Cambridge International Mathematics

Sets (Chapter 2) 63

AVenn diagramconsists of a universal setUrepresented by a rectangle, and sets within it

that are generally represented by circles.

For example, consider the universal set U=fxjx 610 , x 2 Z+g.

We can display the set S=f 2 , 4 , 6 , 7 g on the Venn diagram using a

circle. The elements ofSare placed within the circle, while the elements

of S^0 are placed outside the circle.

Example 5 Self Tutor

If U=f 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 g and E=f 2 , 3 , 5 , 7 g, list the set

E^0 and illustrateEandE^0 on a Venn diagram.

Hence find:

a n(E) b n(E^0 ) c n(U)

E^0 =f 0 , 1 , 4 , 6 g

a Econtains 4 elements, so n(E)=4

b n(E^0 )=4 c n(U)=8

Consider the sets U=f 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 g, A=f 2 , 3 , 5 , 7 g and

B=f 2 , 7 g.

We notice that B½A, so the circle representingBlies entirely within

the circle representingA.

We can use this property to draw a Venn diagram for the special number setsN,Z,Q andR. In this case

R is the universal set, and N μZμQ μR:

D VENN DIAGRAMS [9.3]

0.218734019273004597.....

0.101001000100001.....

Qw_

-5

0

10

0.2 -2

-5\Qr_

Q

Z

N

R

~` 8

~` 5

0.3333.....

~` 2

1

3

5

8

9

10

2

4

(^76)
U
S
U
E
E'
6
4
0
1
2
5 7
3
U
A
B
1
(^86)
3 4
5
2
7
IGCSE01
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_02\063IGCSE01_02.CDR Friday, 14 November 2008 9:38:30 AM PETER