CENG 110 • Midterm • Discrete Structures

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Exam like Question 1

Exam like Question 2

Tautology

Exam like Question 3

Contradiction

Logical Equivalences & De Morgan's Laws

Logical Equivalences & De Morgan's Laws 2

Exam like Question 4

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Valid Argument

Rules of Inferences

Example 1

Example 2

Example 3

Using Rules of Inferences to Build Arguments

Example 4

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

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 1

Sum Notation

Example 1

Logic Basics 1

Logic Basics 2

Logic Basics 3

Logic Basics 4

Quantifiers 1

Quantifiers 2

Rules of Inferences 1

Rules of Inferences 2

Rules of Inferences 3

Sets 1

Sets 2

Sets 3

Functions 1

Functions 2

Summation and Function

What is an algorithm?

Algorithm and Pseudocode 1

Algorithm and Pseudocode 2

Exam Like Question 1

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

Definition of Divisibility

Example 1

Example 2

Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

Example 1

Example 2

Prime Numbers

Example 1

Example 2

GCD Greatest Common Divisor

LCM Least Commun Multiple

Example 1

Euclidian Algorithm

Example 1

Bezout Identity

Example 1

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Example 3

Proof of Divisibility by Induction

Example 1

Example 2

Proof of Inequality by Induction

Example 1

Example 2

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example

Combination

n choose r

Committee Example

Ball Example

Pigeonhole Principle

Pigeonhole Principle Example 1

Pigeonhole Principle Example 2

Pigeonhole Principle Example 3

Growth of Functions 1

Growth of Functions 2

Growth of Functions 3

Growth of Functions 4

Algorithms 1

Algorithms 2

Algorithms 3

Number Theory 1

Number Theory 2

Induction for Formulas 1

Induction for Formulas 2

Induction for Formulas 3

Induction for Formulas 4

Induction Proof for Divisibility 1

Induction Proof for Divisibility 2

Induction for Inequalities 1

Induction for Inequalities 2

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Counting 7

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3