MATH 154 • Final • Discrete Mathematics

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Tautology

Contradiction

Converse Inverse Contrapositive

Practice Problem 1

Practice Problem 2

Practice Problem 3

Logical Equivalences 1

Logical Equivalences 2

De Morgans' Law

Example 1

Example 2

Example 3

Example 4

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Example 1

Example 2

Nested Quantifiers

Example 3

Example 4

Negation of Nested Quantifiers

Example 5

Truth Table & Tautology

Logical Equivalances 1

Logical Equivalances 2

Logical Equivalances 3

Logical Equivalances 4

Tautology

Quantifiers 1

Quantifiers 2

Quantifiers 3

Quantifiers 4

Quantifiers 5

Nested Quantifiers 1

Nested Quantifiers 2

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

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relations 4

Recurrence Relations 5

Recurrence Relations 6

Recurrence Relations 7

Recurrence Relations 8

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 Path and Circuits

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

Graphs 1

Graphs 2

Graphs 3

Graphs 4

Graphs 5

Graphs 6

Graphs 7

Graphs 8

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