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Ppt on SETS Matematics Assginment
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HISTORY OF SETS
The theory of setswas developed byGermanmathematicianGeorg Cantor
(1!"#1$1%& 'erst enco)nteredsets while wor*ing
on +Problems on
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SETS
Collection of ob-ect of a
partic)lar *ind. s)ch as. a pac* of cards. a crowed of
people. a cric*et teametc& /n mathematics ofnat)ral n)mber. prime
n)mbers etc&
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A set is a well dened
collection of ob-ects&
Elements of a set aresynonymo)s terms&
Sets are )s)ally
denoted by capitalletters&
Elements of a set are
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SETS REPRESENTATION
There are two ways torepresent sets
0oster or tab)lar form&
Set#b)ilder form&
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0STE0 0
TA234A0 50M/n roster form. all the
elements of set arelisted. the elements are
being separated bycommas and areenclosed within braces 6
&
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Set name and
S is the name of the set if used.
S = {1,2,3,4}
The symbol ∈ indicates that anelement belongs to the set
The symbol ∉ indicates that an
element does not belong to the sete.
4 ∈ to {1,2,3,4}
! ∉ to S
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"inite#un$nite sets.
%n in$nite set is a set &ith an endless list ofelements.
'={1,2,3,4,(}
"inite sets has a limited numbe) of elements.
%={1,2,3,!}
Set builde) notation allo&s you to &)ite setsusing a *a)iable+
={-- is a natu)al numbe) bet&een 2 and /}
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SET#23/4>E0
FORM/n set#b)ilder form. allthe elements of a set
possess a single common property which is not
possessed by an elemento)tside the set&
e&g& 8 set of nat)ral
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EAMP4E 5 SETS
/B MAT'SB 8 the set of all nat)ral
n)mbers 8 the set of all integersD 8 the set of all rational
n)mbers0 8 the set of all real n)mbers 8 the set of positive integers
D 8 the set of positive rational
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TFPES 5 SETS
Empty sets& 5inite &/nnite sets&
E)al sets& S)bset& Power set& 3niversal set&
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T'E EMPTF SET
A set which doesnHt containsany element is called the
empty set or n)ll set or voidset. denoted by symbol J or6 7&
e&g& 8 let 0 ? 6@ 8 1K @ K 9. @
is a nat)ral n)mber7
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FINITE & INFINITESETS A set which is empty or
consist of a denite
n)mbers of elements iscalled nite otherwise. theset is called innite&e&g& 8 let * be the set of thedays of the wee*& Then * is
nite
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ED3A4 SETS
Given two sets L r aresaid to be e)al if they
have e@actly the sameelement and we write L?0&
otherwise the sets are saidto be )ne)al and we writeL?0&
e&g& 8 let L ? 61.9.:.!7
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SUBSETS
A set 0 is said to be
s)bset of a set L if everyelement of 0 is also an
element L&0 N L This mean all the
elements of 0 contained in
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POWER SETThe set of all s)bset of agiven set is called power
set of that set&The collection of alls)bsets of a set L is called
the power set of denotedby P(L%&/n P(L% everyelement is a set&/f L? O1.9
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UNIVERSAL SET3niversal set is set which
contains all ob-ect. incl)dingitself&e&g& 8 the set of real n)mberwo)ld be the )niversal set ofall other sets of n)mber&
BTE 8 e@cl)ding negative
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SUBSETS OF R
The set of nat)ral n)mbersB? 61.9.:.!.&&&&7
The set of integers ?6.#9. #1. =. 1. 9.
:.&&7
The set of rational n)mbersD? 6@ 8 @ ? pQ. p. R and =
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INTERVALS OF
SUBSETS OF R OPEN
INTERVAL The interval denoted as(a. b%. a &b are real
n)mbers is an openinterval. means incl)dingall the element between a
to b b)t e@cl)din a &b&
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CLOSED INTERVAL
The interval denoted as
Oa. bU. a &b are 0ealn)mbers is an open
interval. means incl)dingall the element betweena to b b)t incl)ding a &b&
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TYPES OFINTERVALS (a. b% ? 6@ 8 a K @ K b7 Oa. bU ? 6@ 8 a V @ V b7 Oa. b% ? 6@ 8 a V @ K b7
(a. b% ? 6@ 8 a K @ V b7
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VENN DIAGRAM
% enn diag)am o) set diag)am is
a diag)am that sho&s allossible logical )elations bet&eena $nite collection of sets. enn
diag)ams &e)e concei*ed a)ound1 by 5ohn enn. They a)eused to teach elementa)y set
theo)y, as &ell as illust)ate
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Wenn consist of
rectangles and closedc)rves )s)ally circles&
The )niversal isrepresented )s)ally byrectangles and its
s)bsets by circle&
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/443ST0AT/B 1& in g 3?6 1. 9 . :. &&. 1= 7 is the)niversal set of which A ? 69. !. :. . 1=7 is a s)bset&
. 2
. 4.
.6
.1
. 3
. /
. 1
. !
. 7
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/443ST0AT/B 9& /n g 3 ? 61. 9. :. &. 1= 7 is the
)niversal set of which A ?6 9. !. ;. . 1= 7 and 2 ? 6 !.; 7 are s)bsets. and also 2 N A&
. 2 %
. . 4
. 6
. 1
. 3
. !
./
. 1
. 7
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3B/B 5 SETS 8 the )nion oftwo sets A and 2 is the set Cwhich consist of all those
element which are either in A or2 or in both&
PURPLE partis the ui!
A U B"UNION#
OPERATIONS ON SETS
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SOME PROPERTIES OF
T$E OPERATION OFUNION
1% A 3 2 ? 2 3 A
( comm)tative law %9% ( A 3 2 % 3 C ? A 3 ( 2 3 C
% ( associativelaw %
:% A 3 J ? A ( law of
identity element %
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SOME PROPERTIES OF
T$E OPERATION OFINTERSECTION1% A X 2 ? 2 X A
( comm)tative law %9% ( A X 2 % X C ? A X ( 2 X C %
( associative law %:% Y X A ? Y. 3 X A ? A( law of
Y and 3 % !% A X A ? A ( idempotent
law %
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COMPLEMENT OF SETS
4et 3 ? 6 1. 9. :. 7 now theset of all those element of3 which doesnZt belongs to
A will be called as Acompliment&
8
%
%9:;
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PROPERTIES OF
COMPLEMENTS OF SETS1% Complement laws 81% A 3 AZ? 3
9% A X AZ ? Y9% >e MorganZs law 8 1% ( A3 2 %Z ? AZ X 2Z
9% ( A X 2 %Z? AZ 3 2Z
:% 4aws of do)ble
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