Table Of ContentAU rillhtsfie r .cd No pad.o rt h'boo k maybe �produ�cedD,a ny rorma neyb�yt mnic
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or mechanimca,eanls (in.clupdhion�goco. pyrecoirdni&ng, ormr orma�iGDai storage ,and
'retrievl) 'Wjpe(rhm+o,iu o�:ni nw ntitDr8a tmb peu blisb.er.
Sell limum. Romabny k o'ra de TypescttiL�1 �H ODBK ong.P rinted abonundd En
theU llitSedl a�,esQ fAm�eca .
Lfbmry Of'COCaDtS tn:sosgi, ng.in-PubDatlai cation
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Contents
"In
I P'REUMJNARIFS
I, PsyeM,fogieal Approaches't oD educt"on 3
SomeE xampleos,f De du.ctiy,e Reaosning: 5
TheC entraloirtD yed uctivReea soning 10
MainT rendisn R easoningR esearch 14
Conclusio,anns,d P ros:pects 29
2 Reaso inagn Lodgi c 31
Formal Prnof 34
42
The:P laceo fL ogici na Theoryo fR easoning 5,8
3
Natuml ..Deducljo n Ru]es
SolvinPgr oblebmy ProvinTgh eor,em '94
4 MenialPr oofs, lidTh ejrP'ClrmalPro pert 10.3·
OverviewofthCco re'T heory 104
109
F orma:P�Jr ope rites 1230
S,nmm,8l)' 138,
Appendix: Proofs,o ft heM ajorP roposit:ions 139
5 'uenees 149
'some Test'S ,gfthe Proof Model ISO
'C,"'0' n'_,!J'.I.� �s. t'e'II'I" 'CI' 'W_Yi_ *U !lL.l�'O :n·,o.r F·lID',d ings• 171
Summary 1.83
1,8S
ExtenditnbgeC ore Sys:temt o 'Variables
For.mal Pr-operties 203
Appendix: proor'0s£ t heM ajorP roposi'tions 215
Preface
Suppossoem feu tuprsey cholaorgiaess tksedt oi nvesttihgmeae tnet al
faculotfai neesw ldyi scovered inltieffloelr iSmge.en tntott hpel anet
thatth ecsree atiunrheastb hipets ,y cholmoagiksoetb ss ervactoinodnusc,t
experimeandtmsi,n itsetsaetnrsdfi , n alcloym poasre ep orftot rh Jeo urnal
ofE xtraterrestIrnri eaaldi nPregsp yotcrhwthie,wos o luolpgdry o.ba bly
nobet tosou rprtiofis nedtd h atthc ere aturehsa vvei ssuyaslt deimffse rent
froomu rasn,dpe rhadpisff erepenrtce ptueaxlpe rieNnocersi .si ht artdo
imagitnhee csree atures hagvrienag(t oevsrram satlmlleyem ro)r cya pac
itByu.st u ppowseae r ael stoo ltdh atthc er eatreujreecsst i mpflaem,i liar
inferepnrcei nciinpf laevosofe r q uaslilmypb luett o o umri ndosb viously
incorprecrti nci.p les.
Tou se arthlainin ngtsu,i tsitvrealiyg htifnofrewraperrndice n ciisp le
thoen el ogicicaanmlslo dpuosn eAccnosr.d itnotg h pirsi nctihppelr eo,p
ositIiFos no -anTdH-EsNso u ch-aannddt- hsperu ocpho sSioti-oann d-so
1
joinetnltyta hipelr oposSiuticohn-u acnhFd.o-erxs ampflreot,mh per op
ositiIoFCn as ldveipno 5s0ci etnsTt HEsN C alwviilnl cgoekatned a
Calvin5 0dc eeponistftiso tl,ls to hwaCsta lwviilnl c ogkWeeetcan . awr ite
thiinst hfeo rsmh owinn( Iw)h,e ret hsee nteanbceosvt ehl ei anreec alled
premiasnedts h see ntebenlceo wt hlei tnhece o nclusion.
(lI)Cf a lvdienp os5i0cet nst Csa,l vwiingl elat c oke.
Calvdienp os5i0cet nst s.
Calvwiingl elat c oke.
