MATH 132 • Final • Discrete Mathematics

Introduction

Homogenous Recurrence Relations

Example 1

Example 2

Example 3

Example 4

Non Homogenous Recurrence Relations

Example5

Example 6

Creating Recurrence Relations

Example 7

Example 8

Example 9

Principle Inclusion-Exclusion

Example 1

Example 2

Exam like Question 1

Definition

Example 1

Example 2

Example 3

Example 4

Extended Binomial Theorem

Counting Problems with Generating Functions

Example 5

Example 6

Example 7

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

Composition of Relations

Example 15

Example 16

Combining Relations

Inverse and Complementary of a Relation

Example 17

Matrix Representation of Relation: Part 1

Matrix Representation of Relation: Part 2

Example 18

Operations on Zero - One Matrices

Example 19

Equivalence Relation

Example 22

Example 23

Example 24

Example 25

Example 26

Example 27

Example 28

Example 29

Example 30

Exam like Question 1

Partially Ordered Set

Example

Example

Example

Totally Ordered Set

Example

Hasse Diagram

Example

Maximal and Minimal Elements

Greatest and Least Elements

Example

Upper and Lower Bound

Least Upper and Greatest Lower Bound

Example

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relation & Advanced Counting Techniques

Principle Inclusion Exclusion 1

Principle Inclusion Exclusion 2

Principle Inclusion Exclusion 3

Principle Inclusion Exclusion 4

Principle Inclusion Exclusion 5

Relations 1

Relations 2

Relations 3

Relations 4

Relations 5

Relations 6

Relations 7

Relations 8

Relations 9

Relations 10

Generating Functions

Generating Functions

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Relations

Relations

Relations

Relations

Counting & Derangement

Counting & Derangement