All material from previous exams (concepts not tested explicitly, but are necessary) Definitions/Terms
reflexivesymmetricantisymmetrictransitiveposet
partial orderingdirected graphundirected graphHasse diagram upper boundlower bound least upper bound greatest lower bound latticetotal order equivalence relationequivalence class partitionpart/cell/block alphabet stringempty string string lengthconcatenation prefix/suffixsubstring language Chapter 7 – More on Relations

Properties: reflexivity, symmetry, antisymmetry, transitivity – know definitions and understand what they mean about a relation, know and be able to construct examples of relations with and without each property (or combination of properties). Be able to count reflexive, symmetric, and antisymmetric relations. Be able to prove whether a described relation has or does not have each of these properties. Representations of relations: as sets, as matrices, and as digraphs. Understand the relationship among these representations. Be able to form compositions of relations, and understand how the notion of composition translates to matrices and digraphs. Understand how relation properties are manifested in each of these representations. Partially ordered sets: definitions, examples, be able to prove that a relation is a partial ordering, be able to construct and analyze Hasse diagrams, be able to spot upper bounds, lower bounds, the greatest lower bound, and least upper bound for a given set. Equivalence Relations: definitions, examples, equivalence classes, partitions, and the relationship between partitions and equivalence relations, be able to construct the partition induced by a given equivalence relation, and the equivalence relation arising from a given partition.

Chapter 6 – Strings
String theory: definitions, alphabets, powers of an alphabet ((0, (n, (*, (+, etc.),...

...1. Define Proposition and provide at least five (5) Proposition and Non-Propositional statements.
Proposition refers to either (a) the "content" or "meaning" of a meaningful declarative sentence or (b) the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence
Examples of Propositions
1.The sun is shining.
2. The sum of two prime numbers is even.
3. 3+4=7
4. It rained in Austin, TX, on October 30, 1999.
5. x+y > 10
Examples of Non-Propositional...

...“DiscreteStructures”
“Q2: Determine whether each of these functions from {a,b,c,d} to itself is onto and/or one-to-one.
a) f(a)=b, f(b)=a, f(c)=c, f(d)=d
a
b
c
d
a
b
c
d
a
b
c
d
a
b
c
d
The above Function is both one-to-one and onto, therefore Its called a BIJECTION Function
b) f(a)=b, f(b)=b, f(c)=d, f(d)=c
a
b
c
d
a
b
c
d
a
b
c
d
a
b
c
d...

...for students to improve their knowledge.
Today, students learn in the most and to the great extent if they will learn it through doing it by themselves. By introducing this type of teaching strategies, E-Module for DiscreteStructures with biometrics is made to enhance the quality of education and instruction inside the classroom.
OVERVIEW OF THE CURRENT STATE OF TECHNOLOGY
In the current system of communication...

...Introduction to DiscreteStructures --- Whats and Whys
What is Discrete Mathematics ?
Discrete mathematics is mathematics that deals with discrete objects. Discrete objects are those which are separated from (not connected to/distinct from) each other. Integers (aka whole numbers), rational numbers (ones that can be expressed as the quotient of two integers), automobiles, houses, people etc. are all...

...ECON-UA 2 PRINCIPLES OF ECONOMICS II CHAPTER 03 HANDOUT
DR. ANDREW PAIZIS – NYU
1
NEW YORK UNIVERSITY
Department of Economics
THE AVIAN FLU
In 2005, both in the United States and Europe the market for chicken had about the same
price, as it can be seen from the following Figure 1:
In 2006, the chicken flu epidemic affected Europe and Asia.
This generated considerable fear among consumers in Europe, and the demand curve shifted
drastically to the left in...

...Submitted to: Professor Faleh Alshamari
Submitted by: Wajeha Sultan
Final Project
Hashing: Open and Closed Hashing
Definition:
Hashing index is used to retrieve data. We can find, insert and delete data by using the hashing index and the idea is to map keys of a given file. A hash means a 1 to 1 relationship between data. This is a common data type in languages. A hash algorithm is a way to take an input and always have the same output, otherwise known as a 1 to 1 function. An...

...Introduction
The context of this paper is to investigate the relationship between capital structure and firm performance on Malaysia plantations industries. According to Brealey and Myers (1988), the capital structure will determine the survival of a business. Damodaran (2001) defined capital structure as the mix of debt and equity used to finance the operation of firms. Capital structure is closed link with corporate performance...

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