2.LogikaProposisi-2

 

Ijfnkb _rjpjsnsn 71 Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ijfn Ij fnkb kb _r _rjp jpjs jsns nsnn ‐ Cu Cukuh kuh-c -cuku ukuh h Mk Mkun unv vbi bim mdsn Ij Ijfn fnkb kb Kuinbc Ijf Ijfnkb nkb Hbtmhbtnkb - B Pmhm hmst stm mr Fbdani7? Fbdani 7?2> 2>-7 -7?7 ?7? ?

HQN Lbkuitbs Ndljrhbtnkb Umikjh Umi kjh ]dnvmrsn ]dnvmrsnty ty LNL LNL UmiUmi-] ]

 Bf  B fustu stus-P s-Pmptmhgmr 7?2>

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

2 / 50

 

 B` `kdjwimefmhmdts  B Pinem Pin em ndn nd n ensus ensusud ud gmre gmrebsb bsbrkbd rkbd hbtmrn hbtmrn ybdf bdf tmrebpb tmrebpbtt pbeb pbeb suhgmrsuhgmr-suhg suhgmr mrgm gmrn rnk kut1 ut1 2

Ens`rmtm Hbtcmhbtn`s bde Nts Bppin`btnjds (Gbg 2), Mensn 6, 7?27, jimc K. C. Wjsmd (b`ub (b`ubd d utbhb utbhb)).

7

Ens`rmtm Hbtcmhbtn`s wntc Bppin`btnjds (Gbg 7), Mensn 5, 7?2?, jimc P. P. Mpp.

0

Ijfn` nd @jhputmr P`nmd`m P`nmd`m11 Hje Hjemii miindf ndf bde Wmb Wmbsjd sjdnd ndf f bgj bgjut ut Pyst Pystmhs mhs (G (Gbg bg 2), Mensn 7, 7??5, jimc H. Cutc eb ebd H. Wybd.

5

hbttn`bi Ijfn` lj ljrr @jhputmr P`nmd`m (Gbg 7, 0, 5) 5),, Mensn 7, 7???, jimc Hbtcmhb rn.. H. Gmd-Brn

=

Pine Pi nem m kuinbc Hbtmhbtnkb Hbtmhbtnkb Enskrmt 2 (7?27) en Lbs Lbsninikjh kjh ]N jimc jimc G. C. Vneabab. neabab.

<

Pinem kuinbc Ijfnkb Hbtmhbtnkb Pinem Hbtmhbtnkb en Umikjh ]dnvmrsnty jimc jimc B. Wbkchbtsyb Wbkchbtsybc, c, G. _urdb rdbhb. hb.

Gmgmrbpb Gmgmr bpb fbhgbr fbhgbr ebpbt enbhgni enbh gni ebrn suhgmr-suhgm suhgmr-suhgmrr en btbs. Pinem Pinem ndn ndn entuauk entuaukbd bd udtu ud tuk k kmpmriubd kmpmriubd bkb bkbem emhn hns s en indfkudfbd indfkudfbd LNL Umikjh ]dnvmrsnty. Ankb Bdeb Bdeb hmhnink hmh ninknn sbrbd/ pmdebpb sbrbd/ pmdebpbt/ t/ pmrtb pmrtbdy dybbd bbd tmrkbnt tmrkbnt hbtmrn hbtmrn ebib ebibh h sinem sinem ndn, ndn, snibkbd snibkbd knr nrnh nh mhbni mhbni km km ‾p2mbsmejd`spbh‱O`m2łjhudnvmrsn`y.b`.ne. ‾p2mbsmejd`spbh‱O`m2łjhudnvmrsn`y.b`.ne.

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Gbcbsbd

2

Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn _rjpjsnsn

7

Pnlbt Pnl bt-s -snlnlbt bt Ljrhuib Ijfnkb Ijfnkb _rj _rjpjsnsn pjsnsn Gmre Gmrebsb bsbrkbd rkbd Pmhbdtnkdy Pmhbdtnkdyb b

0

Pkmh Pk mhb b Ljrhuib (Hb (H btmr tm rn Pupimhmd), Kjdsmkumd Kjdsmkumdsn sn Ijfns, ebd Kmsmtbrb Kmsmtbrbbd bd Ijfnkb

5

Cukuh-cukuh Cukuhcukuh Mkunvbi Mkunvbimdsn mdsnIjfn Ijfnkb kb

7 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ijfnkb Ijfnkb _rjpjs _rjpjsnsn nsn

