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Algebra I: A Basic Course in Abstract Algebra by Rajendra Kumar Sharma, Sudesh Kumari Shah, Asha Gauri Shankar

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Chapter 1

Sets and Relations

In our daily life we come across words such as set, collection, group, clear etc… In this chapter we begin by giving a mathematical definition of the word ”set” and proceed to study various types of relations on them. To make concepts easily comprehensible, lots of examples and diagrams, called Venn diagrams have been given. So, first thing first.

1.1 Sets

Definition 1.1.   (Set): A set is a well defined collection of objects.

The adjective ‘well defined’ means that given an object, it should be possible to decide whether it belongs to the collection or not. There should not be any ambiguity. The objects that belong to a set are called its members or elements.

Example 1.1.   The following are examples of sets:

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