Cambridge International Mathematics

ANSWERS 677

EXERCISE 2D

1a A=f 2 , 3 , 5 , 7 g

bA^0 =f 1 , 4 , 6 , 8 g

c 4 , 4

2a

bV^0 =fb,c,d,f,g,h,j,k,l,m,n,p,q,r,s,t,v,w,x,

y,zg

3a iU=f 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 g

ii N=f 3 , 8 g iii M=f 1 , 3 , 4 , 7 , 8 g

bn(N)=2, n(M)=5 cNo, NμM.

4a b

c

5a/bcitrue

ii true

iii true

d (shaded section

of diagram

alongside)

6a b

cd

e

7

EXERCISE 2E.1

1a iC=f 1 , 3 , 7 , 9 g ii D=f 1 , 2 , 5 g

iii U=f 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 g iv C\D=f 1 g

v C[D=f 1 , 2 , 3 , 5 , 7 , 9 g

bin(C)=4 iin(D)=3 iiin(U)=9

iv n(C\D)=1 vn(C[D)=6

2a iA=f 2 , 7 g iiB=f 1 , 2 , 4 , 6 , 7 g

iii U=f 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 g iv A\B=f 2 , 7 g

v A[B=f 1 , 2 , 4 , 6 , 7 g

bin(A)=2 iin(B)=5 iiin(U)=8

iv n(A\B)=2 vn(A[B)=5

3a

biA\B=f 2 , 9 , 11 g

ii A[B=f 1 , 2 , 7 , 9 , 10 , 11 , 12 g

iii B^0 =f 3 , 4 , 5 , 6 , 7 , 8 , 10 g

cin(A)=5 iin(B^0 )=7

iii n(A\B)=3 iv n(A[B)=7

4aA\B=f 1 , 3 , 9 g

bA[B=f 1 , 2 , 3 , 4 , 6 , 7 , 9 , 12 , 18 , 21 , 36 , 63 g

5aX\Y=fB, M, T, Zg

bX[Y=fA, B, C, D, M, N, P, R, T, W, Zg

6a in(A)=8 iin(B)=10

iii n(A\B)=3 iv n(A[B)=15

bn(A)+n(B)¡n(A\B)=8+10¡3 = 15 =n(A[B)

7an(A)+n(B)¡n(A\B)=(a+b)+(b+c)¡b

=a+b+c=n(A[B)

bA\B=?, ) n(A\B)=0

8a? b U c?

EXERCISE 2E.2

1anot inA- shaded pink bin bothAandB

cA\B^0 din eitherAorB

eA[B^0 f(A[B)^0

g(A\B)^0 hin exactly one ofAorB

U

1

6

A

A'

4

8

2 3 5

7

U

b

c

d f

g h j

k

l

m

n

q r p

s

t

v

x w

y

z V'

V a e i

o u

U

Q

Z

N

0

0.2137005618..... ~` 2

5\Qr_

Qw_

-5

10

0.3

_

Q'

U

A B

1

2

3

4

5

6

U

A 7 B

10

6

9

5

8

4

U

A

B

9

3 5

7 486

U

I

E

U

P

R

U

P T

U

P

R

H

U

I

E

R

U

AB

C

28

26

24

22

18 16 14

12

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6

2 4

5

10

20

30

15

25

(^192127)
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IB MYP_3 ANS
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Y:\HAESE\IGCSE01\IG01_AN\677IB_IGC1_an.CDR Thursday, 20 November 2008 4:06:10 PM PETER