SET LANGUAGE

Teaching Pack – SET and Venn diagrams

Lesson 1
Cambridge IGCSE™
Mathematics 0580

Version 1.0

• Understand how to use Venn diagrams to classify

objects and sort data.

• Interpret Venn diagrams.

Lesson objectives

The village holds an annual Fun Run. Contestants are either classified as
under the age of 13 or adults. Every contestant must enter for either the 3
kilometre run or the 10 kilometre run. This information is shown in the Venn
diagram below:

Entered for

10 km

Under

13

50

7

23

10
•

How many people entered the fun
runs?

•

How many people entered the 10 km
run?

•

How many under 13s did the 10 km run?

•

How many adults did the 3 km run?

Try this!

90

57

7

10

E

• How many people were under 18?
• How many people owned an
iPhone?

• How many people did not own
an iPhone?

• How many under 18s owned an

iPhone?

• How can you describe the people

represented by 10?

Own an iPhone
Under

18

8

5

2

10

In a survey, 25 people were asked their age and if they owned an iPhone.
The results were put into a Venn diagram.

Try this!

7

13

12

5

Over 18 and does not own an iPhone.

E

The village holds an annual Fun Run. Contestants are either classified as
under the age of 13 or adults. Every contestant must enter for either the 3
kilometre run or the 10 kilometre run. This information is shown in the Venn
diagram below:

Entered for

10 km

Under

13

50

7

23

10
•

How many people entered the fun
runs?

•

How many people entered the 10 km
run?

•

How many under 13s did the 10 km run?

•

How many adults did the 3 km run?

Try this!

90

57

7

10

E

8

12

Left handed

Male

10

6

12 males are left handed.
There are 8 females.
10 people are right handed.
There are 36 people in the class.

A class of students were classified using the Venn diagram below.

Try this!

E

The same class of 36 students were asked separately:
a) If they could swim
b) If they could ride a bike
25 said they could swim 18 said they could ride a bike, 4 said they could do
neither.

Is this possible?

Try this!

Can ride a bike

Can swim

4

11

14

7

E

Not in A

A′

Complement of A

The complement of
the set A, A′, are the

elements not in A

Notations used with Venn diagram

B

A

B

A

B

A

12

4
3
6

8

9

1

2

5

7

11

Y

X

10

Try this!

How would you describe the elements in each set?

{3,6,9,12}

{1,2,3,5,6,7,9,10,11}

{12}

{3,4,6,8,9,12}

E

Write down all the elements that are in:

Try this!

Draw a Venn Diagram for the information below:

{2,3}

{1,2,3,4,5,6,7,11,12}

{5,7,8,9,10,11}

{5,7,11}

{2,3,5,7,8,9,10,11}

B

A

2

4

3

6

8

1

5

7

9

10

12

11

{1,4,5,6,7,8,9,10,11,12}

E

(n) Number of elements

B

A

2

4

3

6

8

1

5

7

9

10

12

11

E

Try this!

Draw a Venn Diagram for the information below:

{2,4}

9

{1,3,5,}

B

A

2

8

4

6

7

10

5

3

9

12

1

11

Write down all the elements in the set A ∩ B

Find n(A′)

6

Write down all the elements in A′ ∩ B

Find n(A′ ∩ B′)

3

{2,4,6,7,8,9,10,11,12}

3

E

Describing Shaded Are

Which choice describes the shaded region?

B

A

C

Try this!

E

Which choice describes the shaded region?

A

B

C

Try this!

E

Which choice describes the shaded region?

A

B

C

Try this!

E

Which choice describes the shaded region?

B

A

C

Try this!

C

E

Which choice describes the shaded region?

A

B

C

Try this!

E

Which choice describes the shaded region?

A

B

C

Try this!

E

SHADING VENN DIAGRAM!

E

B
A

a

b

c

d

Shade only region
c.

A

B

C

SHADING VENN DIAGRAM!

E

Draw and use Venn diagrams to solve a range of problems.
This formula will help you (Extended)

Lesson objective

In a class there are 30 students.

17

study History, 18 study Geography and 5 study neither.

How many students study both History and Geography?

Try this!

Geography

History

5

?

7

8
10

E

There are 100 students in a school.

Try this!

85 of the students study at least one of: Physics,
Chemistry or Maths.
5 students study all three subjects.

13 students study Physics and Maths,
15 students study Physics and Chemistry
7 study Chemistry and Maths.
There are 45 maths students
30 physics students.
How many students studied just Chemistry?

Physics

Maths

Chemistry

5
8

10
2

30

7

23

85 – 10 – 7 – 5 – 8 – 2 – 30 = 23
So 23 studied just Chemistry

and

and