ECON 225 • Mathematics for Economists • Midterm

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Tautology

Contradiction

Converse Inverse Contrapositive

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Logical Equivalences & De Morgan's Laws

Logical Equivalences & De Morgan's Laws 2

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Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

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Nested Quantifiers

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Negation of Nested Quantifiers

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Translation of Mathematical Statements

Translation of Statements With Multiple Variables

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Direct Proof

Example 1

Example 2

Example 3

Example 4

Example 5

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Proof by Contraposition

Example 1

Example 2

Example 3

Example 4

Example 5

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Proof by Contradiction

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11

Example 12

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Proof By Cases

Example 13

Example 14

Existence Proof

Example 1

Example 2

Uniqueness Proof

Example 3

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Proofs of Equivalence

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Example 2

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Example 4

Example 5

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Introduction

Proof of Formulas by Induction

Example 1

Example 2

Example 3

Example 4

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Proof of Divisibility by Induction

Example 1

Example 2

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Proof of Inequality by Induction

Example 1

Example 2

Example 3

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Strong Induction

Example 1

Definition and Notation

Subset

Example 1

Union and Intersection of Two Sets

Difference of Two Sets

Example 2

Symmetric Difference

Example 1

Set Identities

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Power Set

Example 1

Example 2

Cartesian Product

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Generalized Intersections and Unions

Example 1

Example 2

Example 3

Truth Tables

Logical Equivalences 1

Logical Equivalences 2

Logical Equivalence & De Morgans Laws

Quantifiers 1

Quantifiers 2

Nested Quantifiers 1

Nested Quantifiers 2

Nested Quantifiers 3

Translations 1

Translations 2

Translations 3

Translations 4