Evaluacion Corte I - Parte 2. 20%. Calculo Proposicional.

 

 

CPAHSAFLBK FB]UC L ‖ _A]UC =. FAHFSHB _]B_BVLFLBKAH. =?%

1.- Lkelquc fuáh ec has sldulcktcs cxprcslbkcs sbk _rbpbslflbkcs, ck fasb ec scrhb lkelquc

su Pahbr Kugìrlfb. a) : cs uk kþgc kþgcrb rb.. m) Pckczucha Pckczucha cs uka Kaflök. Kaflök. f) e) c) ) d)

Pahbr Pahbr _brfcktua _brfcktuah> h> 6%

Elfjbs Elfjbsb b ch ch ármb ármbhh quc quc `brca. `brca. Cs ahs ahsb b qu quc c = + = 7 5. Muc uck kbs eç eça as. Ch mur murök ök cs ga gagç gçc crb. rb. x+y7x

=.- a) Lkelfar fuáh fuáh ec has sldulcktcs sldulcktcs brguhas rcprcscktak ha prbpbslflök eaea> eaea>   ‘Hhcdara ck ch trck ec has :>13 b ck ch ec has 13, sl hhcda ck ch prlgcrb, cktbkfcs   tckerá cgpb para vlsltarkbs‗. 1- ¬p --; q v r =- p v q ---; ;r 6- ( p --; --; q ) ( p r) 5- p v ¬ q ---; ;r 3- ( p v q ) ( p --; --; r )

         

m) Fuah ec has sldulcktcs prbpbslflbkcs ckck ha brga> (p q) --; r2 1- Vl kb vas a ha csta, cktbkfcs Garça, quc ya cstá prcparaea sc ckaeara fbkdb. =- Jakech cs uk drak fbgpbsltbr y Plvahel tagmlìk. 6- Vl ha lk`aflök sumc y jay chcfflbkcs fcrfa cktbkfcs has pckslbkcs sumck. 5- Hhcdar ch trck ec has :>13 b ch ec has 13, sl hhcda ck ch prlgcrb, cktbkfcs tckerá cgpb para vlsltarkbs.

  f) Fuahcs Fuahcs ec ec has sldulcktcs prbpbslflbkcs puceck csfrlmlrsc fbgb> p v (q

r) pa para ra

p, q, y r aecfuaeas2 1- Vl ha lk`aflö lk`aflök k sumc, sumc, jay chcfflb chcfflbkcs kcs b has pckslbkcs pckslbkcs manak manak.. =- _ucecs _ucecs kaear, kaear, b usar usar ha sauk sauka a y ha eufja. eufja. 6- Ulckcs Ulckcs q quc uc fbgp fbgprar rar pak pak,, qucsb qucsb y vlkb. vlkb. 5- Has phaktas phaktas kcfcslt kcfcsltak ak adua adua y ahlgcktb, ahlgcktb, pcrb pcrb kb quc hcs hcs jamhck. jamhck. Kbta>

 

Ecmc lkelfar ch sldklfaeb ec faea sçgmbhb (p, q, y r) para ha prbpbslflök Fbrrcfta, ec kb lkelfarha kb bmtckerá ha tbtahleae ec ha pbkecraflök Eaea.

  Pahbr _brfcktuah> 6%

 

6.- Akahlfc has sldulcktcs prbpbslflbkcs c lkelquc sl cs vcreaecra b ahsa, uhlzakeb has Uamhas ec ha Pcreae. a) 6 cs uk kþgcrb kþgcrb lgpar lgpar y = cs uk kugcrb kugcrb prlg prlgb. b. Pahbr Pahbr _brfcktu _brfcktuah> ah> 5% m) Cstuelb Cstuelb pbr pbr hlmrbs hlmrbs b cstuelb cstuelb pbr pbr apuktc apuktcs. s. f) Ck cst csta a gañaka gañaka vby vby a Ardckka Ardckka b csta gaña gañaka ka vby a Gìxlfb Gìxlfb.. e) Vl aprucmb aprucmb ch cxagck cxagck cktbk cktbkfcs fcs tc prcstb prcstb hbs hbs apuktcs apuktcs.. Kbta> Ecmc akahlzar ha h a rcahleae ec faea prbpbslflök slgphc y

ecmc lkelfar(cxphlfar) ch akáhlsls rcahlzaeb y csfrlmlr ha rcprcscktaflök ec ha prbpbslflök. 5.- Jahhar ha tamha ec ha vcreae ec has prbpbslflbkcs sldulcktcs> a) (p

r) v Y¬p

( p v q)W

 

m) (p --; q) --; ¬q v ¬s

 

f) Y(p --; q) v (¬q

Pahbr _brfcktuah> 6%

p

r) 8--; (r --; q)

3.- Jahhar ha ]cflprbfa y ha Fbktra rcflprbfa ec has sldulcktcs prbpbslflbkcs> a) ‘Vl hhucvc, cktbkfcs vby ah flkc‗. Pahbr _brfcktuah> =%   m) ‘Ebs ákduhbs aeyafcktcs sbk suphcgcktarlbs‗. suphcgcktarlbs‗.  

Kbta>

Ecmc lkelfar ck faea ukb ch aktcfcecktc y ch fbkscfucktc, ec kb lkelfarhb su ]cpucsta cs kuha.

0.- Lkelfar sl has h as sldulcktcs prbpbslflbkcs sbk> uka Uautbhbdça, uka Fbktraelfflök b uka Fbkkdckfla. Fbgprbmarhb Fbgprbmarhb gcelaktc has tamhas ec ha h a vcreae. a) ‘Vl hbs pcrrbs pcrrbs vuchak vuchak y hbs pcrrb pcrrbss kb vuchak, vuchak, cktbkfcs cktbkfcs ch sbh sbh sahc pbr ch cstc. cstc. m) (p --; --; q) (q --; --; p)

¬qW --; ¬p e) (p --; q) (p ¬q) f) Y(p ---; q) q)

Pahbr _brfcktuah > 5% 

4.- Ecgucstrc quc has sldulcktcs prbpbslflbkcs sbk Hödlfagcktc Hödlfagcktc Cqulvahcktcs>    

- p 8--; q y (p

 

   

¬q) Pahbr _brfcktuah> 1%

Fbkcfvbs 7;

 

q) v (¬p

Kcdaflök> ¬ Fbknukflök> Elsyukflök> v Lgphlfaflök(b fbkelflbkah)> --; Ebmhc lgphlfaflök(b Mlfbkelflbkah)> 8--;