SET AND REPRESENTATION OF SET

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SET LANGUAGE

COLLECTION OF FRUITS
COLLECTION OF VEHICLES

COLLECTION OF FLOWERS
 
Any collection of objects is called as SET. 


Do you think the above objects are related to each other? Yes! The trumpet and xylophone, cooling glass and sun, driller and screw driver, skating cycle and bicycle, football ball and soccer ball, ice cream and cone ice cream. These are the objects related to each other. 

COLLECTION OF STATES IN INDIA 

COLLECTION OF CLASSICAL DANCE IN INDIA

COLLECTION OF SMART STUDENTS IN A CLASS
Do you think the above three collections are well defined? The collection of states and classical dance in India are well defined but the collection of smart students in a class are not well defined because it is not specific. 

        Here “well-defined collection of objects” means that given a specific object it must be possible for us to decide whether the object is an element of the given collection or not. The objects of a set are called its members or elements.

A set is a well defined collection of objects.

REPRESENTATION  OF A SET

The set can be represent in three ways.
1.Descriptive form
2.Set builder form or Rule form
3.Roaster form or Tabular form

Descriptive Form

In descriptive form, a set is described in words. For example,  

  • The set of all consonants in English alphabets. 
  •  The set of whole numbers.

Set Builder Form or Rule Form 

In set builder form, all the elements are described by a rule. For example,
  •   A = {x : x is a consonants in English alphabets} 
  •  B = {x|x is a whole number}

Roster Form or Tabular Form ∈∈∈∈

A set can be described by listing all the elements of the set. For example, 
  • A = {b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z} 
  • B = {0, 1, 2, 3,…} 
Notation 
  • A set is usually denoted by capital letters of the English Alphabets A, B, P, Q, X, Y, etc. 
  • The elements of a set is written within curly brackets “{ }” 
  • If x is an element of a set A or x belongs to A, we write x Є A
  •  If x is not an element of a set A or x does not belongs to A, we write x ∉ A.
For example, 
 Consider the set A = {2,3,5,7} then 
  • 2 is an element of A; we write 2 Є A 
  • 5 is an element of A; we write 5 Є A
  • 6 is not an element of A; we write 6 ∉ A

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