Cambridge Additional Mathematics

28 Sets and Venn diagrams (Chapter 1)

AB

U

(a) (b) (c)

Bl Br

U

(a) (b) (c)

(d_)

Bl Br

U

(8) (11) (3)

(5)

4 Use the Venn diagram to show that:

n(A[B)=n(A)+n(B)¡n(A\B)

5 Given n(U)=26, n(A)=11, n(B)=12, and n(A\B)=8, find:

a n(A[B) b n(B, but notA)

6 Given n(U)=32, n(M)=13, n(M\N)=5, and n(M[N)=26, find:

a n(N) b n((M[N)^0 )

7 Given n(U)=50, n(S)=30, n(R)=25, and n(R[S)=48, find:

a n(R\S) b n(S, but notR)

In this section we use Venn diagrams to illustrate real world situations. We can solve problems by considering

the number of elements in each region.

Example 10 Self Tutor

A squash club has 27 members. 19 have black hair, 14 have brown

eyes, and 11 have both black hair and brown eyes.

a Place this information on a Venn diagram.

b Hence find the number of members with:

i black hair or brown eyes

ii black hair, but not brown eyes.

a LetBlrepresent the black hair set andBrrepresent the brown eyes set.

a+b+c+d=27 ftotal membersg

a+b=19 fblack hairg

b+c=14 fbrown eyesg

b=11 fblack hair and brown eyesg

) a=8, c=3, d=5

bin(Bl[Br) = 8 + 11 + 3 = 22

22 members have black hair or brown eyes.

ii n(Bl\Br^0 )=8

8 members have black hair, but not brown eyes.

H Problem solving with Venn diagrams

cyan magenta yellow black

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_01\028CamAdd_01.cdr Thursday, 19 December 2013 1:45:13 PM GR8GREG