Cambridge Additional Mathematics

18 Sets and Venn diagrams (Chapter 1)

EXERCISE 1C

1 Illustrate the following sets in the Cartesian plane. In each case state whether the set is

finite or infinite.

a f(x,y):y=xg b f(x,y):x+y=1g

c f(x,y):x> 0 , y> 0 g d f(x,y):x+y> 1 g

2 LetAbe the set of points in each graph below. State whetherAis finite or infinite.

abc

3 SupposeAis the set of points which define a straight line

andBis the set of points which define a circle.

a Describe in words the meaning of:

b Describe, with illustration, what it means if n(A\B) equals:

UNIVERSAL SETS

Suppose we are only interested in the natural numbers from 1 to 20 , and we want to consider subsets of this

set. We say the set U=fx 2 N :1 6 x 620 g is theuniversal setin this situation.

The symbolUis used to represent theuniversal setunder consideration.

COMPLEMENTARY SETS

ThecomplementofA, denotedA^0 , is the set of all elements ofUwhich arenotinA.

A^0 =fx 2 U:x= 2 Ag

For example, if the universal set U=f 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 g, and the set A=f 1 , 3 , 5 , 7 , 8 g, then the

complement ofAis A^0 =f 2 , 4 , 6 g.

Three obvious relationships are observed connectingAandA^0. These are:

² A\A^0 =? asA^0 andAhave no common members.

² A[A^0 =U as all elements ofAandA^0 combined make upU.

² n(A)+n(A^0 )=n(U)

For example, Q \Q^0 =? and Q [Q^0 =R.

D Complements of sets

y

O x

y

O x

GRAPHING

PACKAGE

y

O x

A

i A\B ii A[B

i 2 ii 1 iii 0

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_01\018CamAdd_01.cdr Thursday, 3 April 2014 3:49:56 PM BRIAN