Cambridge International Mathematics

62 Sets (Chapter 2)

Example 4 Self Tutor

a List the elements of the set:

i fxj¡ 26 x 61 , x 2 Zg ii fxj 06 x< 4 , x 2 Ng

b Write in interval notation: f¡ 3 ,¡ 2 ,¡ 1 , 0 , 1 , 2 , 3 , 4 , ......g

aifxj¡ 26 x 61 , x 2 Zg ii fxj 06 x< 4 , x 2 Ng

=f 0 , 1 , 2 , 3 g

b We first notice that the elements of the set are all integers, so we are dealing with x 2 Z.

f¡ 3 ,¡ 2 ,¡ 1 , 0 , 1 , 2 , .....g=fxjx>¡ 3 , x 2 Zg

EXERCISE 2C

1 Write verbal statements for the meaning of:

a fxjx> 4 g b fxjx 65 g c fyj 0 <y< 8 g

d fxj 16 x 64 g e ftj 2 <t< 7 g f fnjn 63 or n> 6 g

2 List the elements of the set:

a fxj 1 <x 66 ,x 2 Ng b fxjx> 5 ,x 2 Zg c fxjx< 3 ,x 2 Zg

d fxj¡ 36 x 65 ,x 2 Ng e fxjx>¡ 4 ,x 2 Zg f fxjx 66 ,x 2 Z+g

3 Write these sets in interval notation:

a f¡ 5 ,¡ 4 ,¡ 3 ,¡ 2 ,¡ 1 g b f 0 , 1 , 2 , 3 , 4 , 5 g c f 4 , 5 , 6 , 7 , 8 , ......g

d f......,¡ 3 ,¡ 2 ,¡ 1 , 0 , 1 g e f¡ 5 ,¡ 4 ,¡ 3 ,¡ 2 ,¡ 1 , 0 , 1 g f f......, 41 , 42 , 43 , 44 g

4 Write in interval notation:

ab

cd

ef

5 Sketch the following number sets:

a fxj 46 x< 8 ,x 2 Ng b fxj¡ 5 <x 64 ,x 2 Zg c fxj¡ 3 <x 65 ,x 2 Rg

d fxjx>¡ 5 ,x 2 Zg e fxjx 66 g f fxj¡ 56 x 60 g

6 Are the following sets finite or infinite?

a fxj 16 x 610 ,x 2 Zg b fxjx< 4 ,x 2 Zg c fxjx> 5 ,x 2 Z+g

d fxjx< 7 ,x 2 Z+g e fxjx 69 ,x 2 Ng f fxj 26 x 66 ,x 2 Rg

03 x 25 x

-1 2 x

063 x 0 x

05 x

=f¡ 2 ,¡ 1 , 0 , 1 g

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_02\062IGCSE01_02.CDR Monday, 15 September 2008 12:06:08 PM PETER