Cambridge International Mathematics

Sets (Chapter 2) 61

EXERCISE 2B

1 True or false?

a 32 Z+ b 62 Z c^342 Q d

p

22 =Q

e ¡^142 =Q f 2132 Z g 0 : 36842 R h

1

0 : 1

2 Z

2 Which of these are rational?

a 8 b ¡ 8 c 213 d ¡ (^314)
e
p
3 f
p
400 g 9 : 176 h ¼¡¼
3 Show that these numbers are rational: a 0 : 7 b 0 : 41 c 0 : 324
4aExplain why 0 : 527 is a rational number.
b 0 : 9 is a rational number. In fact, 0 : 92 Z. Give evidence to support this statement.
5 Explain why these statements are false:
a The sum of two irrationals is irrational. b The product of two irrationals is irrational.
6 True or false? a N μZ b R μQ c ZμQ.
Interval notationallows us to quickly describe sets of numbers using mathematical symbols only.
For example: fxj¡ 3 <x 62 ,x 2 Rg reads ‘the set of all realxsuch thatxlies
between negative 3 and 2 , including 2 ’.
Unless stated otherwise, we assume we are dealing withrealnumbers. Thus,
the set can also be written as fxj¡ 3 <x 62 g.
We can represent the set on a number line as:
Sometimes we want to restrict a set to include only integers or rationals.
For example: fxj¡ 5 <x< 5 ,x 2 Zg
reads ‘the set of all integersxsuch thatxlies between negative 5 and 5 ’.
We can represent the set on a number line as:
Example 3 Self Tutor
Write in interval notation:
ab
a fxj 16 x 65 ,x 2 Ng
or fxj 16 x 65 ,x 2 Zg
b fxj¡ 36 x< 6 g
C INTERVAL NOTATION [9.2]
05 x -^36 x

• 32

not included included

x

-5 0 5 x

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Y:\HAESE\IGCSE01\IG01_02\061IGCSE01_02.CDR Thursday, 11 September 2008 10:36:27 AM PETER