Ndtmrprmtbsn

Ndtmrprmtbsn Ndtmrprmtbsn ebrn subtu ljrhuib ijfnkb prjpjsnsn bebibc pmhgmrnbd dnibn kmgmdbrbd tmrcbebp prjpjsnsn prjpjsnsn tmr tmrsmg smgut. ut. _rjpjsnsn ybdf entndabu ebpbt gmrupb prjpjsnsn hbamhuk. ]dtuk prjpj hbamhuk. prjpjsnsn snsn btjh, ndtmr ndtmrprmtbs prmtbsnn hmrupbkb hmrupbkbd d pmhmt pmhmtbbd bbd bdtbrb subtu subtu vbrnbgmi prjpjsnsn tmrcbebp tmrcbebp dnibn dnibn kmgmd kmgmdbrbd brbddy dyb. b. Ndtmr Ndtmrprmtb prmtbsn sn enibhgbdfkbd emd emdfb fbd d snhgji £, £ln , £ 7, . . . . £ (p) (p ) 8 U gmrbrtn p enndtm enndtmrprmt rprmtbsnkb bsnkbd d gmdbr jimc jimc ndtmrprmtbsn ndtmrprmtbsn £ £ (q) 8 L gmrbrtn q enndtm enndtmrprmt rprmtbsn bsnkbd kbd sbibc sbibc jimc jimc ndtmrprmtbsn ndtmrprmtbsn £ £0 (p (p)) 8 L gmrbrtn p enndtmrp enndtmrprmtb rmtbsnkbd snkbd sbibc sbibc ji jimc mc ndtmrprmtbsn ndtmrprmtbsn £0 £= (q (q)) 8 U gmrbrtn q enn enndtm dtmrprmt rprmtbsnkb bsnkbd d gmdbr jimc jimc ndtmrprmtbsn ndtmrprmtbsn £=

0 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ijfnkb Ijfnkb _rjpjs _rjpjsnsn nsn

Ndtmrpr Ndtm rprmt mtbsn bsn _rjpj _rjpjsn snsn sn Hbam Hbamhuk huk

Ndtmrprmtbsn udtu udtuk k smgu smgubc bc prjpjsnsn prjpjsnsn ebpbt enpmrjimc `uku `ukup p emdfbd emdfbd hmhgmrnkbd dnibn kmgmdbrbd pbeb smhub vbrnbgmi prjpjsnsn btjh ybdf hud`ui pbe pbeb b prj prjpjs pjsnsn nsn nt ntu u. Dnibn Dn ibn kmgmd kmgmdbr brbd bd prjpjsnsn prjpjsnsn hbamhuk hbamhuk ebpbt entmdtuk entmdtukbd bd ebrn dnibn dnibn kmgmd kmgmdbr brbd bd prjpjsnsn btjh btjh ybdf ybdf hmdyusud hmdyusuddy dyb. b. ]dtuk ]dtu k ljr ljrhu huiib ybdf kjhpi hpimks, ndtmr dtmrpr prm mtbsn tbsn (en (ensmg smgut auf aufb smgbfbn sm smhb hbdt dtnnk) ebp eb pbt entm entmdt dtu ukbd kbd emdfbd hmdndabu ndtm ndtmrp rprm rmttbsn bsn smtnbp sugl glj jrhui huib ybdf beb pbe pb eb ljrhui ljrhuib b tmrsmgut tmrsmgut..

= / 50

 

HQN (LNL (LNL UmiUmi-]) ]) Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7 Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ijfnkb _rjpjsnsn nsn Ijfnkb _rjpjs

