(pound

~ tf(~) 2 - x s r~1dAS 0 ~ -~~

10 3-fro) 1 lt lolt gt10 J

100 t )0 4 300tUoo) = 2 -00 )0 10 -0 gt10 +01+ ( 0amp

gt1B7iJScf32(

~ s A ffa stt~ tWl [0 fClOl

W C fwL tk Soti to AS fIMPj

JC~1 plaquoca AS we lrlce b) bisJ

~OC( fes~ Co= So ~yenI ~ I - 25 J ~z 2 5 bullbullbullJ

or X-=75 X amp x ~ 1

A~~-s solve ~s bj U$~j Qc c~s

2~- XI 87~f3Z (4K+t) If C $ +~ ike

( offr~ ( C~ftGt Q Qj fiI~ 7J(2Xlt i )

( fio f +ampS+32 C t ( g4-S2( [s)

lf -x ~ 2 bull -tleW 2 =+4 t_ ~b) 4 bi 1 1( $ shy

X - l(2Jo+I)I= ~~+f t ~~ trJJ 2~ Xl S +laquo- 411 =- t c

l4A-l4f~b+t) == 4f c- 1 I l

1875f32 i (+J(++() I-shy- I i-= l4d t)(4-x~ l) -== 4-e + 1

4c- ( -= 1-e f i 0 ~o(+W

NL~ -tkltj sAves ~~~bJ st~ ~s -tJ ~lvIIers) )ot hJ ~AAilVi~~

ft

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A s sbset ot S ( 13 ftc~ A) f flItry ~tetcent of A is oso (1 e(tcent af a tv ~S au tNt wnf A E B ~ ftlrt~t(t cent pound S flt (lv(tty Sec S

W SAj A B ~ff A c= a aA S~A ~ gt A IS 0 ftdegrcf SIaset cf t3 ff As Sa( A+8 ~J ~us tAsc tNt kJtIfc ACo ~f2 r-

~~Lt kt A=~II2)~ ~=l~1 ~ I c - J (I 2 3 -ie A c B -= C

~i~ ~efeAtd ekiWets cor~t ~~~

tgt AIId C Ant 3 elttMet sets bull--~ A hAS 2 e(eWIets

~14-+ + -LS i ele~e~-t Otl~ bull

t- -1~-te set 1 XS f )-ampei 1kywfoer 4ele-eS of- X

s l~ ~ 0 ~~-f6 ~~r~ ampl~s ot f

let s be Q ~t 1ke -r-Jer set 0t S lS

ike Stt of ~( ~~sets of S It is tlQMttd bj P(s) 6-r 2 s poundX4-=fks

s~cent ~ ~ tS p(S)=fqJi S =1X -rLe~ cent 1~ ~ s f(s)=f~fx ~ s= iX~1 tk~ ~I fxs ~~I f)(~1 ~ ~

1(S) =i-I fxll ~~1middotflCf ~ If S J4$ V a(-e~s) -fke PCs) ku 2~ Qlt~ts

Sfitt 9re~cM$ Lft AI B C D u b~ sts TAoc(- urio~ s

A u t3 u C 1) u i X S Qfe-t-

11 4t le6se O)e of ~ set AI BClgt1 ~i~ ~ptJ~r =IPlY~ 1X~I7) J ~~wx ~~ -= tT -l x YI 7

lR v 0 12 - Qu ~ 1tJZQ =QJ

S u ~ -= s- -= V S +t a4~ Set S

1 __________ -- ~

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A s sbset ot S ( 13 ftc~ A) f flItry ~tetcent of A is oso (1 e(tcent af a tv ~S au tNt wnf A E B ~ ftlrt~t(t cent pound S flt (lv(tty Sec S

W SAj A B ~ff A c= a aA S~A ~ gt A IS 0 ftdegrcf SIaset cf t3 ff As Sa( A+8 ~J ~us tAsc tNt kJtIfc ACo ~f2 r-

~~Lt kt A=~II2)~ ~=l~1 ~ I c - J (I 2 3 -ie A c B -= C

~i~ ~efeAtd ekiWets cor~t ~~~

tgt AIId C Ant 3 elttMet sets bull--~ A hAS 2 e(eWIets

~14-+ + -LS i ele~e~-t Otl~ bull

t- -1~-te set 1 XS f )-ampei 1kywfoer 4ele-eS of- X

s l~ ~ 0 ~~-f6 ~~r~ ampl~s ot f

let s be Q ~t 1ke -r-Jer set 0t S lS

ike Stt of ~( ~~sets of S It is tlQMttd bj P(s) 6-r 2 s poundX4-=fks

s~cent ~ ~ tS p(S)=fqJi S =1X -rLe~ cent 1~ ~ s f(s)=f~fx ~ s= iX~1 tk~ ~I fxs ~~I f)(~1 ~ ~

1(S) =i-I fxll ~~1middotflCf ~ If S J4$ V a(-e~s) -fke PCs) ku 2~ Qlt~ts

Sfitt 9re~cM$ Lft AI B C D u b~ sts TAoc(- urio~ s

A u t3 u C 1) u i X S Qfe-t-

11 4t le6se O)e of ~ set AI BClgt1 ~i~ ~ptJ~r =IPlY~ 1X~I7) J ~~wx ~~ -= tT -l x YI 7

lR v 0 12 - Qu ~ 1tJZQ =QJ

S u ~ -= s- -= V S +t a4~ Set S

1 __________ -- ~

--

o

shyf

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0

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bull bull

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A s sbset ot S ( 13 ftc~ A) f flItry ~tetcent of A is oso (1 e(tcent af a tv ~S au tNt wnf A E B ~ ftlrt~t(t cent pound S flt (lv(tty Sec S

W SAj A B ~ff A c= a aA S~A ~ gt A IS 0 ftdegrcf SIaset cf t3 ff As Sa( A+8 ~J ~us tAsc tNt kJtIfc ACo ~f2 r-

~~Lt kt A=~II2)~ ~=l~1 ~ I c - J (I 2 3 -ie A c B -= C

~i~ ~efeAtd ekiWets cor~t ~~~

tgt AIId C Ant 3 elttMet sets bull--~ A hAS 2 e(eWIets

~14-+ + -LS i ele~e~-t Otl~ bull

t- -1~-te set 1 XS f )-ampei 1kywfoer 4ele-eS of- X

s l~ ~ 0 ~~-f6 ~~r~ ampl~s ot f

let s be Q ~t 1ke -r-Jer set 0t S lS

ike Stt of ~( ~~sets of S It is tlQMttd bj P(s) 6-r 2 s poundX4-=fks

s~cent ~ ~ tS p(S)=fqJi S =1X -rLe~ cent 1~ ~ s f(s)=f~fx ~ s= iX~1 tk~ ~I fxs ~~I f)(~1 ~ ~

1(S) =i-I fxll ~~1middotflCf ~ If S J4$ V a(-e~s) -fke PCs) ku 2~ Qlt~ts

Sfitt 9re~cM$ Lft AI B C D u b~ sts TAoc(- urio~ s

A u t3 u C 1) u i X S Qfe-t-

11 4t le6se O)e of ~ set AI BClgt1 ~i~ ~ptJ~r =IPlY~ 1X~I7) J ~~wx ~~ -= tT -l x YI 7

lR v 0 12 - Qu ~ 1tJZQ =QJ

S u ~ -= s- -= V S +t a4~ Set S

1 __________ -- ~

~

_

_

shy--shy

~ ~

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0

0

i

~

bullbull

I

~t ~

llo

bull bull

bull

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A

bull bull

t~

I

11

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bull( ~

t

II II

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l

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n

bullbulln

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A s sbset ot S ( 13 ftc~ A) f flItry ~tetcent of A is oso (1 e(tcent af a tv ~S au tNt wnf A E B ~ ftlrt~t(t cent pound S flt (lv(tty Sec S

W SAj A B ~ff A c= a aA S~A ~ gt A IS 0 ftdegrcf SIaset cf t3 ff As Sa( A+8 ~J ~us tAsc tNt kJtIfc ACo ~f2 r-

~~Lt kt A=~II2)~ ~=l~1 ~ I c - J (I 2 3 -ie A c B -= C

~i~ ~efeAtd ekiWets cor~t ~~~

tgt AIId C Ant 3 elttMet sets bull--~ A hAS 2 e(eWIets

~14-+ + -LS i ele~e~-t Otl~ bull

t- -1~-te set 1 XS f )-ampei 1kywfoer 4ele-eS of- X

s l~ ~ 0 ~~-f6 ~~r~ ampl~s ot f

let s be Q ~t 1ke -r-Jer set 0t S lS

ike Stt of ~( ~~sets of S It is tlQMttd bj P(s) 6-r 2 s poundX4-=fks

s~cent ~ ~ tS p(S)=fqJi S =1X -rLe~ cent 1~ ~ s f(s)=f~fx ~ s= iX~1 tk~ ~I fxs ~~I f)(~1 ~ ~

