INDR 201 • Tüm Sınavlar • Discrete Mathematical Structure

Introduction

Negation of a Proposition

Conjunction

Disjunction

Conditional Statements: IF

BiConditional: If and only If

Exclusive OR

Truth Table 1

Truth Table 2

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Tautology

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Contradiction

Converse Inverse Contrapositive

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Logical Equivalences & De Morgan's Laws

Logical Equivalences & De Morgan's Laws 2

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Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

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Nested Quantifiers

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Negation of Nested Quantifiers

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Translations

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Translation of Mathematical Statements

Translation of Statements With Multiple Variables

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Logic Puzzle

Logic Puzzle 2

Valid Argument

Rules of Inferences

Example 1

Example 2

Example 3

Using Rules of Inferences to Build Arguments

Example 4

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Direct Proof

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Contrapositive Proof

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Proof by Contradiction

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Proof by Counterexample

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Existence Proof

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Existence and Uniqueness Proof

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If and Only if Statements

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Logic Basics 1

Logic Basics 2

Logic Basics 3

Logic Basics 4

Logic Basics 5

Logic Basics 6

Logic Basics 7

Translation 1

Translation 2

Translation 3

Translation 4

Quantifiers 1

Quantifiers 2

Quantifiers 3

Quantifiers 4

Quantifiers 5

Quantifiers 6

Proof Techniques 1

Proof Techniques 2

Proof Techniques 3

Proof Techniques 4

Proof Techniques 5

Proof Techniques 6

Proof Techniques 7

Proof Techniques 8

Proof Techniques 9

Proof Techniques 10

Definition and Notation

Subset

Example 1

Union and Intersection of Two Sets

Difference of Two Sets

Example 1

Symmetric Difference

Example 1

Set Identities

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Generalized Intersections and Unions

Example 1

Example 2

Example 3

Definition of Function

Example 1

Injective Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Surjective Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Bijective Function

Composition of Functions

Example 1

Inverse Function

Example 1

Example 2

Example 3

Image of a Set

Example 1

Proof Example For Image of a Function

Preimage of a Set

Example 1

Example 2

Example 3

Proof Example for Preimage of a Function

Example 1

Definition

Example 1

Countable Sets

Properties of Countable Sets

Example 1

Uncountable Sets

Sequences and Recurrence Relations

Recurrence Relation for Arithmetic Sequences

Recurrence Relation for Geometric Sequences

Sets 1

Sets 2

Sets 3

Sets 4

Sets 5

Sets 6

Sets 7

Functions 1

Functions 2

Functions 3

Functions 4

Functions 5

Functions 6

Recurrence Relations 1

Recurrence Relations 2

Cardinality 1

Cardinality 2

Cardinality 3

Cardinality 4

Cardinality 5

Cardinality 6

Cardinality 7

Sets and Functions

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

Linear Search Algorithm

Binary Search Algorithm

Bubble Sort Algorithm

Insertion Sort Algorithm

Insertion Sort Algorithm - Code

Big-O Notation

Example 1

Example 2

Example 3

Example 4

Sum Property of Big-O Notation

Multiplication Property of Big-O Notation

Example 1

Example 2

Big-Omega Notation

Big-Theta Notation

Example 1

Example 2

Cardinality 1

Cardinality 2

Cardinality 3

Cardinality 4

Cardinality 5

Cardinality 6

Cardinality 7

Algorithms 1

Algorithms 2

Algorithms 3

Algorithms 4

Algorithms 5

Algorithms 6

Growth of Functions 1

Growth of Functions 2

Growth of Functions 3

Algorithms and Complexity 1

Algorithms and Complexity 2

Algorithms and Complexity 3

Algorithm and Complexity 4

Algorithm and Complexity 5

Algorithms and Complexity 6

Algorithm and Complexity 7

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Example 3

Example 4

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Proof of Divisibility by Induction

Example 1

Example 2

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Proof of Inequality by Induction

Example 1

Example 2

Example 3

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Induction Related to Fibonacci

Strong Induction

Introduction

Example 1

Graph Terminology

Example 2

Handshaking Theorem

Example 3

Example 4

Special Graphs

Example 5

Example 6

Bipartite Graphs

Example 7

Example 8

Complete Bipartite Graph

Subgraph

Example 10

Subgraph Induced

Edge Contraction

Example 11

Adjacency Matrices - Undirected Graphs

Adjacency Matrices - Directed Graphs

Example 15

Example 16

Incidence Matrices

Example 17

Isomorphism of Graphs

Example 18

Example 19

Example 20

Example 21

Definition of Paths and Circuits

Connected Graphs

Euler Paths and Circuits

Example 22

Hamilton Paths and Circuits

Example 23

Example 24

Induction 1

Induction 2

Induction 3

Induction 4

Induction 5

Induction 6

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

Graphs 17

Graphs & Pigeonhole Principle

Logic Basics

Translation

Quantifiers

Sets

Functions

Sets and Functions

Proof Techniques