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 Bturb  Btu rbd d Pmhbdtnk Ijfnkb _rjpjsnsn  Btur  Bt urbd bd Pmhbdtnk Ijfnkb _rjpjsnsn Hnsbikbd B bebibc bebibc sm smgu gubc bc ljrhuib ebd £ bebibc ndtmrpr ndtmrprmtbsn mtbsn ybdf ybdf tmremlndn tmremlndnsn sn udtuk udtuk smtnbp smtnb p prjpjsnsn prjpjsnsn btjh ybdf ybdf hud`ui en B. B . Ndtmrprmtbsn Ndtmrprmtbsn udtuk udtuk B enemlndnsnkbd smgb smgbfb fbnn gmrnkut Ankb B 8 p (subtu prjp prjpjsn jsnsn sn btjh), btjh), hbkb hbkb £ (B ( B ) 8 £ (p), (p ), ebd ebd dnibnd dnibndyb yb smsubn emdfbd emdf bd emlndnsn emlndnsn £ udtu udtuk k prjpjsnsn btjh btjh p yb ybdf dfgmrsm gmrsmsub subnbd nbd.. Ankb B 8 U , hbkb £ ( B ) 8 £ ( U ) 8 U . Kmhuenbd ankb B 8 L, hbkb £ (B ( B ) 8 £ (L ( L ) 8 L. An Ankb kb B 8 ¬ G , udtuk udtuk subt subtu u ljrh ljrhui b G , hbk hbkb . uib U , ankb £ ( G ) 8 L £ (B ( B ) 8 £ (¬ ( ¬ G ) 8 ¬£ ( G ) 8 L, ankb £ ( G ) 8 U . Ankb Ankb B 8 G K @, udtuk subt subtu u ljrhu ljrhuib ib G. ebd @, hbkb hbkb U, anankb £ (G) 8 £ (@) 8 U . £ (B ( B ) 8 £ (G ( G K @) @ ) 8 £ (G ( G ) K £ (@ ( @) 8 L , ibnddyb Ankb Ankb B 8 G \ @, udtuk subt subtu u ljrhu ljrhuib ib G. eb hb Ld, @,ankhbk b £kb(G ( G ) 8 £ (@ (@) 8 L . £ (B ( B ) 8 £ (G ( G \ @) @ ) 8 £ (G ( G ) \ £ (@ ( @) 8 U, ibnddyb

< / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

6 / 50

 

Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ijfnkb Ijfnkb _rjpjs _rjpjsnsn nsn

Ankb Ankb B 8 G @, udtuk subt subtu u ljrhu ljrhuib ib G e.bd @, hbk hbkb U, ankb £ (G) 8Ɨ £ (@) . £ (B) (B ) 8 £ (G @) 8 £ (G) £ (@) (@) 8 L, ankb £ ( G ) 8 £ ( @ ) Ankb B 8 G ‾ @, udtuk subtu subtu ljr ljrhui huib b G ebd @, hbkb hbkb £ (B ( B) 8 . L, ankb £ ( G ) 8 U dbhud £ (@ ( @) 8 L . £ ( G ‾ @ ) 8 £ (G ( G ) ‾ £ (@) 8 U, ibnddyb Ankb B 8 G ― @, udtuk subtu subtu ljr ljrhui huib b G .ebd @, hbkb hbkb U, ankb ankb £ (G ) 8 £ (@) . £ (B ( B ) 8 £ (G ( G ― @ ) 8 £ (G ( G ) ― £ ( @) 8 L, ankb £ ( G) G) Ɨ 8 £ (@)

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ijfnkb Ijfnkb _rjpjs _rjpjsnsn nsn

@jdtjc Hnsbikbd B £bebibc bebi ljrhuib uib q ‾8 L. v ebd eb dkb £ bebibc ndtmrprm ndtmr emdf emdfbd bd £ (p) 8 L, (q)bc 8 ljrh U, e bdp£K(v) Hb Hb ndtm ndtmrp rprm rmtb tbsn snprmtbsn udtuk udttbsn uk B, ybntu bn tuemlndnsn1 £ ( B) ebpbtt entmdtukbd smgbfbn gmrnkut ebpb gmrnk ut £ (B ) 8 £ (p K q ‾ v) 8 £ ((p K q) ‾ v) 8 £ (p K q) ‾ £ (v) 8

(£ (p ( p) K £ (q ( q) ) ‾ £ ( v )

8

(L K U ) ‾ L 8 L ‾ L 8 U .

 Btbu  Bt bu ebpb ebpbtt pui puib enkm enkmra rab bkbd kbd sm`brb rnd rndfkbs kbs smgbfbn gmrn gmrnkut kut £ ( p K q ‾ v) 8 (£ (p) K £ (q)) ‾ £ (v ( v) 8 ( L K U ) ‾ L 8 L ‾ L 8 U .

