4
1 ; ilIAIt :3200.- IN 1«0 D 70 Iff) V f'! nTH FLo/ZI/))t IN r 'L ON/I/. IltTES T #/- Fall ;2tJ°4' TiNE.' 76" MIN. Ir; : . : . . . !: . fJ-nSt,1)er all 0 qtU?:;!/OJ1.S, fin unius/flled an~wer will receive m p- J j~ Ifllie t:Jr 7'7Dcredil. 671/11 each 'lut?s/Iun on a so/arate. f?cye. it H. [ . (Is) ;: ~~7Y-a}1jlale Itze lo/kwif1J ct1Jurnent IntO:>ymboltc ll;yudfe Cf/zv! !~dzei1 use a Iru/i la6/e 10 dmrm/ne I-I if is t/aIt d. £1I'ter AmI !~ eJr 806 /s Iyln,!. C//!,t?r- BIJ6 tJr Ui!J, / /5' 11tJt Iy/'!f' ,.~,;I t~ LaIty /5 IY in:J J tic e i1 ;I Y11 Y /s a /s 0 IY /r1j' , l H~ (IS) 2(~ Skou) that ! (lc7(;~A) (3 b~A) [ILer); /(b) 1\ ai b] is IOJi.- ,I .lea/I! e7u;//a/et~f ~ (f4~fI){tl6fA) [i{a)=-l(6).~ cl=6] , fA) Lei I: fl( -(:z1-? IR I{;<) = 3X > / sI inJecl/v£: ? ! I X-2 J ! .... (/5) 3 (~Let :J /;.e a lClIn/1y tJ! sets, ])eHl1e .what /s U.J G~jJS't-rIDs e A ft B and A - C C B. j)oes;f h l/ouJ thai J An C =/: r,i? (Give a /7TtJtl or $/lle a C:6u.Pller--bXt:II~rkJ. i .!. (/5) .4 (~Le/; R. 6e a rela /;/OJ'1 ~1 /-1- 10 e C( /1 d S be a re/al/OJ1;d m j. B 10 C, De h'rte w ha fare !( -t. and S fJ R. (fJ.~t I: /l( ~ 1'33 ~ If( -{;l] J I (X) =: ;ZX f- (. h'ne! (-I (X) . I' .U X-3 ii, . . , (;LO) Sl~1Jej;-'tJeWhaf-h an €lu/vaknce relaf/oYl on fl. l€.f ae-II. ;H IJe.h'l'2e what ls t/"'e etLA.ivaknce class @J. (~J Let R be It-£ re!c;c.li~/n on 2 dt?f;-necl hy a I.?6 if a~62. J is a .mu/llj/e CJf G. PrtJvc tho-I R /s an t?fu/t/a/I?NCe re/a-h'on .L 0 YL 2:. and h'nd Ite etui'/a!etrl('~ c /as'ses; 0/ J< . ( ) T?-D) ~(~O Jj.e/tne what /s; a h-lnc!t'tJrl (;z;m A !o B, ~) Ii f:,/I-'3>B cu,.!, 3: 8.7C are!Z..u;!le;lS/ /Jrove jj"d i;! 9 c> f IS Ct .1l4 nct 10M .-{ TOV'Y1 A 1-0 C. Hi 'i!

(fJ.~tfaculty.fiu.edu/~ramsamuj/intro_analysis/FA_04_T1.pdf · 1 II!' I i:1"!:'1 P-JAA 320 - IIVTI(O TtJ I?l>V iV/4TH 'j. j 'jS;r)LI/T/ON5 TO TEST#- I 11,I I, ~1Jn ll~tl) Let Ii-:::

  • Upload
    others

  • View
    5

  • Download
    0

Embed Size (px)

Citation preview

1

;ilIAIt :3200.- IN 1«0 D 70 Iff) V f'! nTH FLo/ZI/))t IN r 'L ON/I/.IltTES T #/- Fall ;2tJ°4' TiNE.' 76" MIN.Ir;:

.

:

.

.

.!:

.fJ-nSt,1)er all 0 qtU?:;!/OJ1.S, fin unius/flled an~wer will receivem p- J

j~ Ifllie t:Jr 7'7Dcredil. 671/11 each 'lut?s/Iun on a so/arate. f?cye.itH.

[ .

(Is) ;: ~~7Y-a}1jlaleItze lo/kwif1J ct1Jurnent IntO:>ymboltc ll;yudfeCf/zv!

!~dzei1 use a Iru/i la6/e 10 dmrm/ne I-I if is t/aItd. £1I'ter AmI

!~ eJr 806 /s Iyln,!. C//!,t?r- BIJ6 tJr Ui!J,/ /5' 11tJt Iy/'!f' ,.~,;I

t~LaIty /5 IYin:J J tic e i1 ;I Y11Y /s a /s 0 IY/r1j' ,l

H~

(IS) 2(~ Skou) that ! (lc7(;~A) (3 b~A) [ILer); /(b) 1\ a i b] is IOJi.-, I

.lea/I! e7u;//a/et~f ~ (f4~fI){tl6fA) [i{a)=-l(6).~ cl=6] ,

fA) Lei I: fl( -(:z1-? IR I{;<) = 3X > /s I inJecl/v£: ?! I X-2 J!....

