Cambridge Additional Mathematics

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Sets and Venn diagrams (Chapter 1) 23

1 Represent setsAandBon a Venn diagram, given:

a U=f 1 , 2 , 3 , 4 , 5 , 6 , 7 g, A=f 2 , 4 , 5 , 6 g, and B=f 1 , 4 , 6 , 7 g

b U=f 2 , 3 , 4 , 5 , 6 , 7 g, A=f 2 , 4 , 6 g, and B=f 5 , 7 g

c U=f 2 , 3 , 4 , 5 , 6 , 7 g, A=f 2 , 4 , 6 g, and B=f 3 , 5 , 7 g

d U=f 3 , 4 , 5 , 7 g, A=f 3 , 4 , 5 , 7 g, and B=f 3 , 5 g

2 Suppose U=fx 2 Z:1 6 x 610 g, A=fodd numbers< 10 g, and B=fprimes< 10 g.

a List setsAandB. b Find A\B and A[B.

c Represent the setsAandBon a Venn diagram.

3 Suppose U=fx 2 Z:1 6 x 69 g, A=ffactors of 6 g, and B=ffactors of 9 g.

a List setsAandB. b Find A\B and A[B.

c Represent the setsAandBon a Venn diagram.

4 Suppose U=feven numbers between 0 and 30 g,

P=fmultiples of 4 less than 30 g, and

Q=fmultiples of 6 less than 30 g.

a List setsP andQ. b Find P\Q and P[Q.

c Represent the setsPandQon a Venn diagram.

5 Suppose U=fx 2 Z+:x 630 g, R=fprimes less than 30 g, and

S=fcomposites less than 30 g.

a List setsRandS. b Find R\S and R[S.

c Represent the setsRandSon a Venn diagram.

6 List the elements of set:

a A b B c A^0

d B^0 e A\B f A[B

g (A[B)^0 h A^0 [B^0

7 This Venn diagram consists of three overlapping circles

A,B, andC.

a List the letters in set:

i A ii B

iii C iv A\B

v A[B vi B\C

vii A\B\C viii A[B[C

b Find: i n(A[B[C)

ii n(A)+n(B)+n(C)¡n(A\B)¡n(A\C)¡n(B\C)+n(A\B\C)

c What do you notice about your answers inb?

EXERCISE 1F.1

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_01\023CamAdd_01.cdr Friday, 6 December 2013 8:26:58 AM GR8GREG