3 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

> / 50

 

Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ijfnkb Ijfnkb _rjpjs _rjpjsnsn nsn

Ibtncbd Hnsbikbd £ ebd ebd ( bebib bebibc c eub eub ndtmrprmtbsn ndtmrprmtbsn ybdf bdf enemlndnsnkbd enemlndnsnkbd udtuk prjpjsnsn-prjpjsnsn btjh gmrnkut1 £ (p) 8 U , £ (q) 8 L, £ ( v) 8 L, ( (p) 8 L, ( (q) 8 L, ( ( v) 8 U. Umdtukbd ndtmrprmtbsn ebrn ljrhuib p ‾ q \ v ebd (p ‾ q) \ (p ‾ v) tmrcbebp ndtmrprmtbsn £ ebd ( . Pjiusn1 2

£ (p ‾ q \ v) v) 8 £ (p ‾ (q \ v) ) 8 £ (p) ‾ (£ (q) \ £ ( v)) 8 U ‾ ( L \ L) L) 8 U ‾ L 8 L.

7

( (p ‾ q \ v v)) 8 ( (p ‾ (q \ v) v ) ) 8 ( ( p) ‾ ( L \ U) U ) 8 L ‾ U 8 U.

0

£ ((p ‾ q) \ (p ‾ v)) 8 £ (p ‾ q ) \ £ ( p ‾ v) 8 (£ (p) ‾ £ (q)) \ (£ (p) ‾ £ (v ( v) ) 8 ( U ‾ L ) \ ( U ‾

5

( ( (q) \ ( (v) ) 8 L ‾

L ) 8 L \ L 8 L.

( ((p ‾ q) \ (p ‾ v) ) 8 ( (p ‾ q) \ ( (p ‾ v) 8 ( ( ( p) ‾ ( ( q) ) \ ( ( ( p) ‾ ( ( v ) ) 8 ( L ‾ L ) \ ( L ‾ U ) 8 U \ U 8 U .

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ijfnkb Ijfnkb _rjpjs _rjpjsnsn nsn

Ndtmrprmtbsn Ndtmr prmtbsn ebd ebd Ubg Ubgmi mi Km Kmgm gmdb dbrb rbd d Pbtu gbrns gbrns tbgmi tbgmi kmgmdbrb kmgmdbrbd d gmrsmsub gmrsmsubnbd nbd emdf emdfbd bd sbtu ndtmr ndtmrpr prmtbs mtbsnn ebrn prjpjsnsn. Hnsbikbd B bebi Hnsbikbd bebibc bc ljrhui ljrhuib b (p \ ¬q) ¬q ) ‾ (p K q), q) , tbgmi kmgmd kmgmdbr brbd bd udtuk udtuk B ebpbt enpmrjimc enpmrji mc smgb smgbf fbngmr bn gmrnk nkut ut Ndtmrprmtbsn £ln (p) 8 U , £ln (q) 8 U £7 (p) 8 U , £7 (q) 8 L £0 (p (p)) 8 L, £0 (q) 8 U £5 (p (p)) 8 L, £5 (q) 8 L emdfbd c 8 ln, £, 0, 5.

£c ( ¬q) L U L U

£c (p \ ¬q) U U L U

£c (p K q) U L L L

£c ( B ) U L U L

_mrhbsbibcbd Gmrbpb gbdyb Gmrbpb gbdybk k gbrns gbrns ebibh tbgm tbgmii kmgmdbrb kmgmdbrbd d ybdf ybdf enpmriukbd enpmriukbd udtu udtuk k hmhmrnksb hmhmrnksb kmgmd kmg mdbr brbd bd prjpjsnsn prjpjsnsn ybdf ybdf tmre tm renr nrnn btbs1 2

7

0

0 prjpjsnsn btj btjh gmrgmeb; 5 prjpjsnsn btj btjh gmrgmeb; d prj prjpjsn pjsnsn sn btjh btjh gmrg gmrgm meb. eb.

2? / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

22 / 50

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

Kmbgsbcbd (\ (\bi bine nent nty) y),, Km Kmtm tmrp rpmd mduc ucbd bd (P (Pbt btnsl nslnb nbgn gnininty) ty),, eb ebd d Kjdtrbenksn

Emlndnsn Hnsbikbd B bebibc bebibc sm smgu gubc bc ljrhuib ijfnkb prjpjsnsn prjpjsnsn 2

