Cambridge Additional Mathematics

Sets and Venn diagrams (Chapter 1) 21

6 Suppose U=Z+, P=ffactors of 12 g, Q=ffactors of 18 g, and R=ffactors of 27 g.

a List the setsP,Q, andR.

b Find: i P\Q ii P\R iii Q\R

iv P[Q v P[R vi Q[R

c Find: i P\Q\R ii P[Q[R

7 Suppose U=Z+, A=fmultiples of 4 less than 40 g, B=fmultiples of 6 less than 40 g, and

C=fmultiples of 12 less than 40 g.

a List the setsA,B, andC.

b Find: i A\B ii B\C iii A\C

iv A\B\C v A[B[C

c Verify that

n(A[B[C)=n(A)+n(B)+n(C)¡n(A\B)¡n(B\C)¡n(A\C)+n(A\B\C).

8 Suppose U=Z+, A=fmultiples of 6 less than 31 g,

B=ffactors of 30 g, and C=fprimes < 30 g.

a List the setsA,B, andC.

b Find: i A\B ii B\C iii A\C

iv A\B\C v A[B[C

c Verify that

n(A[B[C)=n(A)+n(B)+n(C)¡n(A\B)¡n(B\C)¡n(A\C)+n(A\B\C).

AVenn diagramconsists of a universal setUrepresented by a rectangle.

Sets within the universal set are usually represented by circles.

For example:

² This Venn diagram shows setAwithin the

universal setU.A^0 , the complement ofA,

is the shaded region outside the circle.

² The sets U=f 2 , 3 , 5 , 7 , 8 g,

A=f 2 , 7 , 8 g, and A^0 =f 3 , 5 g

are represented by:

SUBSETS

If BμA then every element ofBis also inA.

The circle representingBis placed within the circle

representingA.

F Venn diagrams

A

U A'

A

U A'

2

7

8

5

3

A

B

U

BAμ

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_01\021CamAdd_01.cdr Thursday, 19 December 2013 1:20:19 PM GR8GREG