This document discusses an introduction to set theory. It defines a set as a collection of distinct objects and introduces common set notation using curly brackets. It describes three methods for describing sets: descriptive method using words, tabular method listing elements in curly brackets, and set builder notation writing the characteristic property of elements. Key concepts of sets like order of elements not mattering and no repetition of elements are also covered.

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

2. CS40, Wim van Dam, UCSB

3. CS40, Wim van Dam, UCSB
LOOK AT THESE PICTURES CAREFULLY

4. CS40, Wim van Dam, UCSB

5. CS40, Wim van Dam, UCSB

6. CS40, Wim van Dam, UCSB

7. CS40, Wim van Dam, UCSB

8. CS40, Wim van Dam, UCSB

9. CS40, Wim van Dam, UCSB

10. CS40, Wim van Dam, UCSB

11. CS40, Wim van Dam, UCSB
WHAT DO YOU OBSERVE IN THESE
PICTURES ?

12. CS40, Wim van Dam, UCSB
These are collection of distinct and well defined objects.

13. CS40, Wim van Dam, UCSB
SET THEORY
 Definition
 Notation
 Examples
 Properties of Set
 Methods for the Description of a Set

14. CS40, Wim van Dam, UCSB
History of Set Theory
Georg Cantor (1845–1918)
Founder of modern Set Theory.
SET THEORY

15. CS40, Wim van Dam, UCSB
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

16. CS40, Wim van Dam, UCSB
Definition of Set

17. CS40, Wim van Dam, UCSB
Notation
• Use braces { } around the elements
• Elements are written in small letters
• Use capital letters for set e.g
A = { a,b,c }

18. CS40, Wim van Dam, UCSB
Examples
• Players of cricket team
• Collection of books
• Bundles of sticks
• Bunch of grapes
• Army of Soldiers
• Dinner set

19. CS40, Wim van Dam, UCSB
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.

20. CS40, Wim van Dam, UCSB
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

21. CS40, Wim van Dam, UCSB
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

22. CS40, Wim van Dam, UCSB
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

23. CS40, Wim van Dam, UCSB
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 }

24. CS40, Wim van Dam, UCSB
SET THEORY
 Definition
 Notation
 Examples
 Properties of Set
 Methods for the Description of a Set

25. CS40, Wim van Dam, UCSB

26. CS40, Wim van Dam, UCSB
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.

27. CS40, Wim van Dam, UCSB
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.

28. CS40, Wim van Dam, UCSB
TYPES OF SET