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

Rules of Inference

Rules of Inference

Rules of Inference

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

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 1

Sum Notation

Example 1

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 of Divisibility

Example 1

Example 2

Example 3

Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

Example 1

Example 2

Prime Numbers

Example 1

Example 2

Example 3

GCD Greatest Common Divisor

LCM Least Commun Multiple

Example 1

Euclidian Algorithm

Example 1

Bézout Identity

Example 1

Example 2

Example 3

Inverse of a Number in Modular Arithmetic

Fermat's Little Theorem

Solving Linear Congruences

Example 1

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Example 4

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example

Combination

n choose r

Committee Example

Ball Example

Binomial Theorem

Example 1

Example 3

Example 2

Pascal Identity

Vandermonde's Identity

Example 1

Combinatorial Proof

Example 1

Distributing Objects into Boxes 1

Distributing Objects into Boxes 2

Example 1

Example 2

Pigeonhole Principle

Example 1

Example 2

Example 3

Example 4

Example 5

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Number Theory 5

Number Theory 6

Number Theory 7

Number Theory 8

Number Theory 9

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Counting 7

Principle Inclusion - Exclusion 1

Principle Inclusion - Exclusion 2

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Pigeonhole Principle 5

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)

Modular Arithmetic- True False (Spring 2019)

Modular Arithmetic - Proof (Spring 2019)

Modular Arithmetic - Proof (Spring 2024)

Euclidian Algorithm (Spring 2024)

Euclidian Algorithm (Spring 2025)

Number Theory (Fall 2024)

Number Theory (Fall 2024)

Binomial Coefficient (Spring 2024)

Binomial Identities (Spring 2024)

Binomial Identities (Spring 2025)

Counting (Spring 2019)

Counting (Spring 2019)

Counting (Fall 2024)

Counting (Spring 2024)

Counting (Spring 2025)

Counting (Spring 2025)

Counting (Spring 2025)

Pigeonhole Principle (Fall 2024)

Pigeonhole Principle (Spring 2024)