VENN DIAGRAM

• OLEH:

• LILIA ISMARTI

• PENDIDIKAN

MATEMATIKA

• PPS UNSRI

John Venn

Born in 1834 in England.

Devised a simple diagramatic way to represent sets.

Here set are represented by closed figures such as:

.2

.4 .8.a .i

.x .y

U = “animals”

How to construct a venndiagram?

1. You have to draw a rectangle called “universe”.Theuniverse consists of “everything we are interested right now”. Let's name our universe as “Animals” like below:

2. Let’s say we have to deal with the following lists ofdata: tiger, monkey, elephant, crocodile and peacock.And all the data needs to be classified in two categories(or two sets) as: mammal animal and single bodycolored animal

3. For representing the two sets we have to draw twocircles as below:

U = “animals”

Mammal Single body

colored

4. Now we will put all the data to the suitable areaof the diagram as below:

U = “animals”

Mammal Single body colored

Tiger

monkey

elephant

peacock

crocodile

U = “animals”

Mammal Single body colored

Tiger

monkey

elephant

peacock

crocodile

5. Please observe that “Elephant” and “monkey” fall inboth the category and hence are placed in both circles.Hence the modified Venn diagram will be:

The combined area of the sets (the area, where elephant & monkey are placed) is called the intersection of the

sets and the total area of both the sets (the area, where tiger, elephant, monkey and crocodile are placed) is

called the union of the sets.

A Venn diagram is the graphical representation of different sets of data by means of a closed curve

(normally circles). Individual closed curves (circles) of Venn diagrams represent the individual sets of

data. The Intersection and union of the circles represent interrelations between the different sets

of data.

What is the venn diagram???

EXERCISE!

Let U = {2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 30}A = {2, 4, 6, 8, 10, 12, 14, 30}B = {3, 6, 9, 12, 15, 30}10C = {5, 10, 15, 30}

Represent the set in a Venn diagram!

The question is:

The intersection of set A, B, and C is ……?

The intersection of set A and B is…….….?

The intersection of set A and C is………?

and the intersection of B and C is………?

The union of set B and C is ………..?

The union of set A and B is ………….?

A, B, and C= {30}

A and B={6, 12, 30}

A and C={10, 30}

B and C={15, 30}.

B or C={3, 9, 6, 12, 30, 15, 5, 10}

A or B={2, 4, 8, 14, 10, 30, 6, 12, 3, 9, 15}

The answers is:

AB

C

30

6

12

10

15

2

4

8

14

3

9

5

U

Your Homework:

There are 20 cats. 10 of the cats

have brown hair, 8 have short hair,

and 12 have blue eyes. 2 cats have

brown hair, short hair and blue

eyes. 3 of the cats have brown and

short hair but not blue eyes. 1 cat

has brown hair and blue eyes but

not short hair. 2 of the cats have

short hair and blue eyes but not

brown hair. (Hint: draw a Venn

diagram)