1(S) =i-I fxll ~~1middotflCf ~ If S J4$ V a(-e~s) -fke PCs) ku 2~ Qlt~ts

Sfitt 9re~cM$ Lft AI B C D u b~ sts TAoc(- urio~ s

A u t3 u C 1) u i X S Qfe-t-

11 4t le6se O)e of ~ set AI BClgt1 ~i~ ~ptJ~r =IPlY~ 1X~I7) J ~~wx ~~ -= tT -l x YI 7

lR v 0 12 - Qu ~ 1tJZQ =QJ

S u ~ -= s- -= V S +t a4~ Set S

1 __________ -- ~

i

~

bullbull

I

~t ~

llo

bull bull

bull

~t

A

bull bull

t~

I

11

~

bull( ~

t

II II

~Im

1 t -

to

II

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--

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l

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bull

n

bullbulln

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~- let A ~ ts lot sets

A s sbset ot S ( 13 ftc~ A) f flItry ~tetcent of A is oso (1 e(tcent af a tv ~S au tNt wnf A E B ~ ftlrt~t(t cent pound S flt (lv(tty Sec S

W SAj A B ~ff A c= a aA S~A ~ gt A IS 0 ftdegrcf SIaset cf t3 ff As Sa( A+8 ~J ~us tAsc tNt kJtIfc ACo ~f2 r-

~~Lt kt A=~II2)~ ~=l~1 ~ I c - J (I 2 3 -ie A c B -= C

~i~ ~efeAtd ekiWets cor~t ~~~

tgt AIId C Ant 3 elttMet sets bull--~ A hAS 2 e(eWIets

~14-+ + -LS i ele~e~-t Otl~ bull

t- -1~-te set 1 XS f )-ampei 1kywfoer 4ele-eS of- X

s l~ ~ 0 ~~-f6 ~~r~ ampl~s ot f

let s be Q ~t 1ke -r-Jer set 0t S lS

ike Stt of ~( ~~sets of S It is tlQMttd bj P(s) 6-r 2 s poundX4-=fks

s~cent ~ ~ tS p(S)=fqJi S =1X -rLe~ cent 1~ ~ s f(s)=f~fx ~ s= iX~1 tk~ ~I fxs ~~I f)(~1 ~ ~

1(S) =i-I fxll ~~1middotflCf ~ If S J4$ V a(-e~s) -fke PCs) ku 2~ Qlt~ts

Sfitt 9re~cM$ Lft AI B C D u b~ sts TAoc(- urio~ s

A u t3 u C 1) u i X S Qfe-t-

11 4t le6se O)e of ~ set AI BClgt1 ~i~ ~ptJ~r =IPlY~ 1X~I7) J ~~wx ~~ -= tT -l x YI 7

lR v 0 12 - Qu ~ 1tJZQ =QJ

S u ~ -= s- -= V S +t a4~ Set S

1 __________ -- ~

1

i _

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II n

T~

-0

()

V

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~- let A ~ ts lot sets

A s sbset ot S ( 13 ftc~ A) f flItry ~tetcent of A is oso (1 e(tcent af a tv ~S au tNt wnf A E B ~ ftlrt~t(t cent pound S flt (lv(tty Sec S

W SAj A B ~ff A c= a aA S~A ~ gt A IS 0 ftdegrcf SIaset cf t3 ff As Sa( A+8 ~J ~us tAsc tNt kJtIfc ACo ~f2 r-

~~Lt kt A=~II2)~ ~=l~1 ~ I c - J (I 2 3 -ie A c B -= C

~i~ ~efeAtd ekiWets cor~t ~~~

tgt AIId C Ant 3 elttMet sets bull--~ A hAS 2 e(eWIets

~14-+ + -LS i ele~e~-t Otl~ bull

t- -1~-te set 1 XS f )-ampei 1kywfoer 4ele-eS of- X

s l~ ~ 0 ~~-f6 ~~r~ ampl~s ot f

let s be Q ~t 1ke -r-Jer set 0t S lS

ike Stt of ~( ~~sets of S It is tlQMttd bj P(s) 6-r 2 s poundX4-=fks

s~cent ~ ~ tS p(S)=fqJi S =1X -rLe~ cent 1~ ~ s f(s)=f~fx ~ s= iX~1 tk~ ~I fxs ~~I f)(~1 ~ ~

1(S) =i-I fxll ~~1middotflCf ~ If S J4$ V a(-e~s) -fke PCs) ku 2~ Qlt~ts

Sfitt 9re~cM$ Lft AI B C D u b~ sts TAoc(- urio~ s

A u t3 u C 1) u i X S Qfe-t-

11 4t le6se O)e of ~ set AI BClgt1 ~i~ ~ptJ~r =IPlY~ 1X~I7) J ~~wx ~~ -= tT -l x YI 7

lR v 0 12 - Qu ~ 1tJZQ =QJ

S u ~ -= s- -= V S +t a4~ Set S

1 __________ -- ~

~- let A ~ ts lot sets

A s sbset ot S ( 13 ftc~ A) f flItry ~tetcent of A is oso (1 e(tcent af a tv ~S au tNt wnf A E B ~ ftlrt~t(t cent pound S flt (lv(tty Sec S

W SAj A B ~ff A c= a aA S~A ~ gt A IS 0 ftdegrcf SIaset cf t3 ff As Sa( A+8 ~J ~us tAsc tNt kJtIfc ACo ~f2 r-

~~Lt kt A=~II2)~ ~=l~1 ~ I c - J (I 2 3 -ie A c B -= C

~i~ ~efeAtd ekiWets cor~t ~~~

tgt AIId C Ant 3 elttMet sets bull--~ A hAS 2 e(eWIets

~14-+ + -LS i ele~e~-t Otl~ bull

t- -1~-te set 1 XS f )-ampei 1kywfoer 4ele-eS of- X

s l~ ~ 0 ~~-f6 ~~r~ ampl~s ot f

let s be Q ~t 1ke -r-Jer set 0t S lS

ike Stt of ~( ~~sets of S It is tlQMttd bj P(s) 6-r 2 s poundX4-=fks

s~cent ~ ~ tS p(S)=fqJi S =1X -rLe~ cent 1~ ~ s f(s)=f~fx ~ s= iX~1 tk~ ~I fxs ~~I f)(~1 ~ ~

1(S) =i-I fxll ~~1middotflCf ~ If S J4$ V a(-e~s) -fke PCs) ku 2~ Qlt~ts

Sfitt 9re~cM$ Lft AI B C D u b~ sts TAoc(- urio~ s

A u t3 u C 1) u i X S Qfe-t-

11 4t le6se O)e of ~ set AI BClgt1 ~i~ ~ptJ~r =IPlY~ 1X~I7) J ~~wx ~~ -= tT -l x YI 7

lR v 0 12 - Qu ~ 1tJZQ =QJ

S u ~ -= s- -= V S +t a4~ Set S

1 __________ -- ~

-rkil+~furA of ASCDol Is

A( ~ ( C ( D1 bull -= is A (4 11 ~etJ oM 4 -tk Sets AI fgt c0 1

~~fks 1r$1(1)

H~c_tamp_t ofBiflA IS ~ A 13 ~C ~ euro A til x 8 ~ ~ IRQ I~ -1M set (( i t~J fI~ h~l~-Jhl~ I

Sjx~4 ( 1rx~Jt ( Ltvwt~=f4 42) (R-Q) =1(u1T) U (tt-li~1

~ f Q [0 I] i iC lC e Q A( 0 ~ ~~ tI s(centcent4(Sfoi2~StS -------~----__

-d $A~ vnxlampi of AI ~J C ) ~ is A lC B~C )(1) x r r(1It b c 4l ) A ~A 11 J I I J co )

I be fgt c pound C ~amp-1) bullbullbull 1 6)c4MDeS ID D t J j

+ IfooJ( = (~) C j E IR If~ IN)( ZIltoll = (~I2) XE NJ ~ E -z I

s x ~ - 0 =- rJ ~ L a 0 o~ l 1 lC S ]M CWoctcy ~t S middot If A +IS J ik~ Ax B -F Bx A

s cent =~ J cent -s cent ~ 6H~ SlLt S lI

--e sets AI eIe 1gt1 ~t dsjot1 -ritit i ~ampcf- i s ~~ Stf

-n-e Sets AJ 6 C1 4lte ctJg laquosoii i 1 YI d )

iff -e t~NItda- of 0fey -10 of -fIamp ~ts ~ - -LI D I-u L ~ I S fI~ --T~ St-

FicAe l~t A fltl ~ ~ ~SZ~ cft1t1 I

1kef AJ Ygt I C A~ c1~$jof-t btOWSlt ~ A( a( c = cent

blAt A B c tl~ ~ JIIIampfd~brt ~tcse i

Al~=td1f ~ ~ tst4t4CJt middotmiddotmiddotmiddotf

K~ MtUAA~$jo~t9 Iijoft tmiddot ~ -__ ~

reg Ofl~ tJot~ ~s fOsf~ ~e1

S u $2 u $ - U Sk k1

s ( S2middot 1 SI ~ Sflt I =-

S x ~ c x S gtlt Sk k bttf~r J6+t~

$1 v S-a U SJ V - -= 0 $lt ( U Sic) ~ tc1 kEN

hot too ~ooc1 )0 S S4f (cJ J CgtQshy

(5-ilrlJ for if~lM od GJ-tampIfM ~) ~ If rY E 12-) lQt 12 be -tka ~ 1x r ~ f4t4 J -tIvz J~ s not () eY~ct I l i

