BLM 2521 • Midterm II + Final • Discrete Mathematics

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

Equivalence Relation

Example 15

Example 16

Example 17

Example 18

Example 19

Example 20

Example 21

Example 22

Example 23

Relations 1

Relations 2

Relations 3

Introduction

Graph Terminology

Handshaking Theorem

Example 1

Special Graphs

Example 2

Bipartite Graphs

Example 3

Example 4

Complete Bipartite Graph

Matching

Subgraph

Example 5

Subgraph Induced

Edge Contraction

Example 6

Complementary Graph

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

Planar Graph

Planar Graph - Euler Formula

Example 11

Corollaries about Planar Graph

Example 12

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

Chromatic Number 1

Chromatic Number 2

Language and Grammar

Phase-Structure Grammar

Grammar -> Language Example 1

Grammar -> Language Example 2

Language -> Grammar Example 1

Language -> Grammar Example 2

Finite State Machines with Output

Example 1

Example 2

Finite State Machines with NO Output

Example 3

Example 4

Example 5

Turing Machine

Example 6

Example 7

Grammar -> Language 1

Grammar -> Language 2

Language -> Grammar 1

Language -> Grammar 2

Language -> Grammar 3

Finite State Machines with Output

Finite State Machines with NO Output 1

Finite State Machines with NO Output 2

Turing Machine