Nows uppotsheao tu re xtraterhreasvteerx iaactlthslse ya mien ference
skitlahltws e d ob,u wti tohn iem poretxacenptt Tihoenrey.j ect maoldlu s
poneanrsg umesnutcashs,( Ia)n,da dopitn staec aodn traprryi ncwiep le
mighctam llo dsuhsm onFeronIms Fs: o -anTdH-EssNou ch-aanndd- such
So-antdh-ecsyo on,cl NuOdTes uch-anFodri- nssutcathnh.ceew, yo uld
satyh atthc eo ncluosf(i Ido)oens nf'otl lforwoi mtp sre misbeustt,ah tt he
concluosf(i 2do)oen s .
(2)I Cfa lvdienp os50i cetnst Csa,l vwiingl elat c oke.
Calvdienp os5i0cet nst s.
Calvwiinnl olgt e atc oke.
Thee xistoefcn rcee atwuhreoss y stemadteincmyao ldlupyso neannsd
accempotd ussh monweonusl bed e xtresmuerlpyr isinmgo-rmseuu crh
pristihnatgnh eex istoefcn rcee atwuhreods i ffferro umsi nb aspeircce p
tuaolrm emorayb itliieIsna. s itualtiitkoheni o sn ew,ew oulpdr obably
Preface
Vlll
be moraep tto b lamteh ter aantsilionnt Eon glfirsohwm h atelvaenr
guagtehc er eatsuperaetksh atnoa ccetphtie d etah atth esyi ncerbeely
lieivnme o dussh mon(eDnasv i1d9s7o0n; DennFertet1g 8e19 938/11;9 64;
Lea1r9 8Q2u;i n1e9 7c0h,a pt6)eI.rn deeodu,rr elucttaoan tcet ribute
exotiincf ereevnecetnsoe xotcirce atiusar nei sn terepsrtoipenrogtfo y u r
2
thoupgrocehsts es.Modus poanneodnt sh er inferenlcei ikpter inciples
are
sow eliln tegwriatttheh dre e sotfo utrh inkincegn-tsrtoao ol u nro tion
ofi ntellaingdre antcei onalitcyo-ntthrpaartri yn csieepmlo eusot f t he
questAisLo ena.(r 1 9p8.23 ,8 9p)u tist" ,W ec annbeogitn t om aksee nosfe
thpeo ssiobfisl oimteyow nheo sbeel ieare fusn influebynmod cedus ponens:
wec anngoetat n yh olodn w hahti tsh ougohrat cst ionsbe wloiukled. "
Deep-romootdeeodsft housguhctah st heasreie m porotbajnecto tfps s y
chologiicnalv estisgianttceih oemnya, y w eltlu mo utto p laayc rucial
organizing rolepe ofpolrbee l'isea fnscd o njecturess-oIo wil rl trtyoa rgue.
This bloeoaukdp st ot hceo nclutshiacoton gn itsicviee nsthiosutlsd
considdedeurc trievaes oansia nb ga sfiostr h inkTihnagit.si ,te xplores
thied ea-whIci actlhhl De e ductioHnyp-oStyh-settshteipa mrs inciples
sucahs m oduposn enasr ceen trtaolc ognitbeciaouns et ehyu nderlie
manoyt hceorg niatbiivleiP tairoetfts h.ce o ntoefnt thp irso posialst hat
thmee ntlailof fee vehruym aenm bodceiretsa diend uctpiroinn ciples
thatth epsreci inpalrepesa rotft hheu macno gnitairvceh itaencdnt outr e
justthp er opertoifpeoe psl es chooilnled o giTch.i asp proaalcsvhoi ews
deductasia onna logtooau g se neral-ppruorgproasmesm yisntgJe ums:t
asw ec auns aec omp utlearn gusaugcaehs B asoircP asctaokl ee pt rack
ofo urfi nanceosrt os olsvcei enotrie fincgi neerpirnogb lewmes ,
can
3
usdee ducrteiavseo tnoia ncgc ompalv iasrhi oefmt eyn taalc tiviItni es.
partiCwUewl iaslreel,h owd educatliloonuw sts oa nswqeure stfiroonms
informsattoiroinenm d e mortyop, l aanc titoono sb tagiona lasn,dt o
solcevret akiinn odfps r oblTehmeDes d.u ction-HSyypsottehmie nssec is
essavraiglauytet hpiosi bnutIt,h opet oc lariidtfu yr itnhcgeo urosfte h e
bookI.nt hmee antiimtme a,yh eltpot hionfkd eductsiyosnt eamss
simitloap rr oducstyisotnbe umitsn corpomroaretfl ienxgi bleo ff orms
reprnetsaetainodpnr ocess.
