Discrete Mathematics

----------------------------------------------------------·RELATIONS

143

Conversely, given sets A and B with I A

I=

m and I B

I=

n, a matrix m x n whose entries are zeros and

ones determine a relation.

Example

11 Let R be the relation from A =

{1,

2, 3, 4,

5}

to B = {red, white, blue, green} defined by

R = {(1, red), (1, blue), (3, blue), (4, green)}.

3.5.2

Graph

of

Relation

xQ

xRx

(\,

xo__....,

xRyAyRzAzRx

Digraphs

A is a finite set and R is the relation on A.

Let

A=

{1, 2, 3, 4}

(i) R = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (3, 4), (4, 1)}

The digraph

of

R is

(ii) R = {(I,

I),

(1, 3), (2, 3), (3, 2), (3, 3), (4, 3)}

144 DISCRETE ...