Cambridge Additional Mathematics

Sets and Venn diagrams (Chapter 1) 15

6 True or false?

a 1272 N b^1382792 Q c 3172 =Q d ¡ 114 2 Q

7 Which of these pairs of sets are disjoint?

a A=f 3 , 5 , 7 , 9 g and B=f 2 , 4 , 6 , 8 g b P=f 3 , 5 , 6 , 7 , 8 , 10 g andQ=f 4 , 9 , 10 g

8 True or false? IfRandSare two non-empty sets and R\S=?, thenRandSare disjoint.

9aHow many proper subsets does the set fa,b,c,dg have?

b Copy and complete: “If a set hasnelements then it has ...... proper subsets.”

To avoid having to list all members of a set, we often use a general description of its members. We often

describe a set of all values ofxwith a particular property.

The notation fx:::::::g or fxj::::::g is used to describe “the set of allxsuch that ......”.

For example:

² A=fx 2 Z : ¡ 26 x 64 g reads “the set of all integersxsuch thatxis between

¡ 2 and 4 , including¡ 2 and 4 .”

We can representAon a number line as:

Ais a finite set, and n(A)=7.

² B=fx 2 R : ¡ 26 x< 4 g reads “the set of all realxsuch thatxis greater than or

equal to¡ 2 and less than 4 .”

We representBon a number line as:

Bis an infinite set, and n(B)= 1.

We could also write B=fx:¡ 26 x< 4 g, in which case we wouldassumethat x 2 R.

Example 2 Self Tutor

Suppose A=fx 2 Z:3<x 610 g.

a Write down the meaning of the interval notation.

b List the elements of setA. c Find n(A).

a The set of all integersxsuch thatxis between 3 and 10 , including 10.

b A=f 4 , 5 , 6 , 7 , 8 , 9 , 10 g c There are 7 elements, so n(A)=7.

B Interval notation

the set of all

such that

-2 0 4 x

a filled in circle indicates

-2is included

an open circle indicates

4 is not included

-2-101234x

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_01\015CamAdd_01.cdr Thursday, 3 April 2014 3:32:13 PM BRIAN