Al^ il"t cqna{ L r. k-t L = ( on tn I ^)03 -- {t , ol ,ooll,,oootll , A<t*fr t, onr"+^ a Dfl+ ' r7A ,] Solc: ' ,tlrr) ,rti,c ,,^/,* ,+,r-f"4' kt *l L*-I) (:(s "/+ 4u k1,f -[ t, l=90^i^ o-<ns.J W/.-r^ c ir e C.-,l(*{- n ./. ky* r {L't/"Lt fuTfi&,^lis da b-r J-,,t ,# lL re"stu (*'o|:"iro '*-,* fi* sl k^ J d>^ +/r- szz-e I o ii';, ff l 1. ?^ Tf* 7/' N a ,:i ;fl;4;Y.;irf no Ir rL s+€( "{ tL 7^4 op.t; , tL u7,? *,"/ is L,"1,, tL *ya fu, Of 6 LJ '*a'L '^) f,^fy i&< cre' tl, aL ,rrA't ir( B- N, ,ll^- rL *f * k./"tl A L€*ialrtc Tur,,.L o/r* C frr4) .r a I -tt7[ ^. f'l =( e , z, (, Si rlo , Bt f ), */*, o )a w2 A ;o&i,d xt 4 &4,. t is 4 fr",t sr( , ., lL ! rL ;^S,r( "/r/"L< c" lLt -/* ry ,/1,/,/-t *l5S f a"(, ir e $;'c f u/.( ,l^L,il. cq,- L f4 r^i +d O^f) C ,'&xfu &xt*{t,R} ;s tL e^*?"^'f".,L. r( ?L (*.," |t1,a)=(p, L, D) rtt O.,frJ ) 'Kt g ts f,. Ll"^L ,y*LJ ( B e 7, B 4 r. rc ce :r +L ,o: 1 1e,-{ 642) "{-Gr). t (t'o^"?'ft) 1" € & ir fL l,YA Gry/uJ <rt-,= 6% lrJ/,^ fu lyl is /.q s*t q .J a. C<<- d'{ ; '"J* kf' // *f a' l"f frG t ./-b is lu ' e, t/^f )*,1 ! .""o"/ 4t * "y!9 +L &f L,J b1*.2) cvz '*U ia Jru"?* D Qitl- (L) ft) r7'L,u-nl" fL an-t s+"7 oruyts 4 *f,i" st";1. f"J ,rt4 - tL ?t-j l,/-& o^J 0 Mo =l l*, e+1^ + d* ("',1lrr,; + L o"y,;,f,{ 0'//* tL Ty( A, L- ^"t fa^;t * J- , <L 7pr /"(t nJ ,T,G 4 ,^f( 1,r4. 7vl a' U 4 R'*"-" 7L a d,,nJ p1/e /.*p"*hfu, A ,nJ Ao.n4 onl tt, f"?,* n s a itY U k +L t*t { *'7 t/^t i? @ fu (,^f*f L "{ &r! ,<(, ro! /.lto. IJ L , d' 7'( wf e^, ,^f( sr *r^f iL ofl* ,C* A.^J, /.^! , ,/ 0^ C^ 4k ^' 4 eA '^fr wy,< *J hl+ - c{ l^y' f,{'**-, I / --/ 6xan7 t* r A L - {on ln l^roJ (t) lGf*b -,(./ 4, ffi,4 o *T/ d, rlt^"t l,dT M*B tD ,( tL f"y k*' O/B,R B // o/o,Q t/t/k B'r. -rrL 7U ,rr-{t o/o, L I/LL B/g,L Bf /grA \ @ LFd ,,ll^ -'4^&nL &-^U' /14 a J tt.,+l /", *",t {f"4 c,a,rt L e '+d. (t) tf tfu is to .<zx( (*-vtz-^ , nL 7/4 ;// *7-t onJ 6 L € t**R l*e to,/JY w Q i: il te utv*c t{'',*1 4r 1 Al uv=h, ryz ... -! , ,n/9 =)n --. H.N! = f r, oo,{1,60o0,ullo,.(oo(,IItl. .] hk*{ du'o,f^ (t) Lt.ok^[, ,,) .4, it (; o/B,L g/b,L a le,L f"a#ffi \ ol o,L U t //, L u o/o,k t/t,R g/e 6 L= t*#w lw e (r,rJT =t*,o#o, # l, oo $oo ., ol#'( ., l,#lor[/# ll, J { ct) t<*.{L, /*L,ron tL [fu*, or- s\'rrz lL ;mL ffi^.,( L,te- <ft +< 7.rt ,-d z'. P."