Goals
TheDe duction-HSyypsottehmie scs oinst rovbeortsihinc a olgn,i tsicvie
enceg eneraanldil nyt hpes ychoolfor geya soininnp ga rticSuolmaer .
Prerace IX
curreanptp roaicnch oegnsi tsicviee dneceaw li tdhed uctiinot nh e same
wayt hatth edye awli tmhu ndane cosgknisilutlciashvs t eha eb iltiott eyl l
timoena s tandcalrocdkA .cc orditnotg h easpep roadcehdeusc,it sia o n
similsapecrilayl itzaestdkh aitsu semfauiln floysr o lvpiunzzgl ienls o gic
orp rovtihnego rienmm ast hematics.
Therea rsee veproasls irbelaes foonsrsu ppostihnatgth Dee duction
SystHeymp othiefss ailsFs ier.ts htre,e suolfmt asn pys ycholeoxgpeircial
mentssh otwh astu bjecpetrsf'o rmaonntce a stkhsa etx pliccailftlol ry
deducitsio ofntq euni ptoeo Irfd.e ducwteiroaent rucelnyt rcaolgn itive
abiltihteoynn, ew oulsdu ppotsheape tr ofrmanwceo ulbed n earolpyt i
malS.e coonndem, ighth oltdh adte ducitsii onin te ss senntoid ailffse r
enftr oomt hperro blem-ascotlivvi(inetg.si goe.ls,v c ihnegos rsc rossword
puzzleasn)dc anbe explaaiccnoerdd tione gx actthlseya mper inciples.
Hencet,h emrea y nbeo re asotnos uppotshead ted ucthiaopsns ychologi
caplr imawciytr he specttoo thseurc tha sTkhsi.r tdh,ei rsaep ossibility
thadte ducitsni oostnu fficieflnetxlitybo pl reo vaire daes onabbalsfeio sr
highceorgn itDieodnu.c toipeorna tbeyas d dicnogn cludseiroinfvsre odm
statperedm isaesis n,( Ia)b oev.H owevmeurc,oh f o utrh inkiinnvgo lves
retracbetliinetgfh saw te n ows uspecatr ee rroneaonudds e,d uction
proviudswe ist nho o bviowuasyt od ot ha(tal te aosutt,s oifds epe cial
deducftoirosmnus c ahsr eduadc abtsiuor -dsueemc hapter 2).
Therea res omseh oarnts wersc ouogilnvdee t ot heosbej ectFioorn s.
exampolneec, o uplodi onuttt h aatl,t hopeuogphld eoh avter ouwbilteh
certaino frs eoarstosn ing prdoobpe lrefmecstw,le ylwt lih toehty h etrhse;i r
accuraocnty h lea trtievrta hlesai ccru raocnya lmoasntyc ognittiavsek .
Onec ouallds moe ntitohnam ta ncyo gnitsicviee ntists-sionmcel uding
whot hitnhka dted uctiiosnn o thisnpegc ial-ptraokdeu cstyisotne ms
extresmeerliyo ausas b lays fioscr o gnitpirvoec esYseittnh ge.ss yes tems
operaotnep rinctihpalltoe ossk u spicliiomkuoesd luys poHnoewnesva.e r,
trucloyn vindceifnegon fts heDe e ductionH-ySpyosttheeemns tiassie lts
tinogut th dee taoifsl usca ht heoarnydd emonstrtahtaiitstn u gc cessfully
predimcetnst saulc ceasnsdfe asi lounra re asn ogfce ognittiavseDk esv.e l
opianngdt estsiuncaghp sycholtohgiecaoilrts yh m ea igno aolft hbioso k.
GeneraPll aonft heC hapters
Althotuhghse t uodfyre asonhianasgl onhgi stioner xype rimepnstyal
cholo(segeyW oodwor1t9h3 8, c3h0a)ip,tct soe nrt ribtuoct oignoint ive
x Prerace
theohraybes e ns ligbehcta,u rsees earhcahvteeer nsd teofd oc uosn v ery
specialidzeedd ucttaiso.Okn ns lwyi thtihnle a fsetyw e ahrasv ceo gnitive
psycholcoogimsuetp ws i tmho detlhsaa trea blteod escrmiobert eh aan
trivsimaalsllelyot fi nfereMnycefi sr.sc th apetxearm itnehsle i mitations
oft raditaipopnraola acnhdpe osi nttoss o mdee sifgne atufreomsro re
adequmaotdee ls.
