set !

1. SETS:
MORE THAN JUST CIRCLES !
A REAL WORLD STUDY OF FOOTBALL,BASKETBALL,AND CRICKET
PREFERENCES AT FLUORESCENT SECONDARY SCHOOL
MATHEMATICS
PRESENTATION
Shrisha sapkota
Saskriti pyakurel
Manaswi timisina
Mayuri Shah
Aakanshya Gurung
Adrina shrestha
Neelam Nepal
Members:

2. I’d like to sincerely thank our subject teacher, Mr.
Anand Sapkota Sir for giving us this ample
opportunity to work together, collect data, and
engage in real world learning. This experience
helped us not only to connect theory to practical
even strengthen our teamwork skills. We truly
appreciate the chance to learn beyond books and
collaborate effectively.
Grateful for a valuable learning experience in
Fluorescent secondary school

3. To prepare for our presentation, the first important step was collecting data. Some
team members went to classes 10, 8, and 7, making sure we got the best information.
During the survey, we questions, and students were requested to stand up while
responding. At first, some were shy, but soon everyone got involved. Supportive
teachers CR, VCR helped make the process smooth, and their encouragement made
a huge difference.
Overall, it was a great experience not just about collecting data but also about seeing
how engaged and excited everyone was.
BACK STORY OR THE SURVEY
EXPERIENCE

4. key points or main content
Definition of Sets – Basic concept and meaning of sets.
Types of Sets – Finite, infinite, empty, universal, subset, and more.
Venn Diagram of Sets
Operations on Sets – Union, intersection, complement, and
difference.
Survey Questions & Analysis – from collected data, and
observations.
Conclusion of the presentation

5. A set is a well-defined collection of distinct objects, considered
as an entity. These objects, known as elements, can be anything—
numbers, letters, symbols, or even ideas. Element is unique and
enclosed within curly brackets {}.
Example:
S = {Red, Blue, Yellow}
Fun Fact:
Did you know that the concept of sets is the backbone of modern
mathematics? The German mathematician Georg Cantor developed
set theory in the late 19th century, revolutionizing the way we
understand infinity!
CHAPTER:ONE
TOPIC : SETS

6. THERE ARE DIFFERENT TYPES OF SETS
Empty Set (∅)
Singleton Set
Finite Set
Infinite Set
Universal Set (U)
Subset (⊆)
Proper Subset (⊂)
Disjoint Sets
Union of sets
Compliment of sets
Intersection of sets
We have read different
types of set till class 10
well some of the sets are
explained in brief in next
slide which are Universal
set,intersection of
set,union of set,
compliment of set

7. Types of sets:
INTERSECTION OF SET
The elements common to any two or three sets is called intersection of sets.
The intersection of sets for two Venn diagram A and B is denoted by A ∩B
and its cardinal number by n(A ∩B) where as the intersection of sets for
three Venn diagram A ,B and C is denoted by A ∩B∩C and its cardinal
number by n(A ∩B ∩C)
UNIVERSAL SET
The set that contains all the elements under consideration for a particular discussion or
problem. it is denoted by ‘U’ and its cardinal number by n(U). Subsets Belong to the Universal Set =
Any set A, B, C, ... will always be part of U, meaning A ⊆U, B ⊆U, etc.
Use in Set Theory and Logic – The universal set is useful in operations like complements (A',
meaning elements in U but not in A) and intersections.

8. The union of sets is simply the combination of all elements from the
given sets, ensuring no duplicates. In a two-set Venn diagram, the
union of Set A and Set B (written as A ∪B) includes everything inside
either circle, including the overlapping middle part. This means we
gather all elements belonging to either Set A or Set B.
Expanding this to a three-set Venn diagram, the union of Set A, B, and
C (written as A ∪B ∪C) covers all elements appearing in any of the
three sets. Visually, the union represents everything inside any of the
circles, ensuring all members are included at least once. It’s like
combining multiple groups where everyone gets counted, whether
they belong to one, two, or all three sets. If there is no element in the
compliment of the union of sets then n(U) is same as n (A U BUC) OR
n(A U B) .
UNION OF SETS

9. The elements which belongs to the universal sets but don't belong to
AUB OR AUBUC are the elements of the set (AUB) OR (AUBUC) .
It’s number of elements are denoted by n (AUB) OR n(AUBUC). The
following terms are used to represent the compliment of union.
None, neither, no body, neither A nor B nor C OR neither A nor B nor
both.... etc.
COMPLEMENT OF UNION SETS

10. A Venn diagram is a widely used diagram style that
shows the logical relation between sets, popularized
by John Venn (1834–1923) in the 1880s. The diagrams are
used to teach elementary set theory, and to
illustrate simple set relationships in probability
, logic, statistics, . There are two
types of Venn diagrams which are widely used. They are
two Venn diagram and three Venn diagram.
VENN DIAGRAM

11. Two-Venn diagram
So, A venn-diagram, is a diagram where two circles overlap
with eachother when they share a common number
or elements. Like in given example
A= {1,2,3,4,5}
B={3,4,5,8,9}
n(A∩B) = {3,4,5}
n.(A) n.(B)
n(A∩B)
n(A)
n(B)

