MATH 204 • Midterm I • Discrete Mathematics

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Tautology

Example 1

Contradiction

Converse Inverse Contrapositive

Example 2

Logical Equivalences 1

Logical Equivalences 2

Example 3

Example 4

Example 5

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Example 1

Example 2

Nested Quantifiers

Example 3

Example 4

Negation of Nested Quantifiers

Example 5

Example 6

Translations - Introduction

Translation: English to Logic

Translation: Logic to English

Translation with Quantifiers 1

Translation with Quantifiers 2

Translation of Mathematical Statements

Example 7

Translation of Statements With Multiple Variables

Example 8

Example 9

Logic Basics 1

Logic Basics 2

Logic Basics 3

Logic Basics 4

Logic - Quantifiers 1

Logic - Quantifiers 2

Logic - Quantifiers 3

Logic - Quantifiers 4

Logic - Quantifiers 5

Logic - Quantifiers 6

Logic - Translation 1

Logic - Translation 2

Logic - Translation 3

Direct Proof

Example 1

Example 2

Example 3

Example 4

Proof by Contrapositive

Example 5

Example 6

Proof by Contradiction

Example 7

Example 8

Proof by Counterexample

Example 9

Proof By Cases

Example 10

Proofs of Equivalence

Example 11

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

Example 2

Induction Related to Fibonacci

Strong Induction

Direct Proof 1

Direct Proof 2

Proof by Contrapositive 1

Proof by Contrapositive 2

Proof by Contradiction 1

Proof by Contradiction 2

Proof by Contradiction 3

Proof by Contradiction 4

Proof by Contradiction 5

Proofs of Equivalence 1

Proofs of Equivalence 2

Induction for Formulas 1

Induction for Formulas 2

Induction for Formulas 3

Induction for Formulas 4

Induction for Formulas 5

Induction Proof for Divisibility 1

Induction Proof for Divisibility 2

Direct Proof & Induction 1

Direct Proof & Induction 2

Induction for Inequalities 1

Induction for Inequalities 2

Induction for Inequalities 3

Induction with Fibonacci 1

Induction with Fibonacci 2

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

Example 1

Countable Sets

Properties of Countable Sets

Example 1

Uncountable Sets

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 1

Sum Notation

Example 1

Sets 1

Sets 2

Sets 3

Sets 4

Functions 1

Functions 2

Functions 3

Functions 4

Functions & Sets

Function & Summation

Functions & Sets & Summation

Functions & Summation

Cardinality 1

Cardinality 2

Cardinality 3

Cardinality 4

Cardinality 5

Cardinality 6

Propositional Logic (Spring 2025)

Tautology by Truth Table (Fall 2024)

Quantifiers (Spring 2025)

Nested Quantifiers (Fall 2024)

Negation of Nested Quantifiers (Fall 2024)

Translation (Fall 2024)

Translation (Spring 2025)

Direct Proof (Fall 2024)

Proof Techniques and Sets (Spring 2025)

Induction (Spring 2025)

Induction (Fall 2024)

Functions - Bijection Proof (Spring 2025)

Cardinality (Spring 2024)