~ Je U Q = IR1(Ol) lJ4ot + slofe ~ wE laquolt JJ ~ y~x

( f(~ = (O)O) ~ twE (til

Ex QJIIple s O~ tOof Pfober-S I ---------- ---- shy

If If Ie ~ E ~t~ Q~e lI ~ ie

QIIJ (3) C s 1) J CO ~cl-t~ bull

-tien yrGt A( C S B f D

ftrAtQ~ AC~ftknJ to Jtf~ pound ~e ~t To deckI

bull I bull J)

cc eef~ X e An C 5 Also iA B( J) 1~~ E A nC ~ XEA cl XE- C

(b~ ampef of r )

=7gt i( Eo B ()~C( ( E- D (b~ CD reg J aefmiddot of ~ )

cent) it E Jgt (1)

( b~ clefmiddot of 1 )

A(C ~ e f J) (b) cl~f 01 S )

~sMc Sjlcc ~~s $ ffHJ ~OI MO ltU~ ~CIf As8 AaAI1 cs Tgt -flePo Anc s 8(]) ) to r0e 01 otke sttelt

bull bull

w II _

A1Q tk er- ExattfjIe 1(1) Ie XE IR g(r) = Jl J e Z t = rmiddotI

fro~t lAJ~)C = CAC)u(SC) gt1lt

~

1gt-ferKl f-~s shy

~f ds j 10 4et = I dec Ie ~ od ~ ~f=~ f J

~ oJ I A fMJ)N (0( tllAr 01 4fft~ ) T shyf~ofl X(i(AJamp)C~ xEAVeaJ1Cfc AsdA -tOAsetB (d_-W~ fA-B)

pound ((~ df of ) I ~ A t~ 0t Oss~J To ev~fJ ae A llt~ 1C~ 14 -x~C (b1tmiddotfof u) ~)CA~ OM bE B 11~ b (derel 5flt1I)) I ICE- e ~ is ike v-I-tt of f fA( a

Gst t XE A Ard i( f C ( X E AC A f-i toUlstbe We ( _cl~~~ i t 1- ~~ 0- S~X e~ Co -+cent -f 0 = 0 ) -flet fCt1 -= f[t)

Wtl CE- e aJ1(4 lt l~ clef 0+ ) Ii A Is -tle ~MA~ 6f f A tkWl f ~ XE (AC) v(6C) i B ~ yen CodoAl 0ff- ~ Co~f 1

(L) Jef of U ) ~ I (AuBhe c (AC) v (s-c ) f(A) = j ~ e BII~ ~=f(()~r Sollie 1(fA~

- (bf cle~ 1 pound ) ~ i Is -fk Y1I3 ~14J~ ) of f ~ IX E (A c lJ (6 c) ~ e -J ~ f is ~ ~-b ~ A I ~ ~ x~f c (bJ clef of U ) 01 f ~ II B~V-~ fe~f i

KIt~~ l( E ~c -ric set ( fcIC)) 7C E A $ik3f1t at fSt~rs lt) CaSt 0( CAu ~ bcrlt ) 0 ~s Ot( ~ c -tftr 3~ We ~ (bj cl-t of If Sot ~ iOtA fit _~-euro rll$i4-~JiettLls Ill I

~ ~

CiD _-shy ~jCqcent-es 6) Let f A~ bQ II f-J)M -c( C t A

(i) -k ~laquo ~kf-l- O~ IR~~ -rl-a ~sttd~ 0+ f to C I~ ftc c~ B ~ iv- bl t(x) r 1 ( 2 0 i

oJ ~_ X 1 C lt 0 ~ 301amp ~ fIe (C) = f6c) ~ A(( )Ce- c -rk~(I ~~ ore ~~ OY41 1)laquo~t~ ~ ~~ (MIf 17 J A 0 L f I ) -JIof-fa ~~ 1~ 1 1 ) is ~llrJecr~~ 0(0 1

t~~+I-tlcGoJCI~CA b~t1~sd f(A)=S A ~[3 (AiAftij [0~ ) ~ fcf-- tIell 10 ~SCII~ I_~ becse ~ jrap- ~ -fI- Slaquo- I ~

-ck follow~ ~~ fo clQ~~ ~f-c~ -rI VA(~S of-f j 8 rgt4Ij tareomiddott I bl4ti

s crt we-k~d Ltt X V (_ ) I flo ee~~t of ~_will be o~ifetA ~ ~VAlAlL

-for ~( V~ IN 1)q~c f t(~~~ IR ~ So A hu d leA$-t A W4W1j e~-ls AS 8

C)() n If gt vtat IJt 1(-ltk~IIA( b(~ reg f A~ S is iiectt~_(G oe-tc-~) If+ -= - -- ) 1 ~~t fc7C)1-f ~-=f()CJ f()C-fCj) ~kes x-==~

~res f ftfgtM$ Y$~ middot A ~ -ie vAl-So ~ f il 1$ Jo I~ CD -Tk te~+t~ ~ II st S rs eftA-t I b~-t lto~ eletots

Is S ~ S 4e b I (c) K c ~I XGS fBI ~Ij be ~Ictl4S (J J ~ F fA lA~

reg l~t f ~~amp I 15- C Ie ~t-s 4J1 $0 B ~S ampof (e~ 4S ~4j d~ as A fCA) S S -rk COp9Si~ t j b~ f s

jOf Ac 3f~ b~ (jOf)(1lt) -= 3(f(x))

fo( a~ iecf~~ ~)7A f A~ampI

1kA fyttSC ~ of s 1 ~ (A) ~A tIIf gt fo (V C ~ f(x) =~

-4B )~-f(A_ ~l~

b3 -

(j) r A~ S s loijeJvIl (or G Cl)t-fo-ClNL

fovtesroN1arU__) ff f S eJtie 4( sutjedtvt A -J S ~~ SQ~ )UIoo~ ~(M60~

~en~s

() f A~Bgt S~biject~ iff 3 s= B-gtA s~~-tkcent 3o f=A ~ fOJ-= 18

(6) If f A IS ~ J ~~ C 41e h~-ecftyenIoSJ

0--tl ~of A C ~ b~ect-

(c) Lampt AIamplt~tfA~s~G~th 1f V bE 1$ I i~ kor~ ti~ t =b itersecls if ~ 0- f ~ib OIlCJt I ~ r~ bi jec-t

IE jcltl(A(8fCJl 14df~

1JeGAtf Ael~f~ ~ A ~t S S at~ s~laquot of SxS A 1-t~ R 0 A set s fs 4Wl evP~Jltt1Clt -Iet-

lff CD V Xe S (~x) E R (~~e)(i~ 7) I

reg (1Cj)E ~ ~ (~x)E-tlt (~JtIItetricPr0frt) reg (11 I ) I (OJZ) E Rtgt (x 2 ) ~R (1tAo~ )

I

~laquo~ Wfit~ (V ~ ff (Xi) E 1lt VCE S I Ni-e (Xl =1~ C~ ~1

TcollJ-I e1fJcAca dtUS Fncts (C1k1llh1~ X - ()) VXfS I X-gt ~ xe-()()

=igt U (xl S reg ~s X~ ~ ~ ex1 rj1 becAtts-te i

LECx1 c=9 )( Z (pgt ~ - 2- ~G1 ) x- ~ ~ Gel (11 = (of(~ Zeljlllll

CClp (cl ~ (L Cjl -9 x~ j ~ euro ) )

r-l1)1~l rll ~h _ -J_ t ( ] -~= ~~~WO

lMS ~r

i

reg Ofl~ tJot~ ~s fOsf~ ~e1

S u $2 u $ - U Sk k1

s ( S2middot 1 SI ~ Sflt I =-

S x ~ c x S gtlt Sk k bttf~r J6+t~

$1 v S-a U SJ V - -= 0 $lt ( U Sic) ~ tc1 kEN

hot too ~ooc1 )0 S S4f (cJ J CgtQshy

(5-ilrlJ for if~lM od GJ-tampIfM ~) ~ If rY E 12-) lQt 12 be -tka ~ 1x r ~ f4t4 J -tIvz J~ s not () eY~ct I l i

~ Je U Q = IR1(Ol) lJ4ot + slofe ~ wE laquolt JJ ~ y~x

( f(~ = (O)O) ~ twE (til

Ex QJIIple s O~ tOof Pfober-S I ---------- ---- shy

If If Ie ~ E ~t~ Q~e lI ~ ie

QIIJ (3) C s 1) J CO ~cl-t~ bull

-tien yrGt A( C S B f D

ftrAtQ~ AC~ftknJ to Jtf~ pound ~e ~t To deckI

bull I bull J)

cc eef~ X e An C 5 Also iA B( J) 1~~ E A nC ~ XEA cl XE- C

(b~ ampef of r )

=7gt i( Eo B ()~C( ( E- D (b~ CD reg J aefmiddot of ~ )

cent) it E Jgt (1)

( b~ clefmiddot of 1 )

A(C ~ e f J) (b) cl~f 01 S )

