Download pdf - Logic and Proo fs - Columbia Universityabishek/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr opositional Logic ... 1.6 Intr oduction to Pr oofs 1.7 Pr oof Methods and Strategy coursenotes

Section 1.0 1.0.1

Chapter 1Logic andProofs

1.1 Propositional Logic1.2 Propositional Equivalences1.3 Predicates and Quantifiers1.4 Nested Quantifiers1.5 Rules of Inference1.6 Introduction to Proofs1.7 Proof Methods and Strategy

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 1.1 Propositional Logic 1.1.1

1.1 PROPOSITIONAL LOGIC

PROPOSITIONS


1.1.2 Chapter 1 Logic and Proofs



TRUTH TABLES









CONDITIONAL OPERATOR





COMPOUND PROPOSITIONAL FORMS






Section 1.2 Logical Equivalences 1.2.1

1.2 LOGICAL EQUIVALENCES



CONTRAPOSITIVE, etc.





CATEGORIES of PROPOSITIONAL FORMS



LAWS of LOGIC

AVOIDING BOREDOM


Section 1.3 Predicates & Quantifiers 1.3.1

1.3 PREDICATES & QUANTIFIERS



VARYING THE DOMAIN



CLASSROOM EXERCISE



SCOPE of QUANTIFIERS



NEGATION with QUANTIFIERS

CLASSROOM EXERCISE


Section 1.4 Nested Quantifiers 1.4.1

1.4 NESTED QUANTIFIERS

TRANSPOSING QUANTIFIERS



RECALL NEGATION with QUANTIFIERS

CLASSROOM EXERCISE


Section 1.4 Nested Quantifiers 1.4.3

OPTIONAL CLASSROOM EXERCISE


Section 1.5 Rules of Inference 1.5.1

1.5 RULES OF INFERENCE



VALID ARGUMENTS





FALLACIES



NOTORIOUS FALLACIES



VALIDITY and TRUTH

LOGICAL RULES of INFERENCE





MATHEMATICAL PROOFS (DIRECT)



MATHEMATICAL PROOFS (INDIRECT)



TERMINOLOGY


Section 1.6 Introduction to Proofs 1.6.1

1.6 INTRODUCTION TO PROOFS

TWO FAMOUS PROBLEMS


Section 1.7 Proof Strategy 1.7.1

1.7 PROOF STRATEGY

FORWARD AND BACKWARD REASONING



MATHEMATICAL PROOFS (by CASES)


Section 1.7 Proof Strategy 1.7.3

PROVING QUANTIFIED ASSERTIONS


Section 1.9 Logic Supplement 1.9.1

1.9 LOGIC SUPPLEMENT

PROPOSITIONS



TIME OUT to discuss OBSCENITY


Section 1.9 Logic Supplement 1.9.3
