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CHAPTER 2 : SETS

2.1 Sets

In our daily life, we often talk of a collection of objects. For instance, your class, your baseball team, your family. They all denote collection.

A class is a collection of students.

A team is a collection of players.

A family is a collection of persons.

Now consider the following examples.

1. a, e, i, o, u

2.

3. New York, London, Paris, New Delhi

4. Beautiful women of your area.

5. Rich people of New Jersey.

All these are collections of certain objects such as, vowels, numbers (fractions), women, persons, metropolitan cities etc.

In examples 1, 2 and 3 we know the objects precisely. But in examples 4 and 5 the terms, beautiful women or rich people are relative terms. Hary may be clever by Pat’s standard but may not be so clever by Liza’s. So we can not decide whether to include Hary in our collection. Similarly ’ Rich people’ is also a relative term.

In Mathematics, a collection of well defined and distinct objects is called a set.



Methods of writing a set

We denote sets by capital (bold face) letters A, B, X, Y etc. and its elements by small case letters a, b, c etc.

There are two ways to describe a set

1) listing (Roster) method

2) Rule or set builder method

Listing method

In this method, we describe a set by listing all its elements enclosed in braces, the elements are separated by commas without any repetition.

For example

A = { a, e, i, o, u } , B = { 1, 2, 3, . . . 100 }

N = { 1, 2, 3 . . . } , I = { ... -3, -2, -1, 0, 1, 2, 3, . . . }

Index

2.1 Sets
2.2 Operations on Sets
2.3 The Algebra of Sets

Chapter 3





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