GRAPHS
Discrete Mathematical Structures
<professor>
INTRODUCTION TO GRAPHS
Definition: A simple graph G = (V, E) consists of
V, a nonempty set of vertices, and E, a set of
unordered pairs of distinct elements of V called
edges.
A simple graph is just like
RELATIONS
Discrete Mathematical Structures
<professor>
RELATIONS
To describe a relationship between elements of two sets A
and B, it can use ordered pairs with the first element
taken from A and the second element taken from B.
Since this is a relation be
TREES
Discrete Mathematical Structures
<professor>
Computer Science Department
TREES
Definition: A tree is a connected undirected
graph with no simple circuits.
Since a tree cannot have a simple circuit, a tree
cannot contain multiple edges or loops.
Ther
EQUIVALENCE
RELATIONS
Discrete Mathematical Structures
<professor>
Computer Science Department
EQUIVALENCE RELATIONS
Def 1. A relation R on a set A is called an
equivalence relation if it is reflexive, symmetric,
and transitive.
Example 1.
Let R be the re
BOOLEAN
ALGEBRA
Discrete Mathematical Structures
<professor>
Computer Science Department
BOOLEAN ALGEBRA
Boolean algebra provides the operations and
the rules for working with the set cfw_0, 1.
The three operations are the following:
Boolean complementati