CMPE 139 • Midterm • Logic and 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

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

Rules of Inference with Quantified Statements

Example 5

Example 6

Example 7

Introduction

Boolean Functions

Example 1

Example 2

Boolean Identities

Example 3

Minterm of Boolean Variables

Example 4

Sum of Product Expansion

Karnaugh Maps 1

Karnaugh Maps 2

Example 5

Truth Table & Tautology

Logical Equivalances 1

Logical Equivalances 2

Logical Equivalances 3

Logical Equivalances 4

Tautology

Quantifiers 1

Quantifiers 2

Quantifiers 3

Quantifiers 4

Quantifiers 5

Nested Quantifiers 1

Nested Quantifiers 2

Translations 1

Translations 2

Translations 3

Rules of Inference 1

Rules of Inference 2

Rules of Inference 3

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

Proofs of Equivalence

Example 1

Example 2

Direct Proof 1

Direct Proof 2

Direct Proof 3

Proof by Contrapositive 1

Proof by Contrapositive 2

Proof by Contrapositive 3

Proof by Contradiction 1

Proof by Contradiction 2

Proof by Contradiction 3

Proof by Contradiction 4

Proof by Cases 1

Proof by Cases 2

Proofs of Equivalence 1

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 1

Sum Notation

Example 1

Definition

Example 1

Countable Sets

Properties of Countable Sets

Example 1

Uncountable Sets

Sets (Proof)

Sets (Proof)

Sets (Proof)

Functions

Functions

Functions

Functions

Functions

Cardinality

Cardinality

Cardinality

Cardinality

Sets & Functions

Sets & Cardinality

Cardinality & Functions

Functions & Summation

Functions & Sets & Cardinality

Cardinality & Summation & Function

Sets & Functions & Cardinality & Summation

Functions & Logic & Sets & Cardinality & Summation

What is an algorithm?

Algorithm and Pseudocode 1

Algorithm and Pseudocode 2

Algorithm and Pseudocode 3

Algorithm and Pseudocode 4

Exam-like Question 1

Exam-like Question 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

GCD Greatest Common Divisor

LCM Least Commun Multiple

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

Example 2

Chinese Remainder Theorem

Example 1

Example 2

Algorithms

Algorithms

Algorithms

Algorithms

Number Theory

Number Theory

Number Theory

Number Theory

Number Theory

Number Theory

Number Theory

Number Theory

Number Theory