Cambridge Additional Mathematics

Answers 453

EXERCISE 1A

1a 52 D b 62 =G cd=2fa,e,i,o,ug

df 2 , 5 gμf 1 , 2 , 3 , 4 , 5 , 6 g

ef 3 , 8 , 6 g*f 1 , 2 , 3 , 4 , 5 , 6 g

2a if 9 g iif 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 g

bi? iif 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 g

cif 1 , 3 , 5 , 7 g=A iif 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 g=B

3a 5 b 6 c 2 d 9

4atrue btrue ctrue dtrue

efalse f true gtrue hfalse

5afinite binfinite cinfinite dinfinite

6atrue btrue cfalse dtrue

7adisjoint bnot disjoint 8 true

9a 15 subsets b 2 n¡ 1 ,n 2 Z+

EXERCISE 1B

1afinite binfinite cinfinite dinfinite

einfinite f infinite ginfinite

2a iThe set of all integersxsuch thatxis between¡ 1 and

7 , including¡ 1 and 7.

ii f¡ 1 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 g iii 9

iv

biThe set of all natural numbersxsuch thatxis between

¡ 2 and 8.

ii f 1 , 2 , 3 , 4 , 5 , 6 , 7 g iii 7

iv

ciThe set of all real numbersxsuch thatxis between

0 and 1 , including 0 and 1.

ii not possible iii infinite

iv

diThe set of all rational numbersxsuch thatxis between

5 and 6 , including 5 and 6.

ii not possible iii infinite

iv cannot be illustrated

eiThe set of all real numbersxsuch thatxis between

¡ 1 and 5 , including¡ 1.

ii not possible iii infinite

iv

fiThe set of all real numbersxsuch thatxis between

3 and 5 (including 5 ), or greater than 7.

ii not possible iii infinite

iv

giThe set of all real numbersxsuch thatxis less than or

equal to 1 , or greater than 2.

ii not possible iii infinite

iv

hiThe set of all real numbersxsuch thatxis less than 2 ,

or greater than or equal to 1. (So,Ais the set of all real

numbers.)

ii not possible iii infinite

iv

3aA=fx 2 Z:¡ 100 <x< 100 g

bA=fx 2 R:x> 1000 g

cA=fx 2 Q:2 6 x 63 g

4aA=fx 2 Z:¡ 26 x 63 g

bA=fx 2 Z:x 6 ¡ 3 g

cA=fx 2 R:¡ 36 x< 2 g

dA=fx 2 R:1 6 x 63 [x> 5 g

5aAμB b A*B cAμB d AμB

eA*B f A*B

6aneither b open cneither d open

eclosed f neither

7aThere are infinitely many rational numbers within any given

interval, so we cannot representQas a series of dots like we

can withZ. We cannot representQ with a continuous line

either (like we do withR), as this would imply that irrational

numbers are part ofQ.

bithe set of positive real numbers,

fx 2 R:x> 0 g

ii the set of positive real numbers

and zero, fx 2 R:x> 0 g

EXERCISE 1C

1ainfinite binfinite

cinfinite dinfinite

2ainfinite b finite cinfinite

3a iThe set of all points of intersection between the line and

the circle.

ii The set of all points that lie on either the straight line or

the circle.

y

x

O

y=x

y

O x

1

1

-1 01

-1 01

-101234567x

1234567 x

01 x

-1 5 x

3 45678 x

12 x

0 x

ANSWERS

x+y=1

y

O x

1

1

x+y=1

y

O x

x=0

y=0

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 IB HL OPT
Sets Relations Groups
Y:\HAESE\CAM4037\CamAdd_AN\453CamAdd_AN.cdr Tuesday, 8 April 2014 8:17:01 AM BRIAN