1. TOPIC: venn diagram and sets theory
PRESENTED BY:-
HIMANSHU GAWANDE (A-55)
DEPARTMENT OF ELECTRONICS ENGINEERING
(3RD YR/6TH SEM)
GUIDED BY:- PROF .Sayankar

2. Venn Diagrams
• In set theory, the universe of discourse is
called the universal set, typically designated
with the letter U.
Venn Diagrams were developed by the logician John
Venn (1834 – 1923). In these diagrams, the universal
set is represented by a rectangle and other sets of
interest within the universal set are depicted as
circular regions.

3. Venn Diagrams
• The rectangle represents the universal set, U,
while the portion bounded by the circle
represents set A.
A
U

4. Complement of a Set
• For any set A within the universal set U, the
complement of A, written A', is the set of all
elements of U that are not elements of A.
That is
{ | and }.A x x U x A   

5. Subsets of a Set
• Set A is a subset of set B if every element of A
is also an element of B. In symbols this is
written
.A B
B
AU

6. • 1. From a survey of 100 college students, a
marketing research company found that 75
students owned stereos, 45 owned cars, and
35 owned cars and stereos.
• a) How many students owned either a car or
a stereo?
• b) How many students did not own either a
car or a stereo?

7. • METHOD:
• a) Start with a Venn Diagram and label the different
categories:
b) Fill in the number of students who own both cars
and stereos, which would be in the intersection of
the two sets:

8. • c) Fill in the remaining numbers for the two sets.
• In this case, since a total of 45 students own cars,
and 35 have already been listed, then 45 - 35 = 10
students own cars only.
• Similarly, since 75 students own stereos and 35 have
already been listed, then 75 - 35 = 40 students who
own stereos only:
d) Finally, interpret and answer the questions:

9. • How many students owned either a car or a stereo?
The question asks either ... or which is union of the
sets.
From the diagram, the number of elements in
• A = 10 + 35
and the number of elements in B which are NOT in A
are 40.
So the union would be 10+35+40 = 85
How many students did not own either a car or a
stereo?
The question asks for the number not in either A nor B
(namely, the complement of A B or (A B)' ).
Since there are 100 students in the universe, then the complement is found
by subtracting those who own either a car or stereo from the total number of
students surveyed
or 100 - 85 = 15.