A kecyo nceopftt hteh eodreyv eloipentd h ibso oikst hneo tioofan
mentparlo oAf.c cordtiotn hgia sp proaac pehr,s ofna cedw itah t ask
involdveidnugc attitoenm tpocat rrys iotu tth roaus gehr oifes st etphsa t
takhei mo rh efrr oamni nitdieaslc riopftt hipeor no blteoim ts so lution.
Thesien termedsitaeatpreesl icensbeymd e ntianlf erernucel seusc,ah s
modupso nenwsh,o soeu tput fipeonpdil net uiotbivvieolTuyhs ere. s ult
insgt ructthuurpser oviad ceosn ceptburaildbe gtew eent hper oblem's
"givenasn"di tsso lutOifco onu.r mseen,t parlo oafnsdm entianlf erence
rulaersse u ppotsobee ds imiilnia mrp orrteasnpecttt osp rooafnsdr ules
inl ogiacn dm athematics.2 a Cnhd3a d petscerritsbeh leo gicbaalc k
grouonfdt hecsoen cepatnsdo utltihnere o lteh ehya vpel ayiednc om
puttehre orpermo viAnlgo.nt ghw ea yI,a lstort yod istinpgruoipesrht ies
ofl ogicsayls ttehmasmt a yh avpes ycholreolgiecvaalfn rceo pmr operties
thahta vmeo rteod ow itehl egaonrece ffi cieCnhcayp.t3 ae lrs doe velops
thied etah awtec anu smee ntparolo fnso,ot nltyod eritvhee oreimns
formmaalt hemabtuitc sta,ols soolm voere generoafpl r osbolretmss .
Mya pprotaoct hhp er obloefdm ed uctrievaes oinsti oncg o nstar uct
theoirnty h feo romfa c ompustiemru latthiamotin m itchsae b iloifta i es
persownh oh ahsa dn os pecitarla iinnif nogr mlaolgi cmaelt hoAdlso.n g
thelsien cehsa,p 4td eersc riabem so detlh aitsa blteog eneramteen tal
prooffopsrr obliensm esn ternetaisaol(n ii.fneogi.r n, f erewnhceoss ceo r
rectnesdse pendosn s entence cosnuncecahts iI vF,eA sN D, OaRn,d
NOT)a,n dc hap5te exra misneosm eex pemreinttaels otfts h imso del.
Thec omplmeotdeea llo sh andrleeass owniitnqhgu antivfiaedr iaabsl es,
chapt6ea rnsd7s how.
Likael clo mpumtoedre tlhsi,os n ec ontaliontossfs peciafiscs ump
tions-mtaonoty o t eisnta s inegxlpeer imFeontrt h.are ta socnh,a pters
4-7d escrai vbea rioefts yt udtiheahsti ghldiigffhetrea nstpec tosf t he
theoSroym.oe ft heesmep ltohyte ra ditimoentaholof da skisnugb jtecot s
evalutahtleeo gi cal coorfrs ectinmepaslrseg ume(nptrse mise-conclusion
pairbsu)it,n o thetrhsseu bjaecreta ss ktedo r ecatlhlle i neosfa p rooorf
tod ecid(ew hitlheea yre beitnigm edw)h etthheleri nefso llowe afrrloime r
Prerace xi
oneIsns. tille xopetrhiemres nutbsj,aec reta ss ktedo t hink aastl hoeuyd
trtyos oldveed ucptuizoznl es.
Thel asfto ucrh aptdeerawsli tihm plicaotfti homeno sd eClh.a pt8e r
poinotusst o moef t hper omiosfae s deducticoongn-ibtatishveeedo ry,
applytihnmego detloa n umbeorf w ell-kcnoognwint tiavseik nsc,l uding
categoriaznadmt eimoonrse ya rcIhta. l sdoi scutshsreee sl atoifto hne
modetlosc hemtah eornioensm,o notloongiicacsn ,dt rumtahi ntenance.
