Discrete Mathematics for Computer Science

Strong Form of Mathematical Induction 77 ting TrialFactor equal to 2. Because now Mod(n, TrialFactor) A 0 is FALSE, we call Prin ...

78 CHAPTER 1 Sets, Proof Templates, and Induction that could possibly contain the name. If the name is not on the middle page, t ...

Exercises 79 Solution. We start with FirstPage = 1 and LastPage = 521. MiddlePage = L(1 + 521)/2] = 261. Since Joe Smith should ...

80 CHAPTER 1 Sets, Proof Templates, and Induction 13. The terms of a sequence are given recursively as ao = 0, a 1 = 4, and a, = ...

Chapter Review 81 Challenge: There is a third principle related to induction, the Principle of Well- Ordering for the Natural N ...

82 CHAPTER 1 Sets, Proof Templates, and Induction 1.12.1 Terms, Theorems, Algorithms, and Templates 1.1 Summary TERMS algebraic ...

Chapter Review 83 Distributive Law for Intersection Distributive Law for Meet Distributive Law for Join Distributive Law for Uni ...

84 CHAPTER 1 Sets, Proof Templates, and Induction 1.10 Summary TERMS base cases prime numbers base step(s) recursion closed form ...

Chapter Review 85 Of 26 students who are either females or biology majors, there are 17 females and 23 biology majors. How many ...

86 CHAPTER 1 Sets, Proof Templates, and Induction A survey of reading habits was proposed for the city of Lewisburg. Let U be t ...

Chapter Review 87 duction but not the Principle of Mathematical Induction, that T' = N. Then, use that to show that every natura ...

88 CHAPTER 1 Sets, Proof Templates, and Induction (c) A simpler algorithm to calculate 1.00110°0 is to multiply 1000 copies of 1 ...

Formal Logic It is an old dream to write a formal, mathematical description of the laws of human thought. The goals are to ident ...

90 CHAPTER 2 Formal Logic A proposition is something that is either true or false; it is not both. "The cover of this book is pi ...

Introduction to Propositional Logic 91 Solution. (a) (p A -q) -- r. Since and and but usually both get translated as A, the diff ...

92 CHAPTER 2 Formal Logic As an example of using the truth table for A, suppose you know that both p and q are T. Look in the tr ...

Introduction to Propositional Logic 93 The formal definition of a formula is an inductive definition of a set of strings. The ba ...

94 CHAPTER 2 Formal Logic The theorem that follows is included because it is an example of an easy application of the Principle ...

Introduction to Propositional Logic 95 pvq p q Figure 2.2 Representation for p v q. To introduce the representation structure fo ...

96 CHAPTER 2 Formal Logic If 0p is a formula with expression tree To, then an expression tree for T(-O) is (0) I If 40 and * are ...