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Discrete Mathematics by Babu Ram

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1

Sets, Relations and Functions

In this chapter, we introduce the notions of sets, relations and functions which are the basic tools of discrete mathematics. The set theory was founded by Georg Cantor in late nineteenth century. The concept of a set appears in all mathematical structures.

1.1 SETS

A set is an undefined term of set theory just as sentence, true and false are undefined terms of logic. According to Georg Cantor, a set may be viewed as a well-defined collection of objects, called the elements or members of the set. The term “well defined” means that it is possible to decide if a given object belongs to the collection or not.

The sets are denoted by capital letters such as A, B, C, whereas the elements of a set are denoted by lowercase ...

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