CMPE 139 • Tüm Sınavlar • 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

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

Rules of Inference with Quantified Statements

Example 1

Example 2

Example 3

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

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

Proofs & Sets 4

Functions 1

Functions 2

Functions 3

Functions 4

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

Algorithms 1

Algorithms 2

Algorithms 3

Algorithms 4

Algorithms 5

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

Example 2

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Number Theory 5

Number Theory 6

Number Theory 7

Number Theory 8

Introduction to Counting

Combination & Permutation: Intuition

Combination

Permutation 1

Permutation 2

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Intuition of Conditional Probability

Conditional Probability 1

Conditional Probability 2

Example 1

Example 2

Total Probability Rule

Discrete Random Variables

Expected Value

Variance

Expected Value and Variance Arithmetic

Counting Standard Models 1

Counting Standard Models 2

Counting Standard Models 3

Counting Standard Models 4

Counting Standard Models 5

Counting Standard Models 6

Counting Standard Models 7

Discrete Probability 1

Discrete Probability 2

Discrete Probability 3

Discrete Probability 4

Discrete Probability 5

Discrete Probability 6

Definition of Relation

Example 1

Example 2

Example 3

Example 4

Reflexive Relations

Example 5

Example 6

Symmetric Relations

Antisymmetric Relations

Example 7

Transitive Relations

Example 8

Properties of Relations

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14

Equivalence Relation

Example 15

Example 16

Example 17

Example 18

Example 19

Example 20

Example 21

Example 22

Example 23

Introduction

Graph Terminology

Handshaking Theorem

Example 1

Special Graphs

Example 2

Bipartite Graphs

Example 3

Example 4

Complete Bipartite Graph

Matching

Subgraph

Example 5

Subgraph Induced

Edge Contraction

Example 6

Complementary Graph

Adjacency Matrices - Undirected Graphs

Adjacency Matrices - Directed Graphs

Example 1

Example 2

Incidence Matrices

Example 3

Isomorphism of Graphs

Example 4

Example 5

Example 6

Example 7

Definition of Paths and Circuits

Connected Graphs

Euler Paths and Circuits

Example 8

Hamilton Paths and Circuits

Example 9

Example 10

Planar Graph

Planar Graph - Euler Formula

Example 11

Corollaries about Planar Graph

Example 12

Relations 1

Relations 2

Relations 3

Graphs 1

Graphs 2

Graphs 3

Graphs 4

Graphs 5

Graphs 6

Graphs 7

Graphs 8

Graphs 9

Graphs 10

Graphs 11

Graphs 12

Graphs 13

Graphs 14

Graphs 15

Graphs 16