Question

In how many forms, you can represent a set; explain with the help of examples.

Answer 1

you can represent set in three different forms :

1 ) Roaster Form ( aslo kniwn as Tabular form )
2) Set - Builder form
3 ) Intervals

Firstly we should know what actually a set is ?

consider a collections of any objects . This collection must be well defined ( means there should not be any ambiguity ( giving two or more meanings ) )...

Then you have acollections of objects which is well defined or simply you have collections of well defined objects...The collection of well defined object is called a set...
For example...Set of all the months in a year...There is a collection of months and months are well defined...But if you consider a collection of best cricket player of any cricket team...it will not be a well defined..beacuse the characteristics of being best cricker vary or changes player to player...

1 ) Roaster Form
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This is simplest form of set which is represted by flower bracket or curly brackets and elements in the set are sepretaed by Commas...
Example => Set of all days of a weak begins with letter T ...
X = { Tuesday , Thursday }.

2) Set- Builder form
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This is a descriptive form of set which means this form gives more information about a set rather than Roaster form.
In this form inform is abstract ( hidden ) and assigned in an arbitrary variable.
Example => Set of all vowels of English alphabets
V = { x : x is a vowel of an English alphabets }
Above set can be read as For all x Such that x is a vowels of an English alphabets.
Here x is an arbitrary elements which can store or take each vowels...

3) Intervals
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Intervals are also the way we represent a set..
This is a compact form of a set...
Suppose we want to represent a real number strictly lying between 3 and 4..then we use intervals notation
as x € ( 3 , 4 ) for all x € R where R is a set of all real numbers...
x € ( 3 , 4 ) Read as x belongs to open interval 3 comma 4
if x € ( 3 , 4 ) => 3 < x < 4 for all x € R ( x doesnt take boundry points )

If x € [3 , 4] => 3 《 x 《 4 for all x € R
Read as x belongs to clos3d intervals 3 comma 4 ( here x takes Boundry points 3 and 4 )