-J ?L 6=r, tL frf'/C+ 1 tL (*,t y.,,t * B- 4y ,*,^J F"4 Ltt--* X c) L( rL &f c,tr, + R/{*l Xs ,a^t zM ",ktrr, --{L t^,1L,* bt& , x/k, (. orcb @ *rA\ \ {\ ,{)oht u.\), 0/o, L l/t,L tl+,L +t+< ''Od; r^;, " "a) o/o,p fJ ? l/ k/x,z r,R. D QPor') Xf x.L le,R \n /e'k @ &) f = { ** l- *{", tJ*l (l I I, / -' " l"(o, =f€,0o, (l,oooo// o(o(, 'l ' h(,.J'l-to'tn (t) fi^J d,r. nrlru* JI \ /,il1*t?-;:,o/ -pL L/t*,+ 6te '-Y/ rL A/L+ (a LoA, i ,,rt /,--,- I L t/'*) cnJ 1 * y % {"f*L-',1 'i/t t^ { -rL ^'+#t +L n,J,^t) "k dt' tr**'- ({-e* C/"9 o * X ( , v' & (S'"( 'y'- 4 (, y4^r[ [^rn,t) # {t rL "':JJL . M,::) *"* :*"/ L7"qv A -4 A rr*( ir.. d"- k,^J A( h ou!^- ,,,.< f lro ,,o#znt, .u* ,h,\4 "o. (4 { " 6r** d^ ltt tL A"( bd, ,nm ^atnq etfft^ ,4,*,+ l* -*tl b 7L ,{u*+ u#w or} y/, & ?a, tl L ,/ d. .l ,d.l^ "{ "A +ud,/ CSCtr 222 Horneu.ork 6 (Due Apr. 22) 1. \\'htit is the trutttber rif otrc-to-one func'tions / fiorn thc set U.2....,n) to the set {1.2. ..,n} so that there is at niost o1r().T ri,ith./(r:) :.r'l Givctr ir set ,S. iet /? be thc relatiotr definerl on the po\\cl set P(S) 1;r.AfiB nht:rrevcr A C B aricl A I B foy A. B C S. Pror,.c rvhethcr cir not fr is leflexivc. sr.mnrt,tric," arrtisl'nrrnetric' ol transitir.e. ,) .). 4. Givetr a firrite st't A u,ith rt elctnents. Iet fr lrc the rclation dcfined on the set of firnctions .f , A -+ A lr1' .f rirT u.heno'er the size of rangc {/(r,) | .r: € A} of / is the sanre as tlre siztr of ratrge {g(r) | .r: € Al o{ q. Plrive t}rat R is rrrr equivalenr.c leltition alcl :":,.":, ":,":::**:1,,,:::"" -l-;m,,fi l,r;f ,*',ru,, ). i u, t rrrtlitirrs t)00 l,rl rl,e. II.1 r'orrlirirr ll rrld 1 Jn *"4. !io1rr.* Givc arr itifoltttirl d"=rrd.lTo.ft"rnrirristic Trrrirrg nrat'irirre lirr the lariguagt-. I : thc f.'rn u,rr, but not of the fornr u,ri,n}. {, e@}ffif ll*" +^,1 ,( k/ Ar t,r ^! du -iy** . 6,,u ,r/.< 6t+*, e N,)( . o^ /v i,^(r^/ ^,4! ,{ cAV * Ot,^l Ftsctsr ' ! .*r/", t -/* r J, I o J d" ,-,^yL-''+ a\- AT Tfr*-f l hrLr,,-,-!*"Lra^ (),C-, L*rr"-')'*al,-t ts t, Ji*z^* P,/ ,G*- k 0 1 ol*t rnj" I ' ,/ C,alcq tc L Kr(t-* A /,u *.( ( z>.a>1 ,*7/,,.€! d.o fa ,("r {,,t1 -uH bbirt*, p@ 7, '2'7r'* *rtr-'k' / 2 R), 4. ln ,- J.'-- ]. 4 : o^f,'ynnir.!," /*{ * ,L,"t ^/, k(r- a-e,'J* *L( qt4 A, {fuiv"L,- c/"t*s. ,n l.u of/rA*,{&"fu [o,/ i1 q -r-t { .k( of C" 9s'?1-c fr-r- w? "L* /"^ oo"> * )tt y*l'* 1,,'rrr!_^((L (u,l lr/+*(^st6, 'ff.r'W1"r)^'fi*$h, dt v-Q /o* tllt'*"f^, rr4^/ .