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Section 1.0 1.0.1 Chapter 1 Logic and Proofs 1.1 Propositional Logic 1.2 Applications of Prop. Logic (read-only) 1.3 Propositional Equivalences 1.4 Predicates and Quantiers 1.5 Nested Quantiers 1.6 Rules of Inference 1.7 Introduction to Proofs 1.8 Proof Methods and Strategy coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

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Page 1: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.0 1.0.1

Chapter 1Logic andProofs

1.1 Propositional Logic1.2 Applications of Prop. Logic (read-only)1.3 Propositional Equivalences1.4 Predicates and Quantifiers1.5 Nested Quantifiers1.6 Rules of Inference1.7 Introduction to Proofs1.8 Proof Methods and Strategy

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 2: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.1 Propositional Logic 1.1.1

1.1 PROPOSITIONAL LOGIC

PROPOSITIONS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 3: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.1.2 Chapter 1 Logic and Proofs

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 4: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.1 Propositional Logic 1.1.3

TRUTH TABLES

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 5: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.1.4 Chapter 1 Logic and Proofs

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 6: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.1 Propositional Logic 1.1.5

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 7: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.1.6 Chapter 1 Logic and Proofs

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 8: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.1 Propositional Logic 1.1.7

CONDITIONAL OPERATOR

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 9: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.1.8 Chapter 1 Logic and Proofs

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 10: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.1 Propositional Logic 1.1.9

COMPOUND PROPOSITIONAL FORMS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 11: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.1.10 Chapter 1 Logic and Proofs

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 12: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.1 Propositional Logic 1.1.11

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 13: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.3 Logical Equivalences 1.3.1

1.3 LOGICAL EQUIVALENCES

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 14: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.3.2 Chapter 1 Logic and Proofs

CONTRAPOSITIVE, etc.

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 15: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.3 Logical Equivalences 1.3.3

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 16: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.3.4 Chapter 1 Logic and Proofs

CATEGORIES of PROPOSITIONAL FORMS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 17: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.3 Logical Equivalences 1.3.5

LAWS of LOGIC

AVOIDING BOREDOM

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 18: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.4 Predicates & Quantifiers 1.4.1

1.4 PREDICATES & QUANTIFIERS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 19: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.4.2 Chapter 1 Logic and Proofs

VARYING THE DOMAIN

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 20: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.4 Predicates & Quantifiers 1.4.3

CLASSROOM EXERCISE

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 21: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.4.4 Chapter 1 Logic and Proofs

SCOPE of QUANTIFIERS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 22: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.4 Predicates & Quantifiers 1.4.5

NEGATION with QUANTIFIERS

CLASSROOM EXERCISE

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 23: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.5 Nested Quantifiers 1.5.1

1.5 NESTED QUANTIFIERS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 24: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.5.2 Chapter 1 Logic and Proofs

TRANSPOSING QUANTIFIERS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 25: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.5 Nested Quantifiers 1.5.3

RECALL NEGATION with QUANTIFIERS

CLASSROOM EXERCISE

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 26: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.5.4 Chapter 1 Logic and Proofs

OPTIONAL CLASSROOM EXERCISE

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 27: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.6 Rules of Inference 1.6.1

1.6 RULES OF INFERENCE

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 28: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.6.2 Chapter 1 Logic and Proofs

VALID ARGUMENTS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 29: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.6 Rules of Inference 1.6.3

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 30: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.6.4 Chapter 1 Logic and Proofs

FALLACIES

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 31: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.6 Rules of Inference 1.6.5

NOTORIOUS FALLACIES

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 32: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.6.6 Chapter 1 Logic and Proofs

VALIDITY and TRUTH

LOGICAL RULES of INFERENCE

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 33: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.6 Rules of Inference 1.6.7

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 34: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.7 Introduction to Proofs 1.7.1

1.7 INTRODUCTION TO PROOFS

TWO FAMOUS PROBLEMS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 35: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.7.2 Chapter 1 Logic and Proofs

MATHEMATICAL PROOFS (DIRECT)

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 36: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.7 Introduction to Proofs 1.7.3

MATHEMATICAL PROOFS (INDIRECT)

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 37: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.7.4 Chapter 1 Logic and Proofs

TERMINOLOGY

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 38: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.8 Proof Strategy 1.8.1

1.8 PROOF STRATEGY

FORWARD AND BACKWARD REASONING

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 39: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.8.2 Chapter 1 Logic and Proofs

MATHEMATICAL PROOFS (by CASES)

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 40: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.8 Proof Strategy 1.8.3

PROVING QUANTIFIED ASSERTIONS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 41: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.9 Logic Supplement 1.9.1

1.9 LOGIC SUPPLEMENT

PROPOSITIONS

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 42: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

1.9.2 Chapter 1 Logic and Proofs

TIME OUT to discuss OBSCENITY

coursenotes by Prof. J. L. Gross for Rosen 7th Edition

Page 43: Logic and Proo fs - Columbia Universitycs3203/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional ... (read-onl y) 1.3 Pr opositional Equiv alences 1.4 Predicates and ... 1.7

Section 1.9 Logic Supplement 1.9.3

coursenotes by Prof. J. L. Gross for Rosen 7th Edition