Bridge to Abstract Mathematics: Mathematical Proof and Structures

3.4 QUANTIFICATION OF PROPOSITIONAL FUNCTIONS IN SEVERAL VARIABLES IOQ EXAMPLE 1 Let t(x, y) represent the inequality x S y with ...

104 LOGIC, PART II: THE PREDICATE CALCULUS Chapter 3 Solution Let U, x U, be the domain of discourse for p(x, y), and let P G U, ...

3.4 QUANTIFICATION OF PROPOSITIONAL FUNCTIONS IN SEVERAL VARIABLES 105 y whose existence is being asserted, although not necessa ...

106 LOGIC, PART II: THE PREDICATE CALCULUS Chapter 3 (c) may be either true or false. What does (c) assert? It says that there i ...

3.4 QUANTIFICATION OF PROPOSITIONAL FUNCTIONS IN SEVERAL VARIABLES 107 NEGATION OF PROPOSITIONAL FUNCTIONS IN SEVERAL VARIABLES ...

LOGIC, PART 11: THE PREDICATE CALCULUS Chapter 3 Exercises Given a propositional function p(w, x, y, z) over a domain of disc ...

3.4 QUANTIFICATION OF PROPOSITIONAL FUNCTIONS IN SEVERAL VARIABLES 109 (c) In parts (ii) through (v) of (b), indicate, for each ...

110 LOGIC, PART II: THE PREDICATE CALCULUS Chapter 3 Then we define (a) Prove that - [(Vx E A)(3y E B)p(x, y)] - (3x E A)(Vy E B ...

3.5 ANALYSIS OF ARGUMENTS FOR LOGICAL VALIDITY, PART II (OPTIONAL) 111 No p's are 9's. Some p's are not q's. As seen earlier i ...

112 LOGIC, PART II: THE PREDICATE CALCULUS Chapter 3 Figure 3.2 Venn diagram representation of Example I. We symbolize the fact ...

3.5 ANALMS OF ARGUMENTS FOR LOGICAL VALIDllY, PART I1 (OPTIONAL)^113 Figure 3.3 The argument in Exmnpk 2, represented by the Ven ...

114 LOGIC, PART II: THE PREDICATE CALCULUS Chapter 3 All monotonic functions are one to one. Some monotonic functions are incre ...

Elementarv of Logic In this chapter, we begin to apply the principles of logic developed in Chapters 2 and 3. In Article 4.1 for ...

116 ELEMENTARY APPLICATIONS OF LOGIC Chapter 4 DEFINITION 1 Let A and B be sets: (a) We say that A equals B (denoted A = 6) if a ...

4.1 APPLICATIONS OF LOGIC TO SET THEORY-SOME PROOFS 117 The proofs we have given in Examples 1 through 3 make explicit reference ...

118 ELEMENTARY APPLICATIONS OF LOGIC Chapter 4 Beginning students often complain that the choose method doesn't seem adequate to ...

4.1 APPLICATIONS OF LOGIC TO SET THEORY--SOME PROOFS 119 In addition to its basic structure, involving the choose method, the ot ...

1 ELEMENTARY APPLICATIONS OF LOGIC Chapter 4 EXAMPLE 9 Given sets A and B, prove that A n B = A if and only if A E B. Solution U ...

4.1 APPLICATIONS OF LOGIC TO SET THEORY-SOME PROOFS 12l empty set is a subset of any set (Example 1). Surely, we cannot begin a ...

122 ELEMENTARY APPLICATIONS OF LOGIC Chapter 4 On the other hand, suppose x E X u 0; we must prove x E X. Now, by our suppositio ...