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                            SETS

UNIT-1

                 

SYLLABUS:

Set Theory: Types of Sets- Set Operations-

Laws and Properties of Sets- De-Morgan’s laws-

Applications to business and economic problems.

Definition[set]

A set is a collection of well defined objects.The objects can be anything –people, alphabets,numerals, etc. the objects are known as elements or members of the set.

Notations:

Sets are denoted by Capital letters, A, B, C, D…

The elements are denoted by small letters a, b, c,d….

Methods of Description of sets:

There are two method by which a set is

described. They are:

1. Tabulation Method (Roster Method)

2. Set Builder Method (The Rule Method)

Definition[Tabulation Method]

This is also called Roster Method. Under this

method, the elements are listed, separated by

commas and enclosed by braces{ }.

Example:

1. The set of vowels in English Alphabet is

written as A={a, e, I, o, u}

2. The set of days is written as A={Sunday,

Monday, Tuesday, Wednesday, Thursday,

Friday, Saturday}.

3. The set of all Natural number is written as N={1,2,3,.....}

Definition[Set Builder Method]

This is also called the Rule Method. Under

this method, the letter x is usedt or epresent a typical element. All the objects which possess the properties are the elements of the set. X and the

properties are written within braces.

Example:

1. The set of vowel in English Alphabet is written as

A={x: x is a vowel in English Alphabet}.

2. The set of all days in a week is written as

A={x: x is a day in a week}

3. A set S={1, 2, 3, 4, 5} may be written as

S= {x: x∊N, x<6}

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