~sMc Sjlcc ~~s $ ffHJ ~OI MO ltU~ ~CIf As8 AaAI1 cs Tgt -flePo Anc s 8(]) ) to r0e 01 otke sttelt

bull bull

w II _

A1Q tk er- ExattfjIe 1(1) Ie XE IR g(r) = Jl J e Z t = rmiddotI

fro~t lAJ~)C = CAC)u(SC) gt1lt

~

1gt-ferKl f-~s shy

~f ds j 10 4et = I dec Ie ~ od ~ ~f=~ f J

~ oJ I A fMJ)N (0( tllAr 01 4fft~ ) T shyf~ofl X(i(AJamp)C~ xEAVeaJ1Cfc AsdA -tOAsetB (d_-W~ fA-B)

pound ((~ df of ) I ~ A t~ 0t Oss~J To ev~fJ ae A llt~ 1C~ 14 -x~C (b1tmiddotfof u) ~)CA~ OM bE B 11~ b (derel 5flt1I)) I ICE- e ~ is ike v-I-tt of f fA( a

Gst t XE A Ard i( f C ( X E AC A f-i toUlstbe We ( _cl~~~ i t 1- ~~ 0- S~X e~ Co -+cent -f 0 = 0 ) -flet fCt1 -= f[t)

Wtl CE- e aJ1(4 lt l~ clef 0+ ) Ii A Is -tle ~MA~ 6f f A tkWl f ~ XE (AC) v(6C) i B ~ yen CodoAl 0ff- ~ Co~f 1

(L) Jef of U ) ~ I (AuBhe c (AC) v (s-c ) f(A) = j ~ e BII~ ~=f(()~r Sollie 1(fA~

- (bf cle~ 1 pound ) ~ i Is -fk Y1I3 ~14J~ ) of f ~ IX E (A c lJ (6 c) ~ e -J ~ f is ~ ~-b ~ A I ~ ~ x~f c (bJ clef of U ) 01 f ~ II B~V-~ fe~f i

KIt~~ l( E ~c -ric set ( fcIC)) 7C E A $ik3f1t at fSt~rs lt) CaSt 0( CAu ~ bcrlt ) 0 ~s Ot( ~ c -tftr 3~ We ~ (bj cl-t of If Sot ~ iOtA fit _~-euro rll$i4-~JiettLls Ill I

~ ~

CiD _-shy ~jCqcent-es 6) Let f A~ bQ II f-J)M -c( C t A

(i) -k ~laquo ~kf-l- O~ IR~~ -rl-a ~sttd~ 0+ f to C I~ ftc c~ B ~ iv- bl t(x) r 1 ( 2 0 i

oJ ~_ X 1 C lt 0 ~ 301amp ~ fIe (C) = f6c) ~ A(( )Ce- c -rk~(I ~~ ore ~~ OY41 1)laquo~t~ ~ ~~ (MIf 17 J A 0 L f I ) -JIof-fa ~~ 1~ 1 1 ) is ~llrJecr~~ 0(0 1

t~~+I-tlcGoJCI~CA b~t1~sd f(A)=S A ~[3 (AiAftij [0~ ) ~ fcf-- tIell 10 ~SCII~ I_~ becse ~ jrap- ~ -fI- Slaquo- I ~

-ck follow~ ~~ fo clQ~~ ~f-c~ -rI VA(~S of-f j 8 rgt4Ij tareomiddott I bl4ti

s crt we-k~d Ltt X V (_ ) I flo ee~~t of ~_will be o~ifetA ~ ~VAlAlL

-for ~( V~ IN 1)q~c f t(~~~ IR ~ So A hu d leA$-t A W4W1j e~-ls AS 8

C)() n If gt vtat IJt 1(-ltk~IIA( b(~ reg f A~ S is iiectt~_(G oe-tc-~) If+ -= - -- ) 1 ~~t fc7C)1-f ~-=f()CJ f()C-fCj) ~kes x-==~

~res f ftfgtM$ Y$~ middot A ~ -ie vAl-So ~ f il 1$ Jo I~ CD -Tk te~+t~ ~ II st S rs eftA-t I b~-t lto~ eletots

Is S ~ S 4e b I (c) K c ~I XGS fBI ~Ij be ~Ictl4S (J J ~ F fA lA~

reg l~t f ~~amp I 15- C Ie ~t-s 4J1 $0 B ~S ampof (e~ 4S ~4j d~ as A fCA) S S -rk COp9Si~ t j b~ f s

jOf Ac 3f~ b~ (jOf)(1lt) -= 3(f(x))

fo( a~ iecf~~ ~)7A f A~ampI

1kA fyttSC ~ of s 1 ~ (A) ~A tIIf gt fo (V C ~ f(x) =~

-4B )~-f(A_ ~l~

b3 -

(j) r A~ S s loijeJvIl (or G Cl)t-fo-ClNL

fovtesroN1arU__) ff f S eJtie 4( sutjedtvt A -J S ~~ SQ~ )UIoo~ ~(M60~

~en~s

() f A~Bgt S~biject~ iff 3 s= B-gtA s~~-tkcent 3o f=A ~ fOJ-= 18

(6) If f A IS ~ J ~~ C 41e h~-ecftyenIoSJ

0--tl ~of A C ~ b~ect-

(c) Lampt AIamplt~tfA~s~G~th 1f V bE 1$ I i~ kor~ ti~ t =b itersecls if ~ 0- f ~ib OIlCJt I ~ r~ bi jec-t

IE jcltl(A(8fCJl 14df~

1JeGAtf Ael~f~ ~ A ~t S S at~ s~laquot of SxS A 1-t~ R 0 A set s fs 4Wl evP~Jltt1Clt -Iet-

lff CD V Xe S (~x) E R (~~e)(i~ 7) I

reg (1Cj)E ~ ~ (~x)E-tlt (~JtIItetricPr0frt) reg (11 I ) I (OJZ) E Rtgt (x 2 ) ~R (1tAo~ )

I

~laquo~ Wfit~ (V ~ ff (Xi) E 1lt VCE S I Ni-e (Xl =1~ C~ ~1

TcollJ-I e1fJcAca dtUS Fncts (C1k1llh1~ X - ()) VXfS I X-gt ~ xe-()()

=igt U (xl S reg ~s X~ ~ ~ ex1 rj1 becAtts-te i

LECx1 c=9 )( Z (pgt ~ - 2- ~G1 ) x- ~ ~ Gel (11 = (of(~ Zeljlllll

CClp (cl ~ (L Cjl -9 x~ j ~ euro ) )

r-l1)1~l rll ~h _ -J_ t ( ] -~= ~~~WO

lMS ~r

i

bull bull

w II _

A1Q tk er- ExattfjIe 1(1) Ie XE IR g(r) = Jl J e Z t = rmiddotI

fro~t lAJ~)C = CAC)u(SC) gt1lt

~

1gt-ferKl f-~s shy

~f ds j 10 4et = I dec Ie ~ od ~ ~f=~ f J

~ oJ I A fMJ)N (0( tllAr 01 4fft~ ) T shyf~ofl X(i(AJamp)C~ xEAVeaJ1Cfc AsdA -tOAsetB (d_-W~ fA-B)

pound ((~ df of ) I ~ A t~ 0t Oss~J To ev~fJ ae A llt~ 1C~ 14 -x~C (b1tmiddotfof u) ~)CA~ OM bE B 11~ b (derel 5flt1I)) I ICE- e ~ is ike v-I-tt of f fA( a

Gst t XE A Ard i( f C ( X E AC A f-i toUlstbe We ( _cl~~~ i t 1- ~~ 0- S~X e~ Co -+cent -f 0 = 0 ) -flet fCt1 -= f[t)

Wtl CE- e aJ1(4 lt l~ clef 0+ ) Ii A Is -tle ~MA~ 6f f A tkWl f ~ XE (AC) v(6C) i B ~ yen CodoAl 0ff- ~ Co~f 1

(L) Jef of U ) ~ I (AuBhe c (AC) v (s-c ) f(A) = j ~ e BII~ ~=f(()~r Sollie 1(fA~

- (bf cle~ 1 pound ) ~ i Is -fk Y1I3 ~14J~ ) of f ~ IX E (A c lJ (6 c) ~ e -J ~ f is ~ ~-b ~ A I ~ ~ x~f c (bJ clef of U ) 01 f ~ II B~V-~ fe~f i

KIt~~ l( E ~c -ric set ( fcIC)) 7C E A $ik3f1t at fSt~rs lt) CaSt 0( CAu ~ bcrlt ) 0 ~s Ot( ~ c -tftr 3~ We ~ (bj cl-t of If Sot ~ iOtA fit _~-euro rll$i4-~JiettLls Ill I

~ ~

CiD _-shy ~jCqcent-es 6) Let f A~ bQ II f-J)M -c( C t A

(i) -k ~laquo ~kf-l- O~ IR~~ -rl-a ~sttd~ 0+ f to C I~ ftc c~ B ~ iv- bl t(x) r 1 ( 2 0 i

oJ ~_ X 1 C lt 0 ~ 301amp ~ fIe (C) = f6c) ~ A(( )Ce- c -rk~(I ~~ ore ~~ OY41 1)laquo~t~ ~ ~~ (MIf 17 J A 0 L f I ) -JIof-fa ~~ 1~ 1 1 ) is ~llrJecr~~ 0(0 1

t~~+I-tlcGoJCI~CA b~t1~sd f(A)=S A ~[3 (AiAftij [0~ ) ~ fcf-- tIell 10 ~SCII~ I_~ becse ~ jrap- ~ -fI- Slaquo- I ~

