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The document discusses the fundamentals of set theory, including definitions of sets, elements, subsets, and operations such as union and intersection. It explains how to specify sets through listing elements or defining properties, and introduces concepts like proper subsets and universal sets. Additionally, it covers the complement of sets and the differences between sets.
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Save 1. Set Theory For Later ser THeoRY Lenn d ~
= Wsek may be viewed ar any well defined! collect on
of objects culled the elements of she sete
= Gopal letters AB LY denote sets
= lovercose letker a,b x55; denote elements of sets.
ES denotes thet @ von element of sed S,
abES dercts that aend b me clenents of set S.
in A_S...dendter Met oie nth_en.@ament off nS.
specifying sets (1 wens)
® listing res elements soperoted by comwes end contarnce/
in Ureces Sees p= dyass55, 6255009
Blass bee
@® steting the properties which cheractense the elements
of the sed ec A =Lacl ex ir cman postive integer x23
BaLocloe is an even integer y > 0
Ths or seoel pur the sed of x ach het xe puitve
integer cnel 2c ir less don we
Lsimlerls és the set off x ach ated se iran even rabeser
Conel oe tr giewter then 0.
Rete: Wo sek does not clepenc! on the wou im chic ser
elements ce ohsplagec B sek temeins the some
if st elements cre repented of seerrenyed+
(ey The sets B= Uclooctrso§, Fads) nl
ae Qiyyasiyt ome the somes fasysed
La,g 5204
e = hyssesyeh
o = dyseuod-
Which of the sets above are equal?
aap? They ore all equel s Orler ond sepetition domed
cherge a set+
25 @ lish te elements of eoch sed chee N=diyrs,-9
@ A= dxeNisze2yy
© @ elxeNlas een, ezid
© ¢ =dneNl4tx = 34
@ vo =dxeNly-x = 33
p= Lays,69594
B =hayHyeyg,109
emmy c =D the enpty sed since no partive
inteyer metres toe = 3.
p= diy “Subsebs (€) Lesson %
Soppore evens clemend of set A ts also on clement of
«seh Be Thes @ ts called subset of Be
Sonbelicaly Ce mmnte; Foe Asp oe then woB.
ec) let P = Aijrazs,eh
B 241,39, 455,2%
e = bys nist
D = bess,t5h
Te since ertry clement of @ x aby cnekment of p+
Prince every clanect of pis cho cm clement of p-
© hese DER bt ade
B becuse evay element ofc is chy en clement of B
D becase sec bt so
equelity of sets (=)
Tue seks ore eqel if they both hove the same element
cr, equivelemely if each 1 conteined in the others
Sombelicll, eo ente; A= B Ferd only if PER ond BEA:
an>r>an
OR in
_
_.
ooo
=O since every element of 1s che on clement of 0
encl even element of D is an clement of He
Fy the some weeson P= E md D=E- Proper subsets (C)
[i ed PERC then Ue rey aA utele
peyer subset of B- te PSB md Ap tB > PCR.
eg Lt n= fy2,34
| im bizar 43
e = baja
ACB snce PCB cond PED
og ene 090 onl one
Enez
© nee
wf ace wd BoA, then B=B
@ PAen od Bec, then BoC
Speciol sety
sige Ake! 20d af radaecl mithwenzy. potisive Ge M
be she ret of male stuclentr end let F be He
sed of Bemele stuclemty
muR = U
Mar = @
| Fecer
© ANB SA ond ANB CB
© peAun Baus
complement + The complement of a set A dom ir the
set of elemonts hich belony to Uo bet uhich clo nod
Leleny 42 Ae je wm = deleeusn dy 1%
leet chflerence % the cliffmence of Pend B tr the
seb of skmentr which bebny to A bet ubicly
clo nod belny +2 B ve AB = dxlen sc ¢ BS
FAG is shade:
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| ct Beyence % the synme tie difference of :
(th enel B consisty off thee elements which Nelonyy to.
| or 6 Wt net to bethy i nen = (ors>\CanBy
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sted tek Ue £42935 05 Nhe thd) chive set»
| et A= Uyys4d, B=ds.4s5,695,¢=41535295
Baka sy-¥
| Gah lel aycc8!- oe dijaye9 oy 5 cds ayn,
me a diay me=diwy Weed4ys5674 Me =Lys4
(en adso7y Anaad ew =daya ah
ReB = (evB)\ Gon) = 412,556,739
Bec =HUC\(ened = dayissyb,a.895
p@c = CAVer\ Cane) Liye ytd
pee = Caved\Cane) = Cya,bj310)---5
