Discrete Structures
CMSC 2123
Lecture 8
2.1 Sets
Introduction
DEFINITION 1
A set is an unordered collection of objects.
DEFINITION 2
The objects in a set are called the elements, or members, of the set. A set is
said to contain its elements.
EXAMPLE 1
Des

Discrete Structures
CMSC 2123
Lecture 7
1.7 Introduction to Proofs
Introduction
Formal proofs of theorems designed for human consumption are almost always informal
proofs, where more than one rule of inference may be used in each step, where steps
may be

Discrete Structures
CMSC 2123
Term
argument
valid
premise
fallacy
Lecture 6
1.6 Rules of Inference
Definition
A sequence of statements that ends with a conclusion.
The conclusion, or final statement of the argument, must follow from the truth
of the prece

Discrete Structures
CMSC 2123
Lecture 1
1.1 Propositional Logic
DEFINITION 0
A proposition is a declarative sentence that is either true or false but not
both.
EXAMPLE 1.1
The following is a declarative sentence.
Washington D.C. is the capital of the Unit

Discrete Structures
CMSC 2123
Lecture 2
1.2 Applications of Propositional Logic
Translating English Sentences
EXAMPLE 1
How can this English sentence be translated into a logical expression?
You can access the Internet from campus only if you are a comput

Discrete Structures
CMSC 2123
Project p01
Overview
1. Create file p01.cpp in the root directory of your account for this class on the departmental
computer cs.uco.edu.
2. Enter your author identification block consisting of
2.1. Your name, for example, Mr

Discrete Structures
CMSC 2123
Introduction
EXAMPLE 1
EXAMPLE 2
Lecture 5
1.5 Nested Quantifiers
Express ( + = 0) without the existential quantifier.
Solution: ( + = 0) is the same as () where () is (, )
and (, ) = + = 0
Translate ( > 0) ( < 0) < 0) into E

Discrete Structures
CMSC 2123
DEFINITION 1
Lecture 3
1.3 Propositional Equivalences
A compound proposition that is always true, no matter what the truth values
of the propositions that occur in it, is called a tautology.
A compound proposition that is alw

Discrete Structures
CMSC 2123
Lecture 4
1.4 Predicates and Quantifiers
Introduction
In this section we will introduce a more powerful type of logic called predicate logic.
Predicates
Consider the statement: > 3. The statement has two parts:
1. the variabl