Contents Proving Equations and Inequalities 24 Recap 25 Exercises 25 5 Counterexample 25 Recap 27 Exercises 27 6 Boolean Algebra 27 More Operations 31 Recap 32 Exercises 32 Chapter 1 Self Test 34 1 Collections 37 7 Lists 37 Counting Two-Element Lists 37 Longer Lists 40 Recap 43 Exercises 43 8 Factorial 45 Much Ado About 0! 46 Product Notation 47 Recap 48 Exercises 48 9 Sets l:Introduction,Subsets 49 Equality of Sets 51 Subset 53 Counting Subsets 55 Power Set 57 Recap 57 Exercises 57 10 Quantifiers 58 There Is 58 For All 59 Negating Quantified Statements 60 Combining Quantifiers 61 Recap 62 Exercises 63 11 Sets ll:Operations 64 Union and Intersection 64 The Size of a Union 66 Difference and Symmetric Difference 68vi Contents Proving Equations and Inequalities 24 Recap 25 Exercises 25 5 Counterexample 25 Recap 27 Exercises 27 6 Boolean Algebra 27 More Operations 31 Recap 32 Exercises 32 Chapter 1 Self Test 34 2 Collections 37 7 Lists 37 Counting Two-Element Lists 37 Longer Lists 40 Recap 43 Exercises 43 8 Factorial 45 Much Ado About 0! 46 Product Notation 47 Recap 48 Exercises 48 9 Sets 1: Introduction, Subsets 49 Equality of Sets 51 Subset 53 Counting Subsets 55 Power Set 57 Recap 57 Exercises 57 10 Quantifiers 58 There Is 58 For All 59 Negating Quantified Statements 60 Combining Quantifiers 61 Recap 62 Exercises 63 11 Sets II: Operations 64 Union and Intersection 64 The Size of a Union 66 Difference and Symmetric Difference 68