CENG 115 • Midterm • Discrete Structures

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Tautology

Contradiction

Converse Inverse Contrapositive

Practice Problem 1

Practice Problem 2

Logical Equivalences 1

Logical Equivalences 2

De Morgans' Law

Example 1

Practice Problem 3

Practice Problem 4

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Example 2

Nested Quantifiers

Example 3

Negation of Nested Quantifiers

Example 4

Translations

Example 5

Example 6

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

Direct Proof

Example 1

Example 2

Example 3

Proof by Contrapositive

Example 4

Proof by Contradiction

Example 5

Proof By Cases

Example 6

Proofs of Equivalence

Example 7

Existence Proof

Example 8

Existence and Uniqueness Proof

Example 9

Truth Table & Tautology

Logical Equivalences

Logical Equivalences

Logical Equivalences

Tautology

Quantifiers

Quantifiers

Quantifiers

Nested Quantifiers

Nested Quantifiers

Translations

Translations

Translations

Rules of Inferences 1

Rules of Inferences 2

Rules of Inferences 3

Direct Proof 1

Direct Proof 2

Direct Proof 3

Direct Proof 4

Proof by Contrapositive 1

Proof by Contrapositive 2

Proof by Contradiction 1

Proof by Contradiction 2

Proof by Cases

Proofs of Equivalence

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 (One-to-One) Functions

Example 6

Example 7

Number of Injective Functions

Surjective(Onto) Functions

Example 8

Example 9

Bijective Function

Inverse Function

Example 10

Example 11

Definition

Example 1

Countable Sets

Properties of Countable Sets

Example 1

Uncountable Sets

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 1

Sum Notation

Example 1

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

What is an algorithm?

Algorithm and Pseudocode 1

Algorithm and Pseudocode 2

Algorithm and Pseudocode 3

Linear Search Algorithm

Binary Search Algorithm

Bubble Sort Algorithm

Sets 1

Sets 2

Sets 3

Sets 4

Functions 1

Functions 2

Functions 3

Functions 4

Function & Summation

Functions & Sets

Functions & Sets & Summation

Functions & Summation

Growth of Functions 1

Growth of Functions 2

Growth of Functions 3

Growth of Functions 4

Growth of Functions 5

Algorithms 1

Algorithms 2

Algorithms 3

Algorithms 4

Algorithms 5

Algorithm and Complexity

Algorithm and Complexity