INTRODUCTION TO SETS

Definition Set is a WELL DEFINED collection of objectsExample:

MeaningBag is a set which consists of well

definedObjects i.e. pencils, erasers, scale,books etc. These objects are the

elements ofthis set

Examples

Can a beautiful girl or group of beautiful girls be

a set?The answer is ‘NO’ because beauty is not well defined

ExamplesCan a group of boys be a collection of Set?

‘YES’ , group of boys is a set because numberof boys in the group are well defined

ExamplesA smart man …. Is it a Set?

Ans. ………

ExamplesGroup of teachers in school…….is it acollection of set?

Ans………

ExamplesCollection of prime numbers?

Ans…….

SETSIndiviual object in the set is called ELEMENT

or a MEMBER of the set.Sets are denoted by capital alphabets , e.g. A,

B, C etc.Elements of set are denoted by small

alphabets , e.g. a, b, c,etc Use curly braces to represent set.We could not repeat an element in a set.

Types of Sets

Types of

sets

empty set

Singeltonset

Finiteset

Infiniteset

Types of SetsEmpty set : it’s a set having no element. Also known as

Null set, it is denoted by ФExample: set of all natural numbers between 5 and 6Singleton set : it’s a set having only one elementExample: { 7 }Finite set : it’s a set wherein counting of elements ends at

a certain stageExample: {5,6,7}Infinite set : it’s a set in which counting of elements do not

end at any stageNatural and whole numbers, integers, rational and real

numbers are infinite setsAn empty set is a finite set