(/5) 3 (~Let :J /;.e a lClIn/1y tJ! sets, ])eHl1e .what /s U.J

G~jJS't-rIDs e A ft B and A - C C B. j)oes;f h l/ouJ thaiJ An C =/: r,i? (Give a /7TtJtl or $/lle a C:6u.Pller--bXt:II~rkJ.i

.! .

(/5) . 4 (~Le/; R. 6 e a rela /;/OJ'1~1 /-1- 10 e C(/1d S be a re/al/OJ1;dm

j. B 10 C, De h'rte wha fare !( -t. and S fJ R .

(fJ.~t I: /l( ~ 1'33 ~ If( -{;l] J I (X) =: ;ZX f- (. h'ne! (-I (X) .I'

.U X - 3ii, . . ,

(;LO) Sl~1Jej;-'tJeWhaf-han €lu/vaknce relaf/oYl on fl. l€.f ae-II.

;H IJe.h'l'2e what ls t/"'e etLA.ivaknce class @J.

(~J Let R be It-£ re!c;c.li~/n on 2 dt?f;-necl hy a I.?6 if a~62.

J is a .mu/llj/e CJf G. PrtJvc tho-I R /s an t?fu/t/a/I?NCe re/a-h'on

.L 0 YL 2:. and h'nd Ite etui'/a!etrl('~ c /as'ses; 0/ J< .

( )

T?-D) ~(~O Jj.e/tne what /s; a h-lnc!t'tJrl (;z;m A !o B,

~) Ii f:,/I-'3>B cu,.!, 3: 8.7C are!Z..u;!le;lS/ /Jrove jj"di;! 9 c>f IS Ct .1l4 nct 10M .-{TOV'Y1A 1-0 C.Hi'i!

1

II!'

I

i:1"

!

:'1 P-JAA 320 () - IIVTI(O TtJ I?l>V iV/4TH'j . "._,j

'jS;r)LI/T/ON5 TO TEST#- I11,II,

~1Jn

ll~tl) Let Ii-::: JI~I/ /'5 IYiH 7' /! 1i /"

~H (It 1/ B) A ((8 V , C)!!!!!p

~nb )HI

iIi!It:H'I 'Iit~ill:!

t'

!;i .9," '

n:ili

FLo/ZID/f /lVT'L l/ /III tI.

20011-F II-Lt

B = {5c)b is /yIJ/ C~ ca/t(/ /sly/;'l

{ . ((''-7 A ')

A f3 ~ (-"7~.._:._~,L_.,.~_, (C~;:Y)I '

F F 'T I TT T

T T

T CI

T rr

ii,F T

t

, '

HIi:iiii'~;n'ii

, P' j:: F! I;;::: Fill ' .~;, ':II

H. 5~V1c-e (!~\lr3)f\ (iI3V7C) -7 (C~A) is 0'I'

~ !

,

'

,

C{ YtJ

- lA t/l/l. ~ i'1.1 / S i-/ct //,:1.Hi /;j,illH

2, Uo -? C3aGII)(3bEA-) [I(cl):= I{k) II cr ~6 J

! I; !/1 (11a coA) '(3 b6 A) C I (cr) ~ / (}) It a =Ib JIII tfl (tlaeA) (li 6eA) ,[ 1(0) ~ I{}) " llt-h)Hil/I (l!. aEA)/lIb~A) [ ((d)://{i) v 0=6 JI, - l

,ll!l/ (Vaell) (f/bEA) [ICa)= I[j)~ a=6J'I

i',

'

,Ii

d¥)i' "

I

~!J

Ii,'

il

IU

I

iiIIII

;1I.II

III

i- T 'J

/F Tff

F- T {.'F F '(

T

(

S'I/:Jo,re lea)::: I{i) , n~lI .3 C{a-2

:3a [' b --2):= 3/:; (a -z) L ~ U

{f. 6a= 6t 5:0 C1.=--b.

c:::{Vt /';/1; e c 1/ ve ~ t/I L {/oY] .

T ( -r"T

ITI

T T

T i F

I! T.- I F/ '

i

T i I

1~~>Glt/0; Y} ~

by ll-lav///hpr 11;}. /Cl«"J" II II

b/ /)e ~ (fCin s laH.-'

jee -r?vQx P-l Q .

::= 3b -)'0b-2

'3 a b - {; a:: 3 <-lb -{, J;

lbuC€ I 0

c (A vB)-T f T

\r: I T

)T TI

I

!

r: ! Ti'T

IT

T T" .....-

II I

T T

('rr

nif:;.. ,.

,..

'h/I Z.4.~)I (-[f

c!:d

,j,,

."

.$"0 Xc € A VIt/lci XL' e C . /. X'a ~ A./iC.

Th{;{S' A /1C ~ ~ ,

.*.

