Discrete Mathematics

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Chapter

3

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RELATIONS

3.1

OPERATIONS ON RELATIONS

In this chapter we will study the difference between properties

of

relations and operations on relations. We

will also study types

of

relations such as symmetry, transitivity, reflexivity, and discuss the concept

of

transi-

tive closure (Warshall's algorithm).

3.1.1

Set

Operations

Relations are sets

of

tuples, so we can apply set operations. The intersection

of

two relations gives pairs

satisfying both relations. The union gives pairs satisfying one-the union

of

"brother-of' and "sister-of' is

"sibling-of". Complement gives pairs not satisfying both relations.

3.1.2

Inverse

Definition ...