SET, DEFINITION, METHODS OF DESCRIBING

1. CS40, Wim van Dam, UCSB
SUBJECT : MATHEMATICS
CLASS : MATRIC/O-LEVEL
CHAPTER ( 1/4 ) : SET AND OPERATIONS
ON SETS
LESSON : 01 OF 08
TOPIC : SET THEORY

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LOOK AT THESE PICTURES CAREFULLY

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WHAT DO YOU OBSERVE IN THESE
PICTURES ?

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These are collection of distinct and well defined objects.

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SET THEORY
 Definition
 Notation
 Examples
 Properties of Set
 Methods for the Description of a Set

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History of Set Theory
Georg Cantor (1845–1918)
Founder of modern Set Theory.
SET THEORY

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Definition
 A set is a collection of distinct and well defined objects.
 The objects that make up a set are called elements or
members of the set. Lowercase letters are used for elements and
capital lettes for sets.
A = { a,b,c }
SET THEORY

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Definition of Set

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Notation
• Use braces { } around the elements
• Elements are written in small letters
• Use capital letters for set e.g
A = { a,b,c }

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Examples
• Players of cricket team
• Collection of books
• Bundles of sticks
• Bunch of grapes
• Army of Soldiers
• Dinner set

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Properties of Sets
 The order in which the elements are presented in a
set is not important.
A = {a, e, i, o, u} and B = {e, o, u, a, i} both define
the same set.
 The members of a set can be anything.
 In a set the same member does not appear more
than once.
F = { a, e, i, o, a, u } is incorrect since the element ‘a’
repeats.

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Methods For The Description of Sets
There are three methods for description of a set
namely
Descriptive Method
Tabular Method
Set Builder Notation
SET THEORY

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Descriptive Method
SET THEORY
In descriptive method, sets are
described in words. For example
B = Set of natural number less than six
C = Set of integers greater than minus two and
less than five
D = Set of whole number less than 10

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Tabular Method
In tabular method, sets are described by
listing and enclosing the elements within the braces.
Example
B = {1,2,3,4,5 }
C = {-1,0,1,2,3,4 }
D = {1,2,3……..,9 }
SET THEORY

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Set Builder Notation
SET THEORY
In this method the characteristic
property of all the elements of the set is written.
Example : Suppose that B= {1,2,3,4,5 } and C={-1,0,1,2,3,4}.In
set builder form, the set B and C can be written as
B = {x I x  N x 5 }
C = {x I x  Z -1 x 4 }

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SET THEORY
 Definition
 Notation
 Examples
 Properties of Set
 Methods for the Description of a Set

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Q. What is the definition of a set?
A. A well-defined collection of distinct objects.
Q. What are different methods to describe a set?
A. There are three methods for description of a set:
(i) Descriptive method
(ii) Tabular method
(iii) Set builder notation
Q. What is descriptive method?
A. Sets are described in words.

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Q. What is tabular method?
A. Sets are described by listing the elements within
the braces.
Q. What is set builder notation?
A. The characteristic property of all the elements of
a set is written
Q. A = { a, e, i, o, a, u,e } Why this is not a set ?
A. It is not distinct, since the elements “a” and “e”
are repeated twice.

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TYPES OF SET