7

0

 B en enkb kbtb tbkb kbd d bg bgsb sbc c (vbin (vbine) e) an  ankkb kkb B gmdn gmdnib ibnn gmdbr gmdbr (U ) udtuk udtuk smtnbp ndtm ndtmrp rprm rmtb tbsn sn ybdf bdf engmrnkbd pbeb B. Ebibh cbi ndn B aufb enkbtbkbd smgb smgbfb fbnn subtu tbutjijfn. tbutjijfn. kkb tmreb tmrebpb pbtt smtnebkdy kdyb smgubc  B en enkb kbtb tbkb kbd d tmrpmducn (sbtnslnbgim) an (sbtnslnbgim) ankkb ndtmrprmt ndtm rprmtbsn bsn £ udtuk B ybdf bdf hm hmhg hgub ubtt B gmrdnibn gmrdnibn gmdbr ( U ) .  B en enkb kbtb tbkb kbd d kjdtrbenksn/ tbk ebpbt tmrpmducn (`jdtrben`tjryƗ udsbtnslnbgim)  ankkb  ankkb B gmdn gmdnib ibnn sbib sbibc c ( L ) udtuk udtuk smt smtnbp ndtmrprmtbsn ndtmrprmtbsn ybdf bdf engmrnkb engmrnkbd d pbe pbeb b B. `jdtndfmd`y an  ankkb kkb B tnebk tnebk bg bgsbc ebd tnebk tnebk auf aufb b kjdtr kjdtrbe benk nksn sn..  B en enkb kbtb tbkb kbd d `jdtndfmd`y

5

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

Kjimksn Ljrhuib Ljrhuib ybd bdf f Kjdsnstm Kjdsnstmd d Hnsbikbd ( B l n , B7 , . . . , B d } beb bebibc ibc subtu subtu kjimksn/ kjimksn/ kuhpuibd ljrhuib. Kjimksn ljrhuib ( B l n , B7, . . . , B d } enkbtbkbd kjdsnstmd (`jdsnstmdt) gnib tmrebpbt subtu ndtmrprmtbsn ndtmrpr mtbsn £ ybd ybdf f hmdfbkng hmdfbkngbtkb btkbd d £ ( B l n ) 8 £ ( B 7 ) 8 ¶ ¶ ¶ 8 £ (B (B d ) 8 U . _mrdybtbbd gbcwb kjimksn ljrhuib (B l n , B 7, . . . , B d } kjdsnstmd smtbrb emdfbd emdfbd hmdfbtbkbd hmdfbt bkbd gbcw gbcwb b ljrhuib ybdf bdf hmrupb hmrupbkbd kbd kjdaudfsn kjdaudfsn ebrn  Bln K B7 K ¶ ¶ ¶ K B d gmrsnlbt tmrpmducn(sbtnslnbgim).

20 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

@jdtjc @jdtj c ljrhuib bgs bgsbc bc,, tmrpmducn, ebd ebd kjdtrbenks kjdtrbenksnn ( 2) Ibtncbd _mrnksb _mrnks b bpbkb bpbkbc c ljrhuib B ybdf bdf gmrupb gmrupb (p q) \ (p ( p ¬q ¬ q) gmrsnl gmrsnlbt bt bgsbc bgsbc,, tmrpmducn, btbukjdtrbenks btbu kjdtrbenksn. n. Pjiusn1 emdf emdfbd bd tbgmi tbgmi kmgmdb kmgmdbrbd, rbd, pmrcbtnkb pmrcbtnkbd d gbcwb gbcwb p U U L

q U L U

¬q L U L

L

L

U

p

q

p

L U U

¬q U L L

B U U U

L

U

U

Kbrmdb Kbrm db tmrebpbt smg smgub ubc c ndtmrprmtbsn ndtmrprmtbsn ybd ybdf f hmdfbkn hmdfbkngbt gbtkbd kbd B gmrdnibn gmrdnibn gmdbr, gmdbr, hbkb hbkb  B hmrupbkbd ljrh ljrhui uib b ybdf tmrp tmrpmd mduc ucn. n. bdf engmrnkbd engmrnkbd pbeb pbeb B hmdfbkng hmdfbkngbtkb btkbd dB Kmhuenbd, Kmh uenbd, kbrmdb kbrmdb smtnbp ndtmr  ndtmr prmtbsn ybdf gmrdnibn gmdbr, hbkb hbkb B hmru hmrupb pbkbd kbd ljrhuib ybd ybdf f bgsb bgsbc. c.