-ck follow~ ~~ fo clQ~~ ~f-c~ -rI VA(~S of-f j 8 rgt4Ij tareomiddott I bl4ti

s crt we-k~d Ltt X V (_ ) I flo ee~~t of ~_will be o~ifetA ~ ~VAlAlL

-for ~( V~ IN 1)q~c f t(~~~ IR ~ So A hu d leA$-t A W4W1j e~-ls AS 8

C)() n If gt vtat IJt 1(-ltk~IIA( b(~ reg f A~ S is iiectt~_(G oe-tc-~) If+ -= - -- ) 1 ~~t fc7C)1-f ~-=f()CJ f()C-fCj) ~kes x-==~

~res f ftfgtM$ Y$~ middot A ~ -ie vAl-So ~ f il 1$ Jo I~ CD -Tk te~+t~ ~ II st S rs eftA-t I b~-t lto~ eletots

Is S ~ S 4e b I (c) K c ~I XGS fBI ~Ij be ~Ictl4S (J J ~ F fA lA~

reg l~t f ~~amp I 15- C Ie ~t-s 4J1 $0 B ~S ampof (e~ 4S ~4j d~ as A fCA) S S -rk COp9Si~ t j b~ f s

jOf Ac 3f~ b~ (jOf)(1lt) -= 3(f(x))

fo( a~ iecf~~ ~)7A f A~ampI

1kA fyttSC ~ of s 1 ~ (A) ~A tIIf gt fo (V C ~ f(x) =~

-4B )~-f(A_ ~l~

b3 -

(j) r A~ S s loijeJvIl (or G Cl)t-fo-ClNL

fovtesroN1arU__) ff f S eJtie 4( sutjedtvt A -J S ~~ SQ~ )UIoo~ ~(M60~

~en~s

() f A~Bgt S~biject~ iff 3 s= B-gtA s~~-tkcent 3o f=A ~ fOJ-= 18

(6) If f A IS ~ J ~~ C 41e h~-ecftyenIoSJ

0--tl ~of A C ~ b~ect-

(c) Lampt AIamplt~tfA~s~G~th 1f V bE 1$ I i~ kor~ ti~ t =b itersecls if ~ 0- f ~ib OIlCJt I ~ r~ bi jec-t

IE jcltl(A(8fCJl 14df~

1JeGAtf Ael~f~ ~ A ~t S S at~ s~laquot of SxS A 1-t~ R 0 A set s fs 4Wl evP~Jltt1Clt -Iet-

lff CD V Xe S (~x) E R (~~e)(i~ 7) I

reg (1Cj)E ~ ~ (~x)E-tlt (~JtIItetricPr0frt) reg (11 I ) I (OJZ) E Rtgt (x 2 ) ~R (1tAo~ )

I

~laquo~ Wfit~ (V ~ ff (Xi) E 1lt VCE S I Ni-e (Xl =1~ C~ ~1

TcollJ-I e1fJcAca dtUS Fncts (C1k1llh1~ X - ()) VXfS I X-gt ~ xe-()()

=igt U (xl S reg ~s X~ ~ ~ ex1 rj1 becAtts-te i

LECx1 c=9 )( Z (pgt ~ - 2- ~G1 ) x- ~ ~ Gel (11 = (of(~ Zeljlllll

CClp (cl ~ (L Cjl -9 x~ j ~ euro ) )

r-l1)1~l rll ~h _ -J_ t ( ] -~= ~~~WO

lMS ~r

i

CiD _-shy ~jCqcent-es 6) Let f A~ bQ II f-J)M -c( C t A

(i) -k ~laquo ~kf-l- O~ IR~~ -rl-a ~sttd~ 0+ f to C I~ ftc c~ B ~ iv- bl t(x) r 1 ( 2 0 i

oJ ~_ X 1 C lt 0 ~ 301amp ~ fIe (C) = f6c) ~ A(( )Ce- c -rk~(I ~~ ore ~~ OY41 1)laquo~t~ ~ ~~ (MIf 17 J A 0 L f I ) -JIof-fa ~~ 1~ 1 1 ) is ~llrJecr~~ 0(0 1

t~~+I-tlcGoJCI~CA b~t1~sd f(A)=S A ~[3 (AiAftij [0~ ) ~ fcf-- tIell 10 ~SCII~ I_~ becse ~ jrap- ~ -fI- Slaquo- I ~

-ck follow~ ~~ fo clQ~~ ~f-c~ -rI VA(~S of-f j 8 rgt4Ij tareomiddott I bl4ti

s crt we-k~d Ltt X V (_ ) I flo ee~~t of ~_will be o~ifetA ~ ~VAlAlL

-for ~( V~ IN 1)q~c f t(~~~ IR ~ So A hu d leA$-t A W4W1j e~-ls AS 8

C)() n If gt vtat IJt 1(-ltk~IIA( b(~ reg f A~ S is iiectt~_(G oe-tc-~) If+ -= - -- ) 1 ~~t fc7C)1-f ~-=f()CJ f()C-fCj) ~kes x-==~

~res f ftfgtM$ Y$~ middot A ~ -ie vAl-So ~ f il 1$ Jo I~ CD -Tk te~+t~ ~ II st S rs eftA-t I b~-t lto~ eletots

Is S ~ S 4e b I (c) K c ~I XGS fBI ~Ij be ~Ictl4S (J J ~ F fA lA~

reg l~t f ~~amp I 15- C Ie ~t-s 4J1 $0 B ~S ampof (e~ 4S ~4j d~ as A fCA) S S -rk COp9Si~ t j b~ f s

jOf Ac 3f~ b~ (jOf)(1lt) -= 3(f(x))

fo( a~ iecf~~ ~)7A f A~ampI

1kA fyttSC ~ of s 1 ~ (A) ~A tIIf gt fo (V C ~ f(x) =~

-4B )~-f(A_ ~l~

b3 -

(j) r A~ S s loijeJvIl (or G Cl)t-fo-ClNL

fovtesroN1arU__) ff f S eJtie 4( sutjedtvt A -J S ~~ SQ~ )UIoo~ ~(M60~

~en~s

() f A~Bgt S~biject~ iff 3 s= B-gtA s~~-tkcent 3o f=A ~ fOJ-= 18

(6) If f A IS ~ J ~~ C 41e h~-ecftyenIoSJ

0--tl ~of A C ~ b~ect-

(c) Lampt AIamplt~tfA~s~G~th 1f V bE 1$ I i~ kor~ ti~ t =b itersecls if ~ 0- f ~ib OIlCJt I ~ r~ bi jec-t

IE jcltl(A(8fCJl 14df~

1JeGAtf Ael~f~ ~ A ~t S S at~ s~laquot of SxS A 1-t~ R 0 A set s fs 4Wl evP~Jltt1Clt -Iet-

lff CD V Xe S (~x) E R (~~e)(i~ 7) I

reg (1Cj)E ~ ~ (~x)E-tlt (~JtIItetricPr0frt) reg (11 I ) I (OJZ) E Rtgt (x 2 ) ~R (1tAo~ )

I

~laquo~ Wfit~ (V ~ ff (Xi) E 1lt VCE S I Ni-e (Xl =1~ C~ ~1

TcollJ-I e1fJcAca dtUS Fncts (C1k1llh1~ X - ()) VXfS I X-gt ~ xe-()()

=igt U (xl S reg ~s X~ ~ ~ ex1 rj1 becAtts-te i

LECx1 c=9 )( Z (pgt ~ - 2- ~G1 ) x- ~ ~ Gel (11 = (of(~ Zeljlllll

CClp (cl ~ (L Cjl -9 x~ j ~ euro ) )

r-l1)1~l rll ~h _ -J_ t ( ] -~= ~~~WO

lMS ~r

i

fo( a~ iecf~~ ~)7A f A~ampI

1kA fyttSC ~ of s 1 ~ (A) ~A tIIf gt fo (V C ~ f(x) =~

-4B )~-f(A_ ~l~

b3 -

(j) r A~ S s loijeJvIl (or G Cl)t-fo-ClNL

fovtesroN1arU__) ff f S eJtie 4( sutjedtvt A -J S ~~ SQ~ )UIoo~ ~(M60~

~en~s

() f A~Bgt S~biject~ iff 3 s= B-gtA s~~-tkcent 3o f=A ~ fOJ-= 18

(6) If f A IS ~ J ~~ C 41e h~-ecftyenIoSJ

0--tl ~of A C ~ b~ect-

(c) Lampt AIamplt~tfA~s~G~th 1f V bE 1$ I i~ kor~ ti~ t =b itersecls if ~ 0- f ~ib OIlCJt I ~ r~ bi jec-t

IE jcltl(A(8fCJl 14df~

1JeGAtf Ael~f~ ~ A ~t S S at~ s~laquot of SxS A 1-t~ R 0 A set s fs 4Wl evP~Jltt1Clt -Iet-

lff CD V Xe S (~x) E R (~~e)(i~ 7) I

reg (1Cj)E ~ ~ (~x)E-tlt (~JtIItetricPr0frt) reg (11 I ) I (OJZ) E Rtgt (x 2 ) ~R (1tAo~ )