-( t' . /. 1.R :::- i<b/ a ~ ; (a (b ') & R J

S t) R =- f(Of / C ) ~ (3 b € B ) (4 / h>6 e and (J; / L) (;; S) J

Let y;::: l~(;x:). They[ //'1) ~ x, So

S'o 2 Y+ifj- 3

:::: X 2Yf-/ :::: X!j'- 3/

3X'rl = 3X+/:::- .iJ(X~2-)" - /

I (x):::- '3 X +-1X"-2--

-XY-Zij

Y= ;:Xi-{X-2

AtIl eft.{ I'va Ie'u.t:'e re lex /'0)1 O?1 If is 4 /l)/ relc-l. i'or? O.v1 A

,:J/~/ct. /:;' 7e/~/ve/ sYV1-'tf'1'7£ tri'C Ctt/7d Irc:rYJs>.II'v~.

[a] = {x t!;1- ~ xR~} == fzr=lI.' (x,a)cR)

,.;

z. Z. 1 ) R /' - .a - a ;::: 0 = ~ cD, ,/" a a ,-j717 t:acJ... czc:;P

SUlfoJ:e a R.6. 7l~ a2.- b z.::: 6 k ftr' S(;7Y~ '~Z.5 /2... '2- .. ' .' .

)L R /1.

0 I:J- ~ .= - b k: ~ G"(-k < " . 0 Cl, !K--1AC)?

ft;y anI' tl/6 (;£ a RJ; '-7 6£ cL

F (t't C{! ( '1 S' L-1l/o Se c;? R" c:,:t-u:l b I?c - 7I-u'--- tl ~ b L=. C;):..

.aPt" b~ cL ~ ll! j;y &ome k/! ~Z, 'TluA j'

t2 2.- C e.. .:=- 0 2.--62) ,,'-(f ~c ~:::- r;; (1:1-1 ) '. ,.'. ~L Rc .5'd .f;r ~ IA/ ~ t b"C c: d! cJ£R6 /l 6Rc ..'-:";>Ct£Ie .

.IiJj1j

IIJ

~'p /k.r.-"C£';( IS re/~/r/e (57M1t'Yl~I.JIC ?Jtu/ !rz<I/}s/I>r/e.

j 7h.e e1&l;- {/ t?'l~ c:-Ia .sse~' cf IJ R a---e! {jJ] = r-, " . --6 0 G 12 .,. - ']I (~ / J t' ,- .Ii 0 J = >... .-5" -I I f/- 7 Ii - _. 7I L' ) I ) I I I } .)

I [2 J ~ f.., - ft - 2 t 2, if I 8, /0/ q ,]1 [ 3 ] f' C1 / .-")I . :=:: -- ~ -"3 0 / ."3 ( 5 ." \

I / / I J I

6" 1141. Ii IZ-<. Vl c l.''a 1"1 hht A f-c:) 13 is any 7' e./ a h'0 11 F ~Y}'1. A-Id 1.$j: / --I/,.ft- /t.J /1"\ /7 I .. D \ I /-

> F \! 5 u C?t. (heLl CV de t1) '-..:7: EO-D..-J l<"t.( I E ./.

5"

i" ';'

l'r 5'LA1;f?() s e I: /+,~ B CCfn / r.J ~ B -7 C cZr1'C?-!it i/l C I.C//7 S' ,

I, .cxis/~t~e.: 4I a e Ii f/te,'1 /vLf /;;:= /td) ClIYJcIIi

I J c =- : (t) . 5'u'7 c' € (CI r h)~' I a 1'1cl (/7/c > ~;' ~ t I11j;I!cJt,v s IhJ <:Ci / c.) ~ q 0 /), 5c; (IIO~ 1I)@[EC)('Cjt.e)' ~ /Jqe( .)II (1. C

II

Ii lIfli'l'ct'tlt'SS'.. S''1'/CJse <a, Of'> a"c!Cc:t/c2) 6 :lei, ~

)1 '3.b; I h2 6 13 StA[h Ilv:J (Ci,,6() E I C/I'ld i~/ Ci) ~ ;'

II 0< IAof <a, b2 > <'- I anel (~J c~'" ? . SIt/lce / 0 C<ji ) . z. I .' III ,fitv1~t())/I. an~ (:!~.bf) Clnd (C/l ;'2.) ~ I -7 I ,hl/clw:; ~Cf

II b; ~ 17",. S D <:j, / lei,> 0< n cI (6/, '2 > t" j . S I'" Ce ,J /rI! a ~nc.l;on ,.-f .h//ok/.r thAi c;. = Cz . ~ce11

( ) ( ) ( ),/" .

II Va6A g!uC (<1, c) '" :J ~I . . ;J,lu. '"' 'h:mcl/ur}In fn;vn A fo C r. II

IIIi

lilT. ;(11 Assw me A- 'f;B alA.! A- C C;; 13. S''I1'°se j/./J(' , i6. lei tI GII.

e' III T~ a rf ( P~C4Uf<' I//iC. 56 tU Ii - C :i'nOl Il-C c :I d;;' //<fW< Ii cd ~ e S . 8,J" t-v?d CHb,l,'dry ,'. /I s:: 1:5

II tm,drCAdnllM y f/ '" (3. ~ !i/iC # f5 .III

(