Contents
CHAPTEr 1
Formal Logic
1
1.1 STATEMENTS, SYMBOLIC
REPRESENTATION, AND
TAUTOLOGIES
2
Connectives and Truth Values
2
Tautologies
8
Logical Connectives in the
Real World
10
An Algorithm
12
special interest page
Can “And” Ever Be “Or”?
15
SECTiOn 1.1 Review
16
ExErCiSES 1.1
16
1.2 PROPOSITIONAL LOGIC
25
Valid Arguments
25
Derivation Rules for
Propositional Logic
28
Deduction Method and Other Rules 32
Verbal Arguments
33
SECTiOn 1.2 Review
35
ExErCiSES 1.2
35
1.3 QUANTIFIERS, PREDICATES, AND
VALIDITY
39
Quantifiers and Predicates
39
Translation
42
Validity
48
SECTiOn 1.3 Review
50
ExErCiSES 1.3
50
1.4 PREDICATE LOGIC
58
Derivation Rules for Predicate Logic 58
Universal Instantiation
59
Existential Instantiation
60
Universal Generalization
61
Existential Generalization
62
More Work with Rules
62
Verbal Arguments
67
Conclusion
68
SECTiOn 1.4 Review
69
ExErCiSES 1.4
69
1.5 LOGIC PROGRAMMING
73
Prolog
73
Horn Clauses and Resolution
75
Recursion
79
Expert Systems
81
SECTiOn 1.5 Review
82
ExErCiSES 1.5
82
1.6 PROOF OF CORRECTNESS
84
Assertions
85
Assignment Rule
87
Conditional Rule
90
SECTiOn 1.6 Review
92
ExErCiSES 1.6
92
Chapter 1 Review
95
On the Computer
96
CHAPTEr 2
Proofs, induction, and
number Theory
97
2.1 PROOF TECHNIQUES
98
Theorems and Informal Proofs
98
To Prove or Not to Prove
99
Exhaustive Proof
100
Direct Proof
101
Contraposition
103
Contradiction
104