8. Indexed Sets 24
1.9. Sets that Are Number Systems 28
1.10. Russell’s Paradox 29
2. Logic 31
2.1. Statements 32
2.2. And, Or, Not 36
2.3. Conditional Statements 39
2.4. Biconditional Statements 42
2.5. Truth Tables for Statements 44
2.6. Logical Equivalence 47
2.7. Quantifiers 49
2.8. More on Conditional Statements 52
2.9. Translating English to Symbolic Logic 53
2.10. Negating Statements 55
2.11. Logical Inference 59
2.12. An Important Note 60
3. Counting 61
3.1. Counting Lists 61
3.2. Factorials 68
3.3. Counting Subsets 71
3.4. Pascal’s Triangle and the Binomial Theorem 76
3.5. Inclusion-Exclusion 79