Logic and Proo fs - Columbia Universityabishek/files/DM-Ch1.pdf · Logic and Proo fs 1.1 Pr...

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

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