12. Exploring the Three-Circle Venn Diagram
In class 9 we learned about the two-circle Venn diagram. Now, let's know about the
three-venn diagram.
In a three-circle Venn diagram, you can compare three distinct sets of information. The
intersection of all three circles reveals the items that possess the characteristics shared
by each circle. three different sets of information are able to be compared, and it is
where all three circles intersect that you are able to find the items that share all of the
characteristics of each circle.
Three-Venn diagram n.(A) n.(B)
n.(C)

13. n(u)=n(A)+n(A)’
(n(U)=n(B)+n( B)’
n(U)=n(A u B)+(A U B)’
n(AUB)=n(U)-n(AUB)’
n(AUB)=n(A)+n(B)-n(AnB)
n(AUB)=no(A)+no(B)+n(AnB)
no(A)=n(A)-n(AnB)
no(B)=n(B)-n(AnB)
For two Venn diagram:
For three Venn diagram:
FORMULAE FOR SOLVING PROBLEMS RELATED TO VENN DIAGRAMS ARE :
n(U)= n(AUBUC) - n(AUBUC)’
n(A∩B) = no(A∩B) + n(A∩B∩C)
n(B∩C) = no(B∩C) + n(A∩B∩C)
n(A∩C)= no(A∩C) + n(A∩B∩C)
no(A) = n(A) – no(A∩B) – no(A∩C) – n(A∩B∩C)
no(B) = n(B) – no(B∩C) – no(A∩B) – n(A∩B∩C)
no(C) = n(C) – no(A∩C) – no(B∩C) – n(A∩B∩C)
n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩B) - n(B ∩C)
- n(A ∩C) + n(A ∩B ∩C)
Where (’) is known as compliment

14. QUESTIONS AND THERE SOLUTIONS RELATED TO THE
SURVEY!
what are the data set collected from each class?

15. A SURVEY WAS HELD IN FLUORESCENT SECONDARY SCHOOL
WHERE 360 STUDENTS PARTICIPATED. AMONG THEM THE NUMBER
OF STUDENTS WHO LIKE ONLY FOOTBALL IS 90,WHO LIKED ONLY
BASKETBALL IS 75 AND WHO LIKED ONLY CRICKET IS 85.THE
NUMBER OF STUDENTS WHO LIKE FOOTBALL AND BASKETBALL
BUT NOT CRICKET IS 30, FOOTBALL AND CRICKET BUT NOT
BASKETBALL IS 20 ,BASKETBALL AND CRICKET BUT NOT
FOOTBALL IS 15 AND ALL THREE SPORTS IS 10 . 35 like none of
the sports.
Data collection :

16. Represent the given data in set notation
Prepare a Venn diagram to illustrate the given information
How many students like at least one of the three sports?
(Use the given data to exclude students who do not like any sport.)
Find the total number of students who like exactly two sports.
(Consider students who like two sports but exclude those who like all three.)
Determine the percentage of students who like only one sport.
(Calculate the ratio of students who like only football, only basketball, and only
cricket to the total surveyed students.)
What fraction of students enjoy both football and basketball, including those
who also like cricket?
(Express the number as a simplified fraction of the total surveyed students.)
Compare the popularity of cricket versus basketball by calculating the total
number of students who like each.
Questions obtained from the survey

17. n(U)=360
n⁠
｡(F)=90
n⁠
｡(B)=75
n⁠
｡(C)=85
n⁠
｡(F∩B)=30
n⁠
｡(F∩C)=20
n⁠
｡(B∩C)=15
n⁠
｡(F∩B∩C)=10
n(FUBUC)=35
Solution:
Let ‘U’ be the universal set which represents the student of grade 10,8,7. Now let ‘F’, ‘C’, ‘B’ represent
football, cricket and basketball
1.) REPRESENTING THE GIVEN INFORMATION IN SET NOTATION :

18. U=360
F
B
C
90
75
85
15
30
20
10
35
b) Represent the given information in Venn- Diagram

19. How many students like at least one of the
three sports? find n(FUBUC)
Solution:
By using the formula
n(FUBUC)= n(U)-n(FUBUC)
= 360- 35
=325
325 STUDENTS LIKE AT LEAST ONE OF THE THREE
SPORTS.
Solution:
=n⁠
｡(F∩B)+n⁠
｡(F∩C)+n⁠
｡(B∩C)
=30+20+15
=65
Find the total number of students who like
exactly two sports.

20. Determine the percentage
of students who like only
one sports
AS we know :
Football only: 90 students
Basketball only: 75 students
Cricket only: 85 students
solution :
Total students who like only one
sports= n.(F)+n.(B)+n.(C)
= 90+75+85
= 250
then:
The percentage of students who like only one
sports = 250/360*100%
= 69.44%

21. what fraction of
students like both
football and basketball
including those who
also like cricket?
30 students like football and basketball
but not cricket.
10 students like all three sports: football,
basketball, and cricket.
So, the total number of students who like
both football and basketball (with or
without cricket)
=30 + 10
= 40
To express this as a fraction of the total
student = 40/360
=1/9
Solution:

22. conclusion
clarity
creativity
confidence
you

23. Mathematics is not about numbers,
equations, computations, or
algorithms: it is about understanding."
— William Paul Thurston
THANKYOU !