Cambridge International Mathematics

66 Sets (Chapter 2)

In the Venn diagram alongside,

A=f 2 , 3 , 4 , 7 g and B=f 1 , 3 , 7 , 8 , 10 g.

We can see that A\B=f 3 , 7 g

and A[B=f 1 , 2 , 3 , 4 , 7 , 8 , 10 g.

DISJOINT SETS

Two setsAandBaredisjointif they have no elements in common, or in other words if A\B=?.

IfAandBhave elements in common then they arenon-disjoint.

Example 8 Self Tutor

If U=fpostive integers 612 g, A=fprimes 612 g and B=ffactors of 12 g:

a List the elements of the setsAandB.

b Show the setsA,BandUon a Venn diagram.

c List the elements in: i A^0 ii A\B iii A[B

d Find: i n(A\B) ii n(A[B) iii n(B^0 )

a A=f 2 , 3 , 5 , 7 , 11 g and B=f 1 , 2 , 3 , 4 , 6 , 12 g

b

ciA^0 =f 1 , 4 , 6 , 8 , 9 , 10 , 12 g ii A\B=f 2 , 3 g

iii A[B=f 1 , 2 , 3 , 4 , 5 , 6 , 7 , 11 , 12 g

din(A\B)=2 ii n(A[B)=9

iii B^0 =f 5 , 7 , 8 , 9 , 10 , 11 g,son(B^0 )=6

EXERCISE 2E.1

1aList:

i setC ii setD iii setU

iv setC\D v setC[D

b Find:

i n(C) ii n(D) iii n(U)

iv n(C\D) v n(C[D)

U

AB

9 6

5

2

4

3

7

1

8

10

U

CD

4 6

8

3

7

1

2

9 5

U

AB

(^109)
8
5
7
(^112)
3
1
6
12
4
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Y:\HAESE\IGCSE01\IG01_02\066IGCSE01_02.CDR Thursday, 11 September 2008 11:10:02 AM PETER