I

~laquo~ Wfit~ (V ~ ff (Xi) E 1lt VCE S I Ni-e (Xl =1~ C~ ~1

TcollJ-I e1fJcAca dtUS Fncts (C1k1llh1~ X - ()) VXfS I X-gt ~ xe-()()

=igt U (xl S reg ~s X~ ~ ~ ex1 rj1 becAtts-te i

LECx1 c=9 )( Z (pgt ~ - 2- ~G1 ) x- ~ ~ Gel (11 = (of(~ Zeljlllll

CClp (cl ~ (L Cjl -9 x~ j ~ euro ) )

r-l1)1~l rll ~h _ -J_ t ( ] -~= ~~~WO

lMS ~r

i

6~laquo~es Klthl) -r 51 t TLl

bull CD ((i~O~) S =iLe Set of (AI( +nl1~~s k osectu-Jv~I J- -r- J S c -c_ (1 t1~-r T~ ~ Tc S SI-4V ~ ltt~d)I zF

(T] - 1-~t tf 6laquo( ft+ M~(ltltr-to T g- ictI) fY-ri SQiY~

lAt~e~) S = z ~ n d-) ~- as ~~ [0] =~~t ~A(( ME- Z s-JU Itt-O SQ~

-= f middot J - +1 -11 OJ 2 I 4- J [ 1 J ~ -fkaSet 1 4(( ~ z Su~-M tt-l ~ et

t )-l~-lJ I~ 6) ~reg Are U4~laquos of e~cd4tL a~~

reg Let S=10c ~(K=f(fOt 74 f Sc~e S slIlet-lt ~ fAsit-e ff~ ~c-t ~rt (4t~~~reY beQUCk 0 E-S (

O

O

) 4 R - R is lIat 4 ~JeCIl (4 ~S r- Sets S al S-) ~ 1lt~ r(5 1St) I bj-t-

S V S ~ 3 btsecto- f S ~Sa Tlts ts AW ~I~ -(el~ s S a ~~ ~f ~ $z e Sd c W+y [s) = CA S ts I co14(~llUcJer cf- S

tJot~tS CorJ 1~ 2 rt ~ =K fot ros-rfv4 Imiddot ~~

Cod ~ (2~1 =c~twl N = ~o I LI

()4P 1-4~-

CArd R -= c ~ CotJ-vJ~of ~ Cot~W~

~fu- 3 COCA-tjI~ ~ A 1gtR~t~t tlS+)ste~ So~4

(j) ~ftft ~~Ts 1gtfit-s ASat S ts Co~~ ifr~ Lff

3 ~lec~ f IN ~ S ( ie Campt-tl S -o )

reg A Sft s s cou~~ iff ~ S ~Ir+ C f

cO~~ ~ttUco~ampb= ~ ~J~ OosetV-fccMs

3 blec+~ f IN ~S~ S=1f(df(~)~t(a~ ~ ol~ of efeefs -t s

-1-14 Me te~tfoV no~S r 1 Itt Olllampss

=$)S~I $3J J ~ f M-gt S J~( -y l f() =S

5-gtSlJ s Hjecto-

1() ~ -Jecv (0) =-X XE re at oltCltr ~ COCltofif $c~stt amp~ Let A~ B

is lllcocu-fabis (R S U(OU~+(Yc If 6 is co~t1 J -t A is Cowt(J middot

(1A(c~ (~-rposfJ or ~f A S u~ricJ 1 AssufIAA o () IS cttJ-IJ~ il~tI 8 S ftf c fArltf-J ) ( 16 cpd~~DO oss3 ~j1C~ f ftJ -=gt (6) () So ~es~ B ou~tAbl42 ~ B f jJ haJ I ~

f(1)-= O (l tll 41 4+ middot f ~(ieclv-t- fChW ~ 1$+ of SI we s~1ce Jut lite eltlaquos ~-fc2) O 4z ~ Qz) 4ar 9 e~ XE- fo)) ~t D~ ~ l~ A -rt w 3et ~ Ics-j tfA I

feS) O 4 QSa 41 $ 411- bull fS e~Lt4( fo SirtL tLe $13 of 8 hAS 110 ApetllttI fANl ASS t- SoMe fpoundnf(~) O44t ~l 441 it+r -Ae tiStj of A __ $ ko rerttb ~CSSGI I - Cf1 U~(t 7kotIIw f

5

COI~cle X -= o b b~ b~ I were tt V~ IJ ~ AY is ot~IJ fl U A is ~middot1 PeurofI OJ (= -Ib- l 2 if Gkr = i

(t ~~eRlI if S is Cot4rJ~ I So) f trJ~s is i- t ~ f tJf ~ ( f a~ A Je-k~ aN I s 4 S I As is rf~La i

-rfe~ 0 lt( lt Howeer )(f= f(W) ~eccwsct -tke~middotmiddot U A~ -= U Ar ) is cDCLt-taWe) S6$ YlEIN T bn f AWW 10 AU tI I l lDt~dct~

~ t ~ t 1-tod~ct )C - YtI 4ljtt of f() l ---- AI tttu (In al) bullbull J t ~~ f fpound ti I ~ A J ~ l ) i~0 _ Cot) lS IANIraquotIJ -tk $loiect~ cof J_I L - 2 tia 4~~ Qz~ bullbullbull 7

Af ~~ I J I gt J A~ f ()( ala a1 3 lo) ~~ aie~ b~ ~)=tf1rlx-i) tNJ Cf)kt1tt- SCe-e J I ) I

L v ts Ia~ect- w -f(7C)= 1+ A~~c 9 UA i4uI tt2(I~2a tizl4cSImiddotmiddotmiddot ~ 1

6l~~~~~_~ ~ ~s u~~dJe tlEtN aCIcfc -rercft oloj-tLe w~ I skltf ~Labl -~

1() ~ -Jecv (0) =-X XE re at oltCltr ~ COCltofif $c~stt amp~ Let A~ B

is lllcocu-fabis (R S U(OU~+(Yc If 6 is co~t1 J -t A is Cowt(J middot

(1A(c~ (~-rposfJ or ~f A S u~ricJ 1 AssufIAA o () IS cttJ-IJ~ il~tI 8 S ftf c fArltf-J ) ( 16 cpd~~DO oss3 ~j1C~ f ftJ -=gt (6) () So ~es~ B ou~tAbl42 ~ B f jJ haJ I ~

f(1)-= O (l tll 41 4+ middot f ~(ieclv-t- fChW ~ 1$+ of SI we s~1ce Jut lite eltlaquos ~-fc2) O 4z ~ Qz) 4ar 9 e~ XE- fo)) ~t D~ ~ l~ A -rt w 3et ~ Ics-j tfA I

feS) O 4 QSa 41 $ 411- bull fS e~Lt4( fo SirtL tLe $13 of 8 hAS 110 ApetllttI fANl ASS t- SoMe fpoundnf(~) O44t ~l 441 it+r -Ae tiStj of A __ $ ko rerttb ~CSSGI I - Cf1 U~(t 7kotIIw f

5

COI~cle X -= o b b~ b~ I were tt V~ IJ ~ AY is ot~IJ fl U A is ~middot1 PeurofI OJ (= -Ib- l 2 if Gkr = i

(t ~~eRlI if S is Cot4rJ~ I So) f trJ~s is i- t ~ f tJf ~ ( f a~ A Je-k~ aN I s 4 S I As is rf~La i

-rfe~ 0 lt( lt Howeer )(f= f(W) ~eccwsct -tke~middotmiddot U A~ -= U Ar ) is cDCLt-taWe) S6$ YlEIN T bn f AWW 10 AU tI I l lDt~dct~

~ t ~ t 1-tod~ct )C - YtI 4ljtt of f() l ---- AI tttu (In al) bullbull J t ~~ f fpound ti I ~ A J ~ l ) i~0 _ Cot) lS IANIraquotIJ -tk $loiect~ cof J_I L - 2 tia 4~~ Qz~ bullbullbull 7

Af ~~ I J I gt J A~ f ()( ala a1 3 lo) ~~ aie~ b~ ~)=tf1rlx-i) tNJ Cf)kt1tt- SCe-e J I ) I

L v ts Ia~ect- w -f(7C)= 1+ A~~c 9 UA i4uI tt2(I~2a tizl4cSImiddotmiddotmiddot ~ 1

6l~~~~~_~ ~ ~s u~~dJe tlEtN aCIcfc -rercft oloj-tLe w~ I skltf ~Labl -~

P~tct -rtr fo tE IN ) if AI middotmiddotAr Cou~~ -ikt~ Alx ~ A~ $ lo1lt Recurt t -= 1 s clot

f 2 A -= I e c1 c -1 Aa= ~ ~11 ~JJ bullbull ~

-=9 A)( A-a f(~J it) ()tIl ~)1 (~t~-U (12 ~) (lj) (1-1 jl)Imiddot middot

tA~( (It) ~) (I~ S) (~lf~)middotmiddot o~tj sd_f ~ ~ f ()(I ~)I ()( j) (Xt ~ a) (1- j) (J(~t) ~

