This document defines and provides examples of sets and related concepts: - A set is a well-defined collection of objects, with the individual objects called elements or members. Sets are denoted by capital letters and elements by lowercase letters. - Examples of sets include bags containing pencils and books, where the objects are well-defined. A group of people is not a set if beauty is not well-defined. - Types of sets include empty, singleton, finite, and infinite sets. Finite sets have a countable number of elements, while infinite sets do not. - Key concepts include subsets, where all elements of one set must be in another to be a subset, and universal sets, which are

1. Compiled by
Prof . Sandeep
Gupta

3. Meaning
 Set is a WELL DEFINED collection of objects

4. Meaning

5. Meaning
Bag is a set which consists of well defined
Objects i.e. pencils, erasers, scale,
books etc. These objects are the elements of
this set

6. Examples

7. Examples
Can a beautiful girl or group of beautiful girls be
a set?

8. Examples
The answer is ‘NO’
because beauty is not well defined

9. Examples
Can a group of boys be a collection of Set?
‘YES’ , group of boys is a set because number
of boys in the group are well defined

10. Ur turn to think…..
A smart man …. Is it a Set?
Ans. ………

11. Examples
Group of good teachers in school…….is it a
collection of set?
Ans………

12. Examples
Collection of prime numbers?
Ans…….

13. SETS
 Indiviual object in the set is called ELEMENT or a
MEMBER of the set.
 Sets are denoted by capital alphabets , e.g. A, B, C etc.
 Elements of set are denoted by small alphabets , e.g. a,
b, c etc.
 If a is an element of set X then we write it as a Є X
 If a is not an element of set X, then it is written as a Є X

14. Types of Sets
Types
of sets
empty
set
Singelton
set
Finite
set
Infinite
set

15. Types of Sets
 Empty set : it’s a set having no element. Also known as
Null set, it is denoted by Ф
 Singleton set : it’s a set having only one element
 Finite set : it’s a set wherein counting of elements ends
at a certain stage
 Infinite set : it’s a set in which counting of elements do
not end at any stage
 An empty set is a finite set
 Natural and whole numbers, integers, rational and real
numbers are infinite sets

16. Few concepts worth remembering
 Natural and Whole numbers
 these includes numbers like 1,2,3,4 etc
only difference is we include ‘0’ (zero) in whole
numbers but not in natural numbers
are not fractions, decimals or negative numbers
 Integers
 are positive or negative numbers and includes zero
are whole numbers but can be negative too

17. Few concepts worth remembering
 Rational numbers
Includes integers, fractions and repeating decimals
• Irrational numbers
Includes only decimals that have no pattern and continue
forever
• Real numbers
It includes every thing discussed above

18. Symbols
Symbols commonly used:
Whole numbers W
Integers I
Rational numbers Q
Natural numbers N
Real numbers R

19. Methods of writing sets
 Listing method (Roster form)
 Rule method (Set builder form)
Examples
1. Set of first 20 even natural numbers
Roster form
A = {2, 4, 6, 8, ………40}
Set builder form
A = {x|x is even natural number, 2 ≤ x ≤ 40}

20. Examples
Example 2
Set of first 10 multiples of 5
Roster form
A = {5, 10, 15, 20, …..50}
Set builder form
A = {x|x=5n, n Є N, 1 ≤ n ≤ 10}

21. Concept of Subsets
 If every element of set B is an element of set A, then
set B is subset of set A
 Subset can be proper subset or improper subset
 If set B is subset of set A and set A contains at least one
element which is not in set B, then set B is proper
subset of set A
 If set A is subset of set B and if set B is subset of set A,
then they are improper subsets of each other
 B A is to be read as set B is proper subset of set A

22. Concepts of subsets
 A B is to be read as set A is super set of set B
 A B is to be read as set A is improper subset of set
B
 Every set is subset of itself
 Empty set is subset of every set

23. Universal set
 A non-empty set of which all the sets under
consideration are the subsets of that set is called
universal set
 It is denoted by ‘U’

24. The
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