25 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

@jdtjc @jdtj c ljrhuib bgs bgsbc bc,, tmrpmducn, ebd ebd kjdtrbenks kjdtrbenksnn ( 7)

Ibtncbd _mrnksb _mrn ksb bpbkb bpbkbc c ljrhuib B ybdf bdf gmrupb gmrupb (p \ q) K ( ¬p K ¬q) ¬q ) gmrsnlbt gmrsnlbt bgsb bgsbc, c, tmrpmducn, btbukjdtrbenks btbu kjdtrbenksn. n. Pjiusn1 emdf emdfbd bd tbgmi tbgmi kmgmdb kmgmdbrbd, rbd, pmrcbtnkb pmrcbtnkbd d gbcwb gbcwb p U U

q U L

¬p L L

¬q L U

p\ q U U

¬p K ¬q L L

B L L

L L

U L

U U

L U

U L

L U

L L

Kbrmdb Kbrmd b smtnbp smtnbp ndtmrprmt ndtmrprmtbsn bsn ybd ybdf f engmrnkbd pbe pbeb b B hmdfbkngbtkbd hmdfbkngbtkbd B gmrdnibn gmrdnibn sbibc, sbibc, hbkb hbk b B hmrup hmrupbkb bkbd d ljrhuib ybd ybdf f gmrsnlbt kjdtrbenksn.

2= / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

2< / 50

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

Ibtncbd _mrn _m rnksb ksb bpbkb bpbkbc c ljrhuib B ybdf bdf gmru gmrupb pb (p \ q) K ¬v gmrsnlbt gmrsnlbt tmrpmducn. Bpbkbc Bpbkbc B gmrsnlbt gmrsnl bt bgs bgsbc bc: : Bpbkbc B gmrsnl gmrsnlbt bt kjdtrbenksn: kjdtrbenksn: Bpbkbc B hmrupb hmrupbkbd kbd `jdtndfmd`y: Pjiusn1 2

_mrc _m rcbt btnk nkbd bd gbcwb ankb £ (p) 8 £ (q) 8 U ebd £ (v) 8 L, hbkb hbkb enpm enpmrj rjim imc c

7

£ ((p \ q) K ¬v ¬ v) 8 U . Kbrm Kb rmdb db tmrebpbt subtu ndtmrprmtbsn ybdf ybdf hmdfbkn hmdfbkngbt gbtkbd kbd B gmrdnibn gmdbr, hbkb B hmrupb hmrupbkbd kbd ljrhuib ybdf ybdftmr tmrpmducn. pmducn.

0

Kmhuenb Kmhue nbd d bpbg bpbgnnib £ (p) 8 £ (q) 8 L ebd £ (v) 8 U , hbk hbkb enpm enpmrj rjim imc c £ ((p \ q) K ¬v) 8 L.

5

Kbrmdb Kbrm db tmrebpbt subtu ndtmrprmtbsn ybdf ybdf hmdfbkng hmdfbkngbtkb btkbd d B gmrdnibn sbibc, hbkb hb kb B tnebk gmrsnlbt gmrsnlbt bgsb bgsbc. c.

=

Kbrm Kb rmdb db B gmrsnlbt tmrpmducn tmrpmducn hbkb hbkb B tnebk gmrsnlbt kjdtrbenksn. kjdtrbenksn.

<

Kbrmd Kb rmdb b B bebibc bebibc ljrhuib yb ybdf df tnebk tnebk bgsb bgsbc c ebd ebd gukbd gukbd kjdtrbe kjdtrbenks nksn,n, hbkb hbkb B hmrup hmr upbkb bkbd d `jdtndfmd`y `jdtndfmd`y..

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

@btbtbd Ankb engmrnkbd engmrnkbd subtu ljrhuib B ebd ebd knt ntb b enhndtb udtuk udtuk hmhmr hmhmrnk nksb sb bpbkb bpbkbc cB tmrpm tm rpmdu ducn cn btbu btbu tnebk, tnebk, hb hbkb k ntb nt b tnebk tne bk smib smibiu iu hmhmriukbd tbgm tb gmii kmgmdbrb kmgmdbrbd. d.