Skifb(A~lcs Lf AI 11lt A ~ ft+ fgt 2 As~ Cse - tS rWUA bull ~~

Axmiddotmiddotmiddot ~ At -- (AlC A- ) )( A~ -shyC4se ~-( tS +rutt

-

c4~ 2 ls 7yenUA i

PRclt tkeote~ Aoes ~ bolcl fo~ iApound~fEl1 P4~ (1raquo1101 set~ Sec epr reg _

pound~apU reg Q=~~S-~ wer~I ~ S -f -~ - 0 z ~ ~

J -- shy- -l- - I i

jS-5 a -J-o L z t 2 - 1 I 0 J 2 Ji ~ J a- J bull t

S S bull _-1 -1 () J a J 2 1 J - 3- - Jt ~J 3

S middot r - 2 - D l z i i 11 -= 1 -=-)- 1A Il

J ~ I I J I ~-

V~ fW Z-1p S 1 f(WW)c~ is b~ect~ rshy(wik f(~) ~) ~ ~

S(C 71 i S Co~ffI1 L) b~ec~~ote~J i ~ $ Cor~41011 6) CAIt~ w~J I Q is CO ~+4 t

a) 11 A s uICotlClLt J B s coCamp~+blll -tke A 8 1s UCo+J (11 CClSfl A-= fi( ) S -= Q ~ rIC 0 los UfCOCltIe) ~osm AssuPl1l A (3 tS Coltt~t4tb(ltlt J (t ~

At amp s (3 (AJ 8 c~~~lt ~ Aamp Cou~~C 1

Coampt-la $-bs-t -fNo~ I ~ (A t 6 ) u (A e) A CoCtt~I -+- Cofncct~ ~ f

1-co-tLt ~~ CoCAff-bLt CA4cn 1kO(eM

ru G) Sce ~ ~ ct (lc( ~ s u~COftampCe ~ reg ~ tkt -f(e st L cf 4laquo (~S wifl b~ -tLe Cout4tf slset -ilofe-~ ltC is tLrCau1ablct ~tt j W X +b I wkctc ~J C ~ Q I

s Cotw S 7L lt Q S IR ~ C ~ ~ Cotamp ~~ 7 uW( -ft It

reg 1gtet~MtC2 f A- - r r )t E INJ rE (0 I I) ~ o~e -utMlA

B= rr ME J rE (OJ) f Q ~ OutdJe O~ Rot

i $o~tn fQ(cI~ M -= i I we sc~ I ( 0 ) r IT --E (0 ) ~ A I ~d~a b Co~~t~~ ~fsct teo

A iS UftcoufcJf4

I fi-EfN I let Sm -= Y~ r (0 () n Q 1 1kt (0) f Q ~ Q ~ (01)((2 co-tcJ~

t(O+W(t by(JJJ~

6 ~ U tyoJi S CotJ(e tyen rE (~Ia ~ fih c~~

~~ ~~

B U l)M s eotck ~ Ctl~JJ ~ )WEH ~ 1-1_ ~or

AMiJIamp

s~~tOA 1)c~lI(l f Q ~Q ~ L ~~ letf- f(~) ~e 1k (Ie ~ ~~ 3=~)(+ 11s S A lDj~t~fII wrtk f - SfMt5 ~-I wi e1-fGW ~ =MJCc t-cck T (~J ~Ac (Q)( Q lS o~-~ l ftoclu(t er t J

C04Mt-~ 1 L is Coll~+c b biec-t tNl~

LetAt A-= A=- bull = 10I 1 1 tke shyA x AI A s o~OUftc~fe

~t~ A~cApAA A1-A~Asmiddot $ CoWt~fale bull ~~ 3 ~jt~ f IN Ac~A)1J(

flt) (~ J Q Q - ) A~ a~i =0 0 ~ bull

f(z) (Aa~ ~ )

f(-s)= (Q ~S~41J ) middot - Ji ~o~ 0

l~~ b (L ahbull ) WhUamp b=10 1a = (

CA b= A ~ Al~ shy bull J b - 4 ~ b~(~) ~ f not wiecC~

CordrNwt bull

ru G) Sce ~ ~ ct (lc( ~ s u~COftampCe ~ reg ~ tkt -f(e st L cf 4laquo (~S wifl b~ -tLe Cout4tf slset -ilofe-~ ltC is tLrCau1ablct ~tt j W X +b I wkctc ~J C ~ Q I

s Cotw S 7L lt Q S IR ~ C ~ ~ Cotamp ~~ 7 uW( -ft It

reg 1gtet~MtC2 f A- - r r )t E INJ rE (0 I I) ~ o~e -utMlA

B= rr ME J rE (OJ) f Q ~ OutdJe O~ Rot

i $o~tn fQ(cI~ M -= i I we sc~ I ( 0 ) r IT --E (0 ) ~ A I ~d~a b Co~~t~~ ~fsct teo

A iS UftcoufcJf4

I fi-EfN I let Sm -= Y~ r (0 () n Q 1 1kt (0) f Q ~ Q ~ (01)((2 co-tcJ~

t(O+W(t by(JJJ~

6 ~ U tyoJi S CotJ(e tyen rE (~Ia ~ fih c~~

~~ ~~

B U l)M s eotck ~ Ctl~JJ ~ )WEH ~ 1-1_ ~or

AMiJIamp

s~~tOA 1)c~lI(l f Q ~Q ~ L ~~ letf- f(~) ~e 1k (Ie ~ ~~ 3=~)(+ 11s S A lDj~t~fII wrtk f - SfMt5 ~-I wi e1-fGW ~ =MJCc t-cck T (~J ~Ac (Q)( Q lS o~-~ l ftoclu(t er t J

C04Mt-~ 1 L is Coll~+c b biec-t tNl~

LetAt A-= A=- bull = 10I 1 1 tke shyA x AI A s o~OUftc~fe

~t~ A~cApAA A1-A~Asmiddot $ CoWt~fale bull ~~ 3 ~jt~ f IN Ac~A)1J(

flt) (~ J Q Q - ) A~ a~i =0 0 ~ bull

f(z) (Aa~ ~ )

f(-s)= (Q ~S~41J ) middot - Ji ~o~ 0

l~~ b (L ahbull ) WhUamp b=10 1a = (

CA b= A ~ Al~ shy bull J b - 4 ~ b~(~) ~ f not wiecC~

CordrNwt bull

~ d~

j~~

7t

~ ~

~

rl1

~

bull

2

~

f

t

(I

~

r

V

~

~

-

rshy

t

t

-

III

0-

lt

A

u

V

poundI

1

s

-)

I

Vl

- --

~

J

~-

It- 0

bull ~

It ~

k )-

~

~

~ ~

-

~

gt

bull

cr-

A

rl

~0 ~

~ ~

-

~

-

~

I

l bull

~

bullbull

t -

$It

~~

~

x

i ~~

j

middot bullbull

01

0 bull

-

-

~

~

G

shy

- Il

c

3

~

0

+

$gt

J

to

II

~

s=

u

bull bull ~

~

st

~

(

Jil

t V

~

gt

d

-

pound

II

~

If

I

0

- -~ti

~

0t

~

-

)

~

shyt

s t

t

bull

-

II

til

shy-

~

~~

] -

bull ~

~~

lmiddot

1

0t

~

1

bull

bullIt

bull

-6

Q

bullbull

-

J -

~

-z

0

II)

V

middot -

--

---

~~---

--~ shy

---

---

---

--

-

-~--

shy~

--

-__

_shy

r

~

lt0 Is eetj (fll-e 41 yoot of $oe nOrCotsf-tt f~~amp( wrik i~erCOtfomiddotbullts r

ffj~fffA Let S be as if etitJe tz -rfI S~ US loisfill ~ oJIJ cc-~

hEtN +__ ~ofk CoCamp~t~~4

ff E S J 3 rlflN ~amp tAt f e S ~er te set Rf of 0(( r~ of f i~ f-+~ ~CAII i~ ~4S d 0$( 11 =(thY(l1l f) efIfIe-amp

11e -r U Rf iS COtJof t te fE-~ t (ttJJJ (c~~-tflGl

o~~I~-K_ ~ ~ VJ e-J(T~ ) - lt

IRst lRJy R)s kOIlt~~ r - f S he toIry

utCOf4+dJ~ cOtcfampit I

~fC2fotQ J 1Ae~ IS 4 1e~l tcfWb~r ~ i4 T gt~l A r~~lmiddotlI(kt is rota loot cf laquo1

rotCotsfod po~Ii( 1oI-tk jtt~jfr r1PcAfts (StAcA Go ~~ is ColaquoJ1-(4~SCe~ett~t~)

