Discrete Math Notes:
Chapter 5: Functions and Relations
5.6 Introduction to binary relations
binary relation, between two sets A and B is a subset R of A x B
arrow diagram, the elements of A are listed on the left, the elements of B are listed on the right, in relation R on sets A and B
matrix representation, between A and B is a rectangular array of numbers with |A1 rows and |B I columns.
binary relation on a set A, is a subset of A x A
domain, the set A of the binary relation
self-loop, an element that is related to itself is indicated by an arrow
overview:
People={Sue,Harry, Sam } Files={FileA,FileB,FileC.FileD}
Relation A: pAf if person p has access to file f
Files FileA
People
A={(Sue, FileB),(Sue, FileC).(Sue, FileD) (Harry, FileA),(Harry, FileD)}
Sue
o FileB
Harry
FileC o FileD
Sam :
Captions ^
1.A relation A is defined on a set of people and a set of files. Person p is related to file f under A (pAf) if person p has access to file f. 2. An arrow diagram for A lists the people in a column on the left and the files in a column on the right. 3. Each pair (p, f) in the relation is represented by an arrow pointing from p to f.
A rectangular array of numbers with (A| rows and |B| columns is a matrix representation of relation R between A and B. A subset of A x A is a binary relation on the set A. The domain of the binary relation is referred to as set A. Arrows can enter and exit an element. A self-loop is an arrow that represents a relationship between two elements. A self-loop exits the element and then returns to i