Cambridge International Mathematics

74 Sets (Chapter 2)

3 Show this information on a Venn diagram:

a U=f 10 , 11 , 12 , 13 , 14 , 15 g, A=f 10 , 12 , 14 g, B=f 11 , 12 , 13 g

b U=fquadrilateralsg, S=fsquaresg, R=frectanglesg

c U=N, A=fmultiples of 2 g, B=fmultiples of 3 g, C=fmultiples of 4 g.

4 IfAis the set of all factors of 24 andBis the set of all factors of 18 , find:

a A\B b A[B

5 Suppose U=fxjx 610 , x 2 Z+g, A=fprimes less than 10 g, and

B=fodd numbers between 0 and 10 g.

a Show these sets on a Venn diagram.

b List: i A^0 ii A\B

c True or false? i A½B ii A\BμA

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

6 On separate Venn diagrams like the one shown, shade the region

representing:

a B^0 b inAand inB c (A[B)^0

7 Using separate Venn diagrams like the one shown,

shade regions to verify that

(A\B)[C=(A[C)\(B[C):

8 A survey was conducted with 120 students in a school to see how many students were members

of extra-curricular clubs. The following results were recorded for the jazz band, drama club and

rowing team.

10 students were not members of any of the three clubs;

50 were members of the jazz band;

50 were members of the drama club;

50 were members of the rowing team;

15 were members of the jazz band and drama club;

10 were members of the drama club and rowing team;

20 were members of the jazz band and rowing team.

Draw a Venn diagram and use it to find how many students were members of all three clubs.

U

A B

U

A B

C

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_02\074IGCSE01_02.CDR Friday, 12 September 2008 10:46:28 AM PETER