Cambridge Additional Mathematics

14 Sets and Venn diagrams (Chapter 1)

DISJOINT SETS

Two sets aredisjointormutually exclusiveif they have no elements in common.

IfAandBare disjoint then A\B=?.

Example 1 Self Tutor

M=f 2 , 3 , 5 , 7 , 8 , 9 g and N=f 3 , 4 , 6 , 9 , 10 g

a True or false? i 42 M ii 62 =M

b List the sets: i M\N ii M[N

c Is i MμN ii f 9 , 6 , 3 gμN?

ai 4 is not an element ofM,so 42 M is false.

ii 6 is not an element ofM,so 62 =M is true.

biM\N=f 3 , 9 g since 3 and 9 are elements of both

sets.

ii Every element which is in eitherMorNis in the

union ofMandN.

) M[N=f 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 g

ciNo. Not every element ofMis an element ofN.

ii Yes, as 9 , 6 , and 3 are also inN.

EXERCISE 1A

1 Write using set notation:

a 5 is an element of setD b 6 is not an element of setG

c dis not an element of the set of all English vowels

d f 2 , 5 gis a subset off 1 , 2 , 3 , 4 , 5 , 6 g e f 3 , 8 , 6 gis not a subset off 1 , 2 , 3 , 4 , 5 , 6 g.

2 Find i A\B ii A[B for:

a A=f 6 , 7 , 9 , 11 , 12 g and B=f 5 , 8 , 10 , 13 , 9 g

b A=f 1 , 2 , 3 , 4 g and B=f 5 , 6 , 7 , 8 g

c A=f 1 , 3 , 5 , 7 g and B=f 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 g

3 Suppose A=f 0 , 3 , 5 , 8 , 14 g and B=f 1 , 4 , 5 , 8 , 11 , 13 g. Write down the number of elements in:

a A b B c A\B d A[B

4 True or false?

a Z+μN b N ½Z c N =Z+ d Z¡μZ

e Q ½Z f f 0 gμZ g ZμQ h Z+[Z¡=Z

5 Describe the following sets as either finite or infinite:

a the set of counting numbers between 10 and 20

b the set of counting numbers greater than 5

c the set of all rational numbersQ

d the set of all rational numbers between 0 and 1.

To write down ,

start with and add to

it the elements of

which are not in.

MN

M

N

M

[

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Additional Mathematics
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