12 Sets and Venn diagrams (Chapter 1)Opening problem
A city has three football teams in the national league: A,B, andC.
In the last season,20%of the city’s population saw teamAplay,24%saw teamB, and28%saw
teamC. Of these,4%saw bothAandB,5%saw bothAandC, and6%saw bothBandC.
1%saw all three teams play.
Things to think about:
a Writing out all of this information in sentences is very
complicated. How can we represent this information more
simply on a diagram?
b What percentage of the population:
i saw only teamAplay
ii saw teamAorteamBplay but not teamC
iii did not see any of the teams play?SET NOTATION
Asetis a collection of numbers or objects.
For example:
² the set of digits which we use to write numbers is f 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 g
² ifVis the set of all vowels, then V =fa,e,i,o,ug.The numbers or objects in a set are called theelementsormembersof the set.We use the symbol 2 to meanis an element ofand 2 =to meanis not an element of.So, for the set A=f 1 , 2 , 3 , 4 , 5 , 6 , 7 g we can say 42 A but 92 =A.The set fgor? is called theempty setand contains no elements.SPECIAL NUMBER SETS
The following is a list of some special number sets you should be familiar with:
² N =f 1 , 2 , 3 , 4 , 5 , 6 , 7 , ....g is the set of allnaturalorcounting numbers.
² Z=f 0 ,§ 1 ,§ 2 ,§ 3 ,§ 4 , ....g is the set of allintegers.
² Z+=f 1 , 2 , 3 , 4 , 5 , 6 , 7 , ....g is the set of allpositive integers.
² Z¡=f¡ 1 ,¡ 2 ,¡ 3 ,¡ 4 ,¡ 5 , ....g is the set of allnegative integers.
² Q is the set of allrational numbers, or numbers which can be written in
the form
p
qwherepandqare integers and q 6 =0.² R is the set of allreal numbers, which are all numbers which can be placed
on the number line.A SETS
The set of natural
numbers is often
defined to include.N
0cyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_01\012CamAdd_01.cdr Friday, 29 November 2013 10:10:17 AM GR8GREG