SET THEORY

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

LOOK AT THESE PICTURES CAREFULLY

WHAT DO YOU OBSERVE IN THESE
PICTURES ?

These are collection of distinct and well defined objects.

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

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

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

Definition of Set

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

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

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.

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

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

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

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 }

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.

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.

TYPES OF SET

SET THEORY

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SET THEORY