shy

C~t--+J(o(~) ~ t- ( ~ 7

-Jyen 2

-I I 2 3 0

euroJA sv~~~u j VtI4=middotO s Jo~ ~k So~~~~5v-rt

6 - ~ S ~ S~I0-- ~~ 4~4tAQll( J

w~cJ ~ 4t(SO i~v (j) At 1M$amp~ ) fuC~ ~It ltA ~ssit at ~iAf~C~ ~s~c ($f~~l tc ~-t ~

~~~-I middotAt ~~

l

reg ReMCtrllts 0 E)(4tf(es k CkGgttt( ~

CD Eer~ ~tttveJ 1 ~~~ et least ~o J-etS S t1tCD1ampViltbQ

~W ~j All Et W~ ctltb1iQtr (QIo)~ SaACe f (0 () -+(4~) A~ec( lPy

fcJ() (b-tl)X+4 has ietSre ~~ 1(4fb)~ (01 )

1()tj = C- Q

f is ~ ~jctmiddotcM b=Q ~ Stct (0 I I) is tt~o~+-J( hJ flCc-fe 1- ( 101 i~ cJMIo+~c- b b~-ecf~ teo~ -bull middot 1- s vto(oc-t~~ CorJJ~ ~ts~t ~6r

reg Wet ~re~t a Seco~c1 sJd~ -to f(4wr4t 1 Fo~ ee~j b) e Q J( Q I JlP

L(rtIl) be ~e set CsseJ of ~ Hi W~ ~t~ ~ 1)(1-

-d L U= LcM) l)fQ1C~e et~eWt ~t ~ ~ ft~ se~

~(Otlt~~~ ~ Co-t6Wtl 5t~ ctt_ J I ~ ~ ~QotEJ ~t ~t01 ttO(RIM1 - is CoC4ftbQ

SUo A ~ of COCt~ 4 Q~d tMJCI uwof~Y- Sets I r

~ 4 i

I ~Couyent~lt Sets

- Fi~r~ Sets ro ~ IIOIIJs IJIij j-tt~tsfNJI)(Q [NjtN

0~ble X u~bfe 5~~St$ +CP-tJk SJ-s rt~ a [I (]

~couo~ Sets shy( 0 l) I tR I Wte(~Js wL ~t (e~ 2 11(~eWS

([ tR 41 J

~(lN) 10 ~ fa l xol1 x middot

l1C)t~k )( NIQ~j b~ Stj~~

~ I

~

lt0 Is eetj (fll-e 41 yoot of $oe nOrCotsf-tt f~~amp( wrik i~erCOtfomiddotbullts r

ffj~fffA Let S be as if etitJe tz -rfI S~ US loisfill ~ oJIJ cc-~

hEtN +__ ~ofk CoCamp~t~~4

ff E S J 3 rlflN ~amp tAt f e S ~er te set Rf of 0(( r~ of f i~ f-+~ ~CAII i~ ~4S d 0$( 11 =(thY(l1l f) efIfIe-amp

11e -r U Rf iS COtJof t te fE-~ t (ttJJJ (c~~-tflGl

o~~I~-K_ ~ ~ VJ e-J(T~ ) - lt

IRst lRJy R)s kOIlt~~ r - f S he toIry

utCOf4+dJ~ cOtcfampit I

~fC2fotQ J 1Ae~ IS 4 1e~l tcfWb~r ~ i4 T gt~l A r~~lmiddotlI(kt is rota loot cf laquo1

rotCotsfod po~Ii( 1oI-tk jtt~jfr r1PcAfts (StAcA Go ~~ is ColaquoJ1-(4~SCe~ett~t~)

shy

C~t--+J(o(~) ~ t- ( ~ 7

-Jyen 2

-I I 2 3 0

euroJA sv~~~u j VtI4=middotO s Jo~ ~k So~~~~5v-rt

6 - ~ S ~ S~I0-- ~~ 4~4tAQll( J

w~cJ ~ 4t(SO i~v (j) At 1M$amp~ ) fuC~ ~It ltA ~ssit at ~iAf~C~ ~s~c ($f~~l tc ~-t ~

~~~-I middotAt ~~

l

reg ReMCtrllts 0 E)(4tf(es k CkGgttt( ~

CD Eer~ ~tttveJ 1 ~~~ et least ~o J-etS S t1tCD1ampViltbQ

~W ~j All Et W~ ctltb1iQtr (QIo)~ SaACe f (0 () -+(4~) A~ec( lPy

fcJ() (b-tl)X+4 has ietSre ~~ 1(4fb)~ (01 )

1()tj = C- Q

f is ~ ~jctmiddotcM b=Q ~ Stct (0 I I) is tt~o~+-J( hJ flCc-fe 1- ( 101 i~ cJMIo+~c- b b~-ecf~ teo~ -bull middot 1- s vto(oc-t~~ CorJJ~ ~ts~t ~6r

reg Wet ~re~t a Seco~c1 sJd~ -to f(4wr4t 1 Fo~ ee~j b) e Q J( Q I JlP

L(rtIl) be ~e set CsseJ of ~ Hi W~ ~t~ ~ 1)(1-

-d L U= LcM) l)fQ1C~e et~eWt ~t ~ ~ ft~ se~

~(Otlt~~~ ~ Co-t6Wtl 5t~ ctt_ J I ~ ~ ~QotEJ ~t ~t01 ttO(RIM1 - is CoC4ftbQ

SUo A ~ of COCt~ 4 Q~d tMJCI uwof~Y- Sets I r

~ 4 i

I ~Couyent~lt Sets

- Fi~r~ Sets ro ~ IIOIIJs IJIij j-tt~tsfNJI)(Q [NjtN

0~ble X u~bfe 5~~St$ +CP-tJk SJ-s rt~ a [I (]

~couo~ Sets shy( 0 l) I tR I Wte(~Js wL ~t (e~ 2 11(~eWS

([ tR 41 J

~(lN) 10 ~ fa l xol1 x middot

l1C)t~k )( NIQ~j b~ Stj~~

~ I

reg ReMCtrllts 0 E)(4tf(es k CkGgttt( ~

CD Eer~ ~tttveJ 1 ~~~ et least ~o J-etS S t1tCD1ampViltbQ

~W ~j All Et W~ ctltb1iQtr (QIo)~ SaACe f (0 () -+(4~) A~ec( lPy

fcJ() (b-tl)X+4 has ietSre ~~ 1(4fb)~ (01 )

1()tj = C- Q

f is ~ ~jctmiddotcM b=Q ~ Stct (0 I I) is tt~o~+-J( hJ flCc-fe 1- ( 101 i~ cJMIo+~c- b b~-ecf~ teo~ -bull middot 1- s vto(oc-t~~ CorJJ~ ~ts~t ~6r

reg Wet ~re~t a Seco~c1 sJd~ -to f(4wr4t 1 Fo~ ee~j b) e Q J( Q I JlP

L(rtIl) be ~e set CsseJ of ~ Hi W~ ~t~ ~ 1)(1-

-d L U= LcM) l)fQ1C~e et~eWt ~t ~ ~ ft~ se~

~(Otlt~~~ ~ Co-t6Wtl 5t~ ctt_ J I ~ ~ ~QotEJ ~t ~t01 ttO(RIM1 - is CoC4ftbQ

SUo A ~ of COCt~ 4 Q~d tMJCI uwof~Y- Sets I r

~ 4 i

I ~Couyent~lt Sets

- Fi~r~ Sets ro ~ IIOIIJs IJIij j-tt~tsfNJI)(Q [NjtN

0~ble X u~bfe 5~~St$ +CP-tJk SJ-s rt~ a [I (]

~couo~ Sets shy( 0 l) I tR I Wte(~Js wL ~t (e~ 2 11(~eWS

([ tR 41 J

~(lN) 10 ~ fa l xol1 x middot

l1C)t~k )( NIQ~j b~ Stj~~

~ I

(i) MjeJlrI~(~

Let f A B be iIIjt~I4 rf i3 5 CO~fALIc J

~eA s COt~Ic (CtOfosl~ ~f A i s u~COUM--ttk J ~~ ~ S ll~Cot~1 t J t~A~ Let - A~f(A) eJ~~J ~~)=fx~ Tie ~ is jfct1t (sce f $ ~i~middot)

A Cil -9 ~ ~laquotject (sI~ ~(A)= f(A)) ~ ~ bjectv-t Sca fQ) S B cac(

B is Co-~l ~ See fltA)s (olamp fit((~ middot A is (ot~b(-c --t b~ t~l S-ampJSe-t

~ b~ ~iJmiddotQct~~ -Hie0 i

~-S-tfdo-ct ~ Le 3 A (3 be svrp2ctve zf A lS (e4~1 I

~ 6 is (Of4Ilt (C+~1 if B s I uWco(CC ) 1ke A S LctccJ-~ltt) I

FC~ B ~(A)= U ~(tl5 ~ Ski- t~ ICE tJ 1 itot

J (o~-t~lc IS COIItbla ~fIte Co~ iCIO ~e(e

6jCcl~s_ Egt 1gte~AQ f Q -I) z~ IN b~

f(x= (M n) I wkete X= ~ (trlf~ EN) ~I -t4 tv4esf 1O~ ~e~ f 1 S f

0 3t4fbf (0 dltl-soY

1(lt) f(~)(~) ~ C ~ Ie I

- f i) ifct-v-t ~Ct ZxAl-$ (J~4 fshy

i ~~ f0(cod l0lc- ts cc6tL ~ fIa

i i~ject~ ~o~

j l LetA1 M ucu~JJ 0( A2~ ~ A be il

~ ~nobull -tj Se ts -de~ AI )t A)C )( A is ~

(JCot~bM

J t

gt04ffft ~eFtamp ~ AlC A1)( middotcAoo ~ AI ~ r

~(xt](~) Xoo ) =XI snCt A bullbullbull Aool~ 3 41E A - abullbull E Aroo ~e VxeA ~(~I aLl ~DO) = X So ~ S Sf4rjecfbull bull

SifCJt A s WCOl~1t I A- A1J bull J( A rs

UICAllfw ~~ ~~j~~ote

bullbull )

I

bullbull )

I