Cambridge Additional Mathematics

y

O x

y

x

3

• Ew

y=2x+

O

y

-2 2 x

2

O

we write A*B.

IfAisnota subset ofB,

-3 -2 -1 0 1 2 x 012345 x

Sets and Venn diagrams (Chapter 1) 17

4 Write using interval notation:

a f¡ 2 ,¡ 1 , 0 , 1 , 2 , 3 g b f....,¡ 6 ,¡ 5 ,¡ 4 ,¡ 3 g

cd

5 State whether AμB:

a A=?, B=f 2 , 5 , 7 , 9 g

b A=f 2 , 5 , 8 , 9 g, B=f 8 , 9 g

c A=fx 2 R :2 6 x 63 g, B=fx 2 Rg

d A=fx 2 Q :3 6 x 69 g, B=fx 2 R :0 6 x 610 g

e A=fx 2 Z:¡ 106 x 610 g, B=fz 2 Z:0 6 z 65 g

f A=fx 2 Q :0 6 x 61 g, B=fy 2 Q :0<y 62 g

6 For each of the following sets, determine whether the interval described is closed, open, or neither:

a [2,5) b (¡ 1 ,3) c (¡1,¡4] d (4, 1 ) e [¡ 2 ,2] f [0,11)

7 Given that Q is the set of rational numbers, we can define

Q+as the set of positive rational numbers, fx 2 Q :x> 0 g

and Q+ 0 as the set of positive rational numbers and zero, fx 2 Q :x> 0 g.

a Explain why the setQ cannot be illustrated on a number line.

b Describe in words, in interval notation, and using a number line, what would be meant by the set:

i R+ ii R+ 0

Arelationis any set of points which connect two variables.

You should be familiar with points (x,y) in the Cartesian plane.

Any set of these points is a relation.

For example:

²f(x,y):y=2x+3g is the set of points

which form a straight line with gradient 2 and

y-intercept 3.

²f(x,y):x^2 +y^2 =4g is the set of points

which form a circle with radius 2 units centred

at the origin.

C Relations

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_01\017CamAdd_01.cdr Thursday, 3 April 2014 3:47:42 PM BRIAN