082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

5.2 Set theory 177
Example5.1 Useset notation todescribe the intervals on thexaxis given by
(a) [0,2] (b) [0,2) (c) [−9,9]
Solution (a) {x :x∈Rand 0 x 2}
(b) {x:x∈Rand0 x < 2}
(c) {x:x∈Rand−9 x 9}
SometimesweshallbecontenttouseanEnglishdescriptionofasetofobjects,suchas
5.2.1 Equalsets
M is thesetof capacitors madebymachine M
N is thesetof capacitors madeby machineN
Q is thesetof faulty capacitors
Twosetsaresaidtobeequaliftheycontainexactlythesamemembers.Forexample,the
sets {9,5,2}and {5,9,2}areidentical.Theorderinwhichwewritedownthemembers
isimmaterial.The sets {2,2,5,9} and {2,5,9} are equal since repetition of elements is
ignored.
5.2.2 Venndiagrams
Venndiagramsprovideagraphicalwayofpicturingsetswhichoftenaidsunderstanding.
The sets are drawn as regions, usually circles, from which various properties can be
observed.
Example5.2 Suppose we are interested in discussing the set of positive whole numbers between 1
and10.LetA = {2,3,4,5}andB = {1,3,5,7,9}.TheVenndiagramrepresentingthese
sets is shown in Figure 5.1. The set containing all the numbers of interest is called the
universalset, E. Eisrepresentedbytherectangularregion.SetsAandBarerepresented
bytheinteriorsofthecirclesanditisevidentthat2,3,4and5aremembersofAwhile1,
3, 5, 7 and 9 are members ofB. It is also clear that 6 /∈A,6/∈B,8/∈A,8/∈ B. The
elements 3 and 5 are common toboth sets.
E
8
A
2
3
1
5
4 9
6
7
B
10
Figure5.1
Venn diagram forExample 5.2.
Theset containing all the members ofinterest iscalled the universal set E.
Itisusefultoaskwhethertwoormoresetshaveelementsincommon.Thisleadstothe
following definition.