This presentation discusses sets and set theory. It defines what a set is and provides examples of different types of sets such as empty, singleton, finite, and infinite sets. The presentation outlines basic set operations like union, intersection, complement, and difference. It discusses how Venn diagrams can be used to represent sets and subsets. Applications of sets in daily life are presented, such as organization in kitchens and stores. Formulas related to 2 and 3 Venn diagrams are provided.

1. Presentation on Set
Prepared By:
 Sabin Dhakal
 Sagar Chapagain
 Prasiddha Chand
 Binita Rimal
 Sadikshya Khadka
Mathematics is not about numbers, equations,
computations, or algorithms: it is about understanding.
— William Paul Thurston, American mathematician

2. 5
Topic Of Presentation
4
3
2
1
 Definition of Sets
 Types of sets
 Finding of Sets
 Application of Sets in
Daily Life
 Formulas of Set

3.  Sets are an organized collection of objects and can be represented in set-builder form or
roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a
set.
Also,
 Sets are represented as a collection of well-defined objects or elements and it does not
change from person to person. A set is represented by a capital letter.
 The basic operations on sets are:
• Union of sets
• Intersection of sets
• A complement of a set
• Cartesian product of sets.
• Set difference

4. Types of sets
 Empty Set:
If a set doesn’t have any elements, it is known as an empty set or
null set or void set. For e.g. consider the set,
Q = {y : y is a whole number which is not a natural number, y
≠ 0} 0 is the only whole number that is not a natural number. If y ≠ 0, then
there is no other value possible for y. Hence, Q = ϕ.

5.  Singleton Set
If a set contains only one element, then it is called a singleton set. For e.g.
A = {x : x is an even prime number}
B = {y : y is a whole number which is not a natural number}
 Finite Set
If a set contains no element or a definite number of elements, it is called a finite set.
If the set is non-empty, it is called a non-empty finite set. Some examples of finite sets are:
A = {x : x is a month in a year}; Set A will have 12 elements.

6. Infinite Set:
Infinite sets are the sets containing an uncountable or infinite number of elements.
Infinite sets are also called uncountable sets. For e.g.
A = {x : x is a natural number}; There are infinite natural numbers. Hence, A is an infinite set.
 Sub Set:
If A={-9,13,6}, then, Subsets of A= ϕ, {-9}, {13}, {6}, {-9,13}, {13,6}, {6,-9}, {-9,13,6}. So,
we can define sub set as If a set A contains elements which are all the elements of set B as
well, then A is known as the subset of B.

7.  Universal Set:
A universal set is a set which contains all objects, including
itself. For e.g. The set of real numbers is a universal set of integers, rational
numbers, irrational numbers.

8.  Difference of two sets:
The difference of set A and B denoted by A- B is a new set which contains
all the elements of set A but not the elements of set B. Example: Let A = {a,
b, c, d} and B = {b, d, e}. Then A – B = {a, c} and B – A = {e}.
 Complement of set:
If set A is a subset of universal set U, the complement of a set is the set of
elements of U but not the elements of set A.

9. Finding of sets
• Jhon Venn, an English mathematicians, used ovals for the first time to
represent sets and subsets in diagrams. These diagrams are named after
his name as Venn diagrams.
• Set theory is the branch of mathematical logic that studies sets, which can
be informally described as collections of objects.
• Set theory begins with a fundamental binary relation between an
object o and a set A.
• A set is described by listing elements separated by commas, or by a
characterizing property of its elements, within braces { }.
• Set theory is commonly employed as a foundational system for the whole
of mathematics.
• Different types of sets are classified according to the number of elements they have.

10. Application of Sets
 In Kitchen:
Kitchen is the most important place in our home. In kitchen
all the things, utensils are kept in order. For example: set of same
utensils, spices are kept in same place.

11. Shopping Mall:
In shopping mall there are different stores where we can get different
things. For example: cloth shops are in different place and food counters
are in different place.
Rule:
Every school for company have different sort of rules which should be
followed by each and every student or employees.
For example: Timing rule, disciplinary rule, rule for asking a leave etc.
School Bags:
School bags of children is also a form of set as books and text copies
are generally kept in different place.

12. In Business :
Theory of set can assist in planning and operations. Each and every
element of business can be grouped into at least one set as accounting,
management, marketing, production, sales etc. In some cases set also
intersects as sales operations can intersect the operation set and the
sales set.
Universe:
As we all know that there are millions of galaxies present which are
separated from each other by some distance. In this case universe act
as a set.
Playlist
We all like to listen songs. Most of us have different kind of playlist in our
smart phone or computer. Rock music are different from classical or
other genre. Hence playlist is a example of set.

13. Formulas of 2 Venn-diagram
1. If A and P are overlapping set, n(A∪B)=n(A)+n(B)–
n(A∩B)
2. If A and B are disjoint set, n(A∪B)=n(A)+n(B)
3. n(U)=n(A)+n(B)–n(A∩B)+n(A∪B)
4. n(A∪B)=n(A−B)+n(B−A)+n(A∩B)
5. n(A−B)=n(A∩B)−n(B)
6. n(A−B)=n(A)−n(A∩B)

14. Formulas of 3 Venn-Diagram
• n(AᴜBᴜC) = n(A) + n(B) + n(C) – n(A∩B) – n(B∩C) – n(C∩A) + n(A∩B∩C)
• n(U)= n(A) + n(B) + n(C) – n(A∩B) – n(B∩C) –
n(C∩A) + n(A∩B∩C)+n(AUBUC)
• n(U)= n(AᴜBᴜC) + n(AUBUC)
• n(AUBUC)=n(U)- n(AᴜBᴜC)

15. Life is a math equation. In order to gain the most, you have to
know how to convert negatives into positives.