MAT 2033 • Midterm • Discrete Mathematics

Introduction

Negation of a Proposition

Compound Proposition

Truth Table 1

Truth Table 2

Tautology

Contradiction

Converse Inverse Contrapositive

Practice Problem 1

Practice Problem 2

Practice Problem 3

Practice Problem 4

Logical Equivalences 1

Logical Equivalences 2

De Morgans' Law

Practice Problem 1

Practice Problem 2

Practice Problem 3

Practice Problem 4

Practice Problem 5

Practice Problem 6

Universal Quantifiers

Existential Quantifiers

Propositions with Quantifiers I

Propositions with Quantifiers II

Propositions with Quantifiers III

Quantifiers with Multiple Variables I

Quantifiers with Multiple Variables II

Quantifiers with Multiple Variables III

Negation of Quantifiers I

Negation of Quantifiers II

Translations: Introduction

Translation: English to Logic

Translations: Logic to English

Translation of Statements With Multiple Variables

Direct Proof

Example 1

Example 2

Example 3

Proof by Contraposition

Example 4

Example 5

Example 6

Proof by Contradiction

Example 7

Example 8

Proof by Counterexample

Example 9

Proofs of Equivalence (if and only if)

Practice Problem

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Example 3

Example 4

Proof of Divisibility by Induction

Example 1

Example 2

Proof of Inequality by Induction

Example 1

Truth Tables 1

Truth Tables 2

Logical Equivalances with Table 1

Logical Equivalances with Table 2

Logical Equivalance with De Morgan's 1

Logical Equivalance with De Morgan's 2

Quantifiers with Multiple Variables 1

Quantifiers with Multiple Variables 2

Quantifiers with Multiple Variables 3

Quantifiers with Multiple Variables 4

Negation of Quantifiers 1

Negation of Quantifiers 2

Translations 1

Translations 2

Translations 3

Translations 4

Valid Argument

Direct Proof 1

Direct Proof 2

Proof by Contrapositive 1

Proof by Contrapositive 2

Proof by Contrapositive 3

Proof by Contradiction 1

Proof by Contradiction 2

Proof by Contradiction 3

Induction for Formulas 1

Induction for Formulas 2

Induction for Formulas 3

Induction Proof for Divisibility 1

Induction Proof for Divisibility 2

Induction for Inequalities

Definition and Notation of a Set

Subset

Example 1

Union and Intersection of Two Sets

Difference of Two Sets

Set Identities

Example 2

Power Set

Example 3

Cartesian Product

Example 4

Proof Example 1

Definition of Function

Example 5

Number of Functions

Injective Functions

Example 6

Example 7

Number of Injective Functions

Surjective Functions

Example 8

Example 9

Bijective Function

Inverse Function

Example 10

Example 11

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 2

Sum Notation

Example 3

Definition

Example 1

Countable Sets

Properties of Countable Sets

Example 1

Uncountable Sets

Sets 1

Sets 2

Sets 3

Sets 4

Sets 5

Sets 6

Functions 1

Functions 2

Functions 3

Functions 4

Functions 5

Cardinality 1

Cardinality 2

Function & Summation & Cardinality

Functions & Sets

Functions & Sets & Summation & Cardinality

Functions & Summation