CSE 231 • Final • Discrete Structures

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 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

Functions 1

Functions 2

Functions 3

Relations 1

Relations 2

Relations 3

Relations 4

Relations 5

Relations 6

Relations 7

Relations 8

Relations 9

Relations 10

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

Matching

Example 9

Subgraph

Example 10

Subgraph Induced

Edge Contraction

Example 11

Complementary Graph

Example 12

Example 13

Example 14

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

Introduction

Rooted Tree

Terminology for Rooted Trees

Full m-ary Trees

Some Formulas

What is a Minimum Spanning Tree?

Prim's Algorithm

MST Example 1

MST Example 2

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 18

Trees 1

Trees 2

Trees 3

MST Exam Like Question 1

MST Exam Like Question 2

MST Exam Like Question (T/F)