Asi fth etsoep iwcse renc'otn troveenrosuighma,ol s otf t hree sotft he
boodke awlist rhi vtahle oirnit ehpses ychoolfro egays oning itself. Some
oft heaslet ernavtiievgweosa lownigt thh ied eoafi nferernucel aensd
proboufqt u arrelt hpweai rtthi rcuulloearpsr r osotfr attehgiaeItas m
advocaItd ienscgr.is beo moef t heaslet ernaitnic vheasp 9t,eb ru tm y
tendeinstc oty r tyoa ccommodatthee se ivnti hecewu sr refnrta mework
rathetrh atno t rtyo d iscrimaimnoanttghe e emx perimenOttahlelry .
alternattihvoeusghe,,x plidceinttylh yne ee df orru laensdp rooafnsd
attetmosp utb stpistyuctheo lvoegircsaoilfoE nuslc eirr cledsi,a gVreanmns ,
truttahb loerss i,m idliaarg rmaemt ho(dsesEe r ick1s9o7an4n dJ ohnson
Laiarndd B yrne1 991C)h.a pt1e0ir sa c ritoifqt uheip so sitFiionna.l ly,
chapIteIdr e awlist sho mgee neorbajlect iotnods ed uctionc-obgnaised
titvhee oarnidte rsi teoss u mmartizeh essyes tesmuscce's saensdl imits.
Ofc ourtsheis,se lectoifto onp idcoess nc'otv aelrtl h otshea mti ghbet
treatiedna w orokn re asonionreg v,ei nno neo nd eductreiavseo niAn g.
majoorm issiisaos ny stemtaretaitcmo efnre ts earocnch h ilddreenv'esl
opmeonftre asonsiknigTl hlesl .i teraitntu hrieas re ai sv asets,pe cially
whePni agesttiuadnai reiesn cluidnedd;ee Pdi,a gelto'giiscsi tstehlef
tarogfes te vemroanlo grapihnsc,l uOdsihnegr 1s9o7n4a an dS eltamnadn
Seltm1a9n8B 5e.c amuysf ea miliwairtdihet vye lopmiesnstiuassel ls i Im ,
stimcaki ntloya durleta sonIim negn.t ifionnd infgrsot mh dee velop
mentalli terwahteutnrh eebe ya ro nt hmea ipnr oblbeummtsy ,c overage
oftheimns a rrFoowr.t unBatrealiaynen, dR umai(n1'9s8re 3v)i eowfl ogi
carle asoinnci hnigl ddrisceuns tsheaisrs e frao ma p oionfvt i eswi mitloa r
thoen dee velionpedt hecshea pters.
What'sN ew?
Chapt1e-3ra sr ien tenidnped a rth etlaopd vanueendd ergraodru ates
gradusattued einntt hsce o gnitsicviee unncedse rsrteceanntrd e seaornc h
Prerace
Xli
deductainodtn h,es yee mt oh avweo rkfeiadr wleyl ilnt hcel aswsheesr e
I'avued ititohneePmda. r Ita lso codnitsaciunstshs aitoh nosIpe w ilbel
ofi nteestrto e xperitnst hiasr eba,u Ite xpectt heesxepe rttosf o cuosn
thlea tswtpo a trsp-articounl atmrhalety e rtihaahlta sna'ptpe areelds e
wherHee.ri esa b rigeufi fdoret hem to whTahtet' hse oonrfesy we :n ten
tiraelsa oniinncg h ap4te irsa rfienemeonfat n e arlpireorp o(sRailp s
1983b)u,it t al scoo ntasionmsne e wr eusltosn tchoem pletoeftn heses
theowriytr he specttoc lasssietcnenatlil aolgiL ci.k ewcihsaep,5t r epero rts
somree tacion-dtaittmahe a hta veanp'peta rperdve ioubsulatyl ,s sou m
marizae fwse oldeexrpe rimeonntt hsse e tnentmioadle Iln.a ddition,
chap5ta eprp ltihemeso deflort hfier stti mteos omwee ll-krneouswlnt s
onr esaoniwnigt h neagnadtc iovniedtnsia olTsh.e thfeoro rqyu antified
variaabnldte hsse u pporetxipenrgi mienntc sh apt6e ras7n a dr e entirely
newS.o f,or t hmeo spta rt,t heaexr tee nsiocnosm paanrdii snpo anrIstI I.
