MATH 112 • Midterm I • Discrete Mathematics

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Tautology

Contradiction

Converse Inverse Contrapositive

Practice Problem 1

Practice Problem 2

Practice Problem 3

Logical Equivalences 1

Logical Equivalences 2

De Morgans' Law

Example 1

Example 2

Example 3

Example 4

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

Translations

Example 6

Example 7

Exam-like Question 1

Translation of Statements With Multiple Variables

Valid Argument

Rules of Inferences

Example 1

Example 2

Example 3

Using Rules of Inferences to Build Arguments

Example 4

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Truth Table & Tautology (Fall 2022)

Logical Equivalances (Spring 2023)

Logical Equivalances (Spring 23: Make-Up)

Logical Equivalances (Summer 2020)

Logical Equivalances (Spring 2017)

Tautology (Fall 2022)

Quantifiers 1

Quantifiers 2

Quantifiers (Spring 2023)

Quantifiers (Spring 2023: Make-UP)

Quantifiers 3

Nested Quantifiers 1

Nested Quantifiers 2

Translations (Fall 2020)

Translations (Summer 2020)

Translations (Spring 2019)

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 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

Direct Proof 3

Direct Proof 4

Proof by Contrapositive (Fall 2020)

Proof by Contrapositive 1

Proof by Contrapositive 2

Proof by Contrapositive 3

Proof by Contradiction 1

Proof by Contradiction 2

Proof by Contradiction (Fall 2022)

Proof by Contradiction 4

Proof by Contradiction 5

Proof by Contradiction (Fall 2020)

Proof by Cases 1

Proof by Cases 2

Proofs of Equivalence 1

Proofs of Equivalence 2

Proofs of Equivalence 3

Induction for Formulas 1

Induction for Formulas 2 (Fall 2017)

Induction for Formulas 3 (Summer 2020)

Induction for Formulas 4 (Spring 2023)

Induction for Formulas 5 (Spring 23: Make-Up)

Induction Proof for Divisibility 1

Induction Proof for Divisibility 2

Direct Proof & Induction (Spring 2023)

Direct Proof & Induction (Spring 23: Make-Up)

Induction for Inequalities 1

Induction for Inequalities 2 (Fall 2022)

Induction Proof for Inequalities 3

Induction with Fibonacci (Spring 2019)

Induction with Fibonacci (Fall 2020)

Definition and Notation

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

Example 5

Proof Example 1

Proof Example 2

Definition of Function

Example 1

Number of Functions

Injective Functions

Example 2

Example 3

Example 4

Number of Injective Functions

Surjective Functions

Example 5

Example 6

Example 7

Bijective Function

Inverse Function

Example 8

Example 9

Proofs & Sets 1

Proofs & Sets 2

Proofs & Sets 3 (Spring 2023)

Proofs & Sets 4

Proofs & Sets 5

Proofs & Sets 6

Proofs & Sets 7 (Spring 2023 - Make Up)

Functions 1

Functions 2

Functions 3 (Spring 2023)

Functions 4 (Spring 2023 - Make Up)

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example 1

Identical Objects Example 2

Identical Objects Example 3

Combination

n choose r

Committee Example 1

Committee Example 2

Ball Example 1

Ball Example 2

Binomial Theorem

Example 1

Example 2

Example 3

Pascal Identity

Combinatorial Proof

Example 4

Counting Standard Models 1

Counting Standard Models 2

Counting Standard Models 3

Counting Standard Models 4

Counting Standard Models 5

Counting Standard Models 6 (Spring 2023)

Counting Standard Models 7 (Spring 2023 - Make Up)

Counting Standard Models & Binomial Coefficients 1

Binomial Identities

Combinatorial Proof 1