Cambridge International Mathematics

64 Sets (Chapter 2)

Example 6 Self Tutor

Illustrate on a Venn diagram:

p

3 , 812 ,¡ 2 , 7 : 1 , 16 , 0 : 115

If two setsAandBhave elements in common, but A*B and B*A, the circles for these sets overlap.

Example 7 Self Tutor

Consider the sets U=fxj 06 x 612 ,x 2 Zg, A=f 2 , 3 , 5 , 7 , 11 g

and B=f 1 , 3 , 6 , 7 , 8 g. ShowAandBon a Venn diagram.

We notice that 3 and 7 are in bothAandBso

the circles representingAandBmust overlap.

We place 3 and 7 in the overlap, then fill in the

rest ofA, then fill in the rest ofB.

The remaining elements ofUgo outside the two

circles.

EXERCISE 2D

1 Suppose U=fxjx 68 ,x 2 Z+g and A=fprime numbers 68 g.

a Show setAon a Venn diagram. b List the setA^0. c Find n(A) and n(A^0 ).

2 Suppose U=fletters of the English alphabetg and

V=fletters of the English alphabet which are vowelsg.

a Show these two sets on a Venn diagram. b List the setV^0.

3aList the elements of:

i U ii N iii M

b Find n(N) and n(M).

c Is MμN?

4 ShowAandBon a Venn diagram if:

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

b U=f 4 , 5 , 6 , 7 , 8 , 9 , 10 g, A=f 6 , 7 , 9 , 10 g, B=f 5 , 6 , 8 , 9 g

c U=f 3 , 4 , 5 , 6 , 7 , 8 , 9 g, A=f 3 , 5 , 7 , 9 g, B=f 4 , 6 , 8 g

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Y:\HAESE\IGCSE01\IG01_02\064IGCSE01_02.CDR Thursday, 11 September 2008 10:55:39 AM PETER