Cambridge International Mathematics

Sets (Chapter 2) 73

2 Suppose U=fxjx 612 ,x 2 Z+g and A=fmultiples of 3612 g.

a ShowAon a Venn diagram. b List the setA^0 :

c Find n(A^0 ): d True or false? If C=f 1 , 2 , 4 g then CμA.

3 List the proper subsets of M=f 1 , 3 , 6 , 8 g:

4 True or false? a NμZ+ b Q μZ

5aList:

i setA ii setB iii setU

iv setA[B v setA\B

b Find:

i n(A) ii n(B) iii n(A[B)

6 Consider U=fxjx 610 ,x 2 Z+g, P=f 2 , 3 , 5 , 7 g and Q=f 2 , 4 , 6 , 8 g.

a Show these sets on a Venn diagram.

b List the elements of: i P\Q ii P[Q iii Q^0

c Find: i n(P^0 ) ii n(P\Q) iii n(P[Q)

d True or false? P\QμP

7 Describe in words the shaded region of:

abc

8 In a survey at an airport, 55 travellers said that last year they had been to Spain, 53 to France, and

49 to Germany. 18 had been to Spain and France, 15 to Spain and Germany and 25 to France

and Germany, while 10 had been to all three countries. Draw a Venn diagram to illustrate this

information, and use it to find how many travellers took part in the survey.

Review set 2B

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1aTrue or false? i ¡ 22 Z+ ii p^172 Q

b Show that 0 : 51 is a rational number.

c Write in interval notation:

d Sketch the number set fxjx 63 or x> 7 ,x 2 Rg.

2 Illustrate these numbers on a Venn diagram like the

one shown:

¡ 1 ,

p

2 , 2 , 3 : 1 ,¼, 4 : 2

U

A B

6

3

5

4

1

2

7

U

X Y

U

X Y

U

X Y

-3 4 t

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Y:\HAESE\IGCSE01\IG01_02\073IGCSE01_02.CDR Thursday, 11 September 2008 2:28:57 PM PETER