sets slides2

8/20/2019 Sets Slides2

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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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