Cambridge Additional Mathematics

Sets and Venn diagrams (Chapter 1) 27

Venn diagrams allow us to easily visualise identities such as

n(A\B^0 )=n(A)¡n(A\B)

n(A^0 \B)=n(B)¡n(A\B)

Example 9 Self Tutor

Given n(U)=30, n(A)=14, n(B)=17, and n(A\B)=6, find:

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

We see that b=6 fas n(A\B)=6g

a+b=14 fas n(A)=14g

b+c=17 fas n(B)=17g

a+b+c+d=30 fas n(U)=30g

) b=6, a=8, and c=11

) 8+6+11+d=30

) d=5

a n(A[B)=a+b+c=25 b n(A, but notB)=a=8

EXERCISE 1G

1 In the Venn diagram given,(2)means that there are 2 elements

in the set A\B.

How many elements are there in:

a B b A^0

c A[B d A, but notB

e B, but notA f neitherAnorB?

2 In the Venn diagram given,(a)means that there areaelements

in the shaded region.

Notice that n(A)=a+b. Find:

a n(B) b n(A^0 )

c n(A\B) d n(A[B)

e n((A\B)^0 ) f n((A[B)^0 )

3 The Venn diagram shows that n(P\Q)=a and n(P)=3a.

a Find:

i n(Q) ii n(P[Q) iii n(Q^0 ) iv n(U)

b Findaif:

i n(U)=29 ii n(U)=31

Comment on your results.

A B

U

(7) (2) (5)

(9)

AB

U

(b) (c)

(d)

(a)

PQ

U

(2a) (a) (a+4)

(a-5)

A B

U

(a) (b) (c)

(d)

A B

U

AB'\

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_01\027CamAdd_01.cdr Thursday, 9 January 2014 10:35:06 AM BRIAN