Expermtasy be especiianlrtleetysed i nt hues oef tdheduec ttihoeno troy
handplreo blseoml vincga taengadot riiiozncn h ap8ta enrdi nt hdei scus
sioonfp ragmatscihce mas Daanrdw inailoagrni tihnmCs h apt9e.Tr h e
commenotnms en tal moddreaolwns e arlier( Rpia1ppe9sr8 s16 9,90 b)
buatr e updtaott eadki en taocco unsto mlea tdeervl eopments.
Thefi eldd eodfu crteioavnsei inscg u rremnitnledwy i tcho ntroversies.
Althougmha ktehtsih fisee lmdo rien teannsdie n teretshtaiintnh ga d
beeni nt hlea sfwet decadeista, l smoa keisth artdo i ssfiunea jldu g
mentIsh .o peh,o wevtehra,t pe rtshpecet iIvd ee vehleorpie s s taa bolnee ,
andt haitt willh eplpufrlto oov teh eirnds i scrimipnraotgrifenorsgms
polemics.
Acknowledgments
Ih avaecc umulastoe dm ainnyt elldecetbuitansl wrtihtiisn gtb hoaotk
its eemsn oc oincitdheanitcete ndisn c hapt1e1Mr.y mositm medi
atceedr itoarrsDe e niCsuem minJso,n atEhvaann Lse,o Gnr osPsh,i lip
Johnson-MLaatiKtru dr,b Jaoth,Mn a cnamaJrea,ff Schanskev,e raanld
anonymroveuise wwehros dtihdeibe rs tt og emte t oi mprovtehc eh ap
terJse.aff l shoe lpewdi tsho moef t heex perimerpenotrst hede raesd, id
RutBho neFhr,ed ConDraavdiC,do rtnJeirLa,i S ,a ndMraar cuasn,d
othersc.o nFvaoetrri soanbso upsty cholaongidlc oagilc maalt teItr hsa,n k
especiaClhlryi stoCphheemirAa lkl,a n CDeodlrleGi ennst,n Weirl,l iam
Prerace xiii
HarpeRre,i Hda stDiaev,iI ds rael,M aDlaavmieRdno tnM, cC lamrock,
Ed SmitRho,g eTro urangaenadmu a,n oyt hearts Utnhiev erosfCi htiy
cagSot,a onrfdU niverMsIiTta,yn ,dt hUeni versoifAt rizyo naT.h anks
alstooO lviiPaa rkfeorr permistsoui sotenh j ea ckpehto taon dt oJ iLai
forh elwpi tthh ien dex.
Iu seddr tasoff c hapt1e-ri1snc 0 l asastCe hsi cagoc,o mamnedfn ortms
thset udeanrert sesp onsfiorbm laen cyh angFeosar.c tumaoln etsaurpy
porIt' gmr atfeorfN uIlM Hg raMnHt3 963a3n dfor Caa ttFeoluln dation
flelowshiepn atbhmlaeedtt os penads abbayteicaaartl Sftoradwn orking
ont hpirsjo ect.
Ia lsfoeel daee p dteoba nt u mbeorf t eachwehrohs a veem bodfiored
mei,n d ieffrewnaty tsh,e iodfre iaglaosnr dc lariintt hyi nkTihneghy.a ve
beena ni nspiriantt hieo nr easnedwa rricthti hnogu,tg hhbi oso cekr tainly
flalfsra s hoorftw hatth ewyo ulldi kBeu.tm ,o riem porttahnehtya, v e
convinmceedt h actl araintdry i gaorrwe hatth set uodfyre asoniinsg
reaalbloy urta,t htehrat nh dee taoifcl ast egosryilclaolgio srm stf ouhre
carpdr oblIetgm oe.s w ithsoauyti tnhgao tu tr hinkiisnnag'l tw acylse ar
orr igorbouustsp ;o riacdailtl yai nsdi, ti 'msp orttaotn rttyo u nderstand
howt hiisps o ssible.
Finawlhliyl,e atatn"e anudtishn'bgo r reaaksftf"or msye ven-year-old
daughatnedhr e crl assmaaf twee mso ntahgso I,r ealizetdh aItw ast he
only meomfmbe yri mmedifamaitlew yh o watshne' ta uotfah b ooroA ks.
byf ra mbyi ggest credibeteno rrsme,a rtkhahebeyll'yupv lafe n dr meark
ablpya tiwehnliteI 'vbeee nt ryitnocg a tucphw itthh em.
