MATH 204 • Midterm • Discrete Mathematics

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Exam like Question 1

Exam like Question 2

Tautology

Exam like Question 3

Contradiction

Converse Inverse Contrapositive

Exam like Question 4

Exam-like Question 5

Logical Equivalences & De Morgan's Laws

Logical Equivalences & De Morgan's Laws 2

Exam like Question 6

Exam like Question 7

Exam like Question 8

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Nested Quantifiers

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Negation of Nested Quantifiers

Exam like Question 9

Exam like Question 10

Translation of Mathematical Statements

Translation of Statements With Multiple Variables

Exam like Question 11

Exam like Question 12

Exam like Question 13

Exam like Question 14

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 - Translation 1

Logic - Translation 2

Logic - Translation 3

Logic - Translation 4

Logic - Translation 5

Direct Proof

Example 1

Example 2

Example 3

Example 4

Proof by Contrapositive

Example 1

Example 2

Example 3

Proof by Contradiction

Example 1

Example 2

Proof by Counterexample

Example 1

Proof By Cases

Example 1

Example 2

Example 3

Proofs of Equivalence

Example 1

Example 2

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

Proof by Cases 1

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

Primitive Root

Discrete Logarithm

Fermat's Little Theorem

Solving Linear Congruences

Example 1

Example 2

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Example 4

Introduction to Counting

Combination & Permutation: Intuition

Combination

Permutation 1

Permutation 2

Principle Inclusion-Exclusion

Example 1

Example 2

Distributing Objects into Boxes

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Pigeonhole Principle

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Definition

Example 1

Example 2

Example 3

Example 4

Extended Binomial Theorem

Counting Problems with Generating Functions

Example 5

Example 6

Example 7

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

Number Theory 10

Number Theory 11

Number Theory 12

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Counting 7

Counting 8

Counting 9

Counting 10

Counting 11

Counting 12

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Pigeonhole Principle 5

Principle Inclusion - Exclusion 1

Principle Inclusion - Exclusion 2

Generating Functions 1

Generating Functions 2

Generating Functions 3