Bridge to Abstract Mathematics: Mathematical Proof and Structures

2.2 TAUTOLOGY, EQUIVALENCE, THE CONDITIONAL, AND BICONDITIONAL 83 I would do if I finished my work" and made no commitment other ...

64 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 Let p represent the statement "I pass the test." Let q symbolize "I pass ...

2.3 THEOREMS OF THE PROPOSITIONAL CALCULUS 65 EXAMPLE (^1) Find pairs of equivalent statement forms among p -+ q, q -) p, *q -+ ...

66 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter '2 Solution We construct truth tables as shown in Figures 2.7~ and 2.7b: Fi ...

2.3 THEOREMS OF THE PROPOSITIONAL CALCULUS 67 form is logically equivalent to that of the original. Examples 1 and 2 pro- vide s ...

68 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 conjunction involves disjunction (and the negation of the original com- p ...

2.3 THEOREMS OF THE PROPOSITIONAL CALCULUS 89 (conjunction distributes over disjunction) (biconditional law; strategy in an iff ...

70 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 The tautology in Example 5, known as modus ponens, is a particularly impo ...

2.3 THEOREMS OF THE PROPOSITIONAL CALCULUS n i ditional). Furthermore, precisely three of the conditional statement forms in The ...

72 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 that, up to now, has been used in every known derivation of the conclusio ...

2.3 THEOREMS OF THE PROPOSITIONAL CALCULUS 73 Exercises (a) In Exercise 3, Article 2.2, find any examples of pairs of statement ...

74 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 Let p, q, and r represent statements defined as follows: p: lines x and ...

2.3 THEOREMS OF THE PROPOSITIONAL CALCULUS 75 q: If a, b, and p are integers and if p divides ab, then either p divides a or p d ...

76 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 Figure 2.9 Truth table deJining the Shefer stroke. involving A and - only ...

2.4 ANALYSIS OF ARGUMENTS FOR LOGICAL VALIDITY, PART 1 (OPTIONAL) 77 partial premises must logically imply the conclusion. State ...

78 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 I in symbolic form, looks like Therefore p -, s Proceeding by either cons ...

2.4 ANALYSIS OF ARGUMENTS FOR LOGICAL VALIDITY, PART 1 (OPTIONAL) 79 question now shifts to whether we can derive s from this ex ...

80 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 decrease in exports is halted. A drop in interest rates is necessary to w ...

LOGIC, PART 11: THE PREDICATE CALCULUS CHAPTER 3 There are many kinds of statements that we wish to make in mathematics (and in ...

82 LOGIC, PART II: THE PREDICATE CALCULUS Chapter 3 to be saying "either P is a subset of Q or Q is a subset of P," which would ...