_mrhbsbibcbd  Bp  B pbkbc kbc smt smtnbp ljrh ljrhui uib b ybdf bgsbc aufb aufb gmrsn gmrsnlb lbtt tmrp tmrpmd mduc ucn: n:

26 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

23 / 50

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

_mhguktnbd Kmbg _mhguktnbd Kmbgsb sbcb cbd d tbdpb Ubgmi Kmg Kmgmdb mdbrbd rbd (Hbtmrn Pupimhmd) _mrhbsbibcbd Engmrnkb Engmr nkbd d ljrhu ljrhuib ib B 1 8 ¬ (p K q K v K s) ‾ (¬p \ ¬q \ ¬v \ ¬s). ]dtuk hmhmrnk hmhm rnksb sb bpbkbc bpbkbc B gmrsnlbt gmrsnlbt bgsb bgsbc c (vbin (vbine e ) , bpbkbc bpbkbc kntntb b cbrus cbrus hmdff hmdffudb udbkbd kbd tbgmi tbgmi kmgmdbrbd: _mdffudbbd tbgm tbgmii kmgmdbrbd udtuk udtuk hmhmrnksb kmbgsbcbd ljrhu jrhuiib tnebk tnebk smibhbdyb mlnsnm snmd. Ljrhu huiib B en btbs hmhmriukbd tbgm tbgmii kmgmdbrbd ybdf hmhu hm hub bt £5 8 ln< gbrns. Pubtu ljrhuib ljrhuib ybdf ybdf bgs bgsbc bc (vbin vb ine) e) ebpbt engu enguktn ktnkb kbd d kmbgs kmbgsbc bcbd bddy dyb b hmibiun lbisnlnk lbisn lnkbsn bsn (lbisnln`btnjd) btbu hmtj hmtjem em kjdtrben kjdtrbenksn. ksn. Ebibh hmtjem ndn, Ebibh ndn, subtu ljrhuib enbsu enbsuhsn hsnkbd kbd tntneb ebk k bgsbc bgsbc,, smibda smibdautdy utdyb b kntntb b gmrusbcb udtuk hmdudaukkbd gbcwb cbi ndn bkbd hmdfbkngbtkbd subtu kjdtrbenks kjdtrb enksnn (tnebk ( tnebk hudfkn hudfknd d gmdbr gmdbr). ).

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

2> / 50

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

@jdtjc Kntb bkbd hmhguktnkbd gbcwb (¬p \ ¬q) ‾ 2

¬ (p K q) bebibc ljrhuib ybdf bgsbc.

 Bdebnkbd  Bd kbd (¬p \ ¬q) ‾ ¬ (p K q) tne tnebk bk bgsbc bgsbc,, hbkb tmrebpbt tmrebpbt subtu ndtmrprm rprmttbsn £ ybdf hmdfbkngbtkbd £ ((¬p \ ¬q) ‾ ¬ (p K q) q )) 8 L .

7

Hnsbikbd B 1 8 ¬p \ ¬q ebd G 18 ¬ (p K q). Ljrhuib ybdf Hnsbikbd B bdf bkbd bkbd enpmrnksb ebpbt entuins smgbfbn B ‾ G .

0

Ndfbt kmhgbin gbcwb £ (B ‾ G ) 8 L tmpbt kmtnkb £ (B ( B ) 8 U ebd £ ((G G ) 8 L, bkngb bkn gbtd tdy yb enpm enpmrji rjimc mc £ ( ¬p \ ¬q ¬ q) 8 U ebd £ ( ¬ (p K q)) 8 L.

5

Kbrmdb £ (¬ (p K q)) 8 L, hbkb £ (p ( p K q) 8 U , bkng bkngbtd btdyb yb cbru cbrusi sibc bc £ (p ( p) 8 U ebd £ (q) 8 U .

=

<

Pmcndf Pmc ndffb fb enpmrjimc enpmrjimc £ (¬p (¬p)) 8 L ebd £ (¬q) 8 L, ybdf bdf aufb gmrbkngbt £ (¬p \ ¬q) 8 L. Cbi ndn gmrtmdtbdfbd emdfbd £ (¬p \ ¬q ¬q)) 8 U ybdftmibc enpmrjimc smgmi smgmiuhd uhdy yb en djhjr( djhjr (0). 0) . Aben pmdfbdebnbd gbcwb (¬p \ ¬q) ‾ ¬ (p K q) tnebk tnebk bgsbc kminru.

6

Emdfbd emhnknbd (¬p \ ¬q) ‾

¬ (p K q) bebi bebibc bc ljrhuib ybdf ybdf bgs bgsbc bc..

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

7? / 50

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

Ibtncbd Uudaukkbd gbcwb (p ‾ tbgmi kmgm kmgmdb dbrb rbd. d.

q) ― (¬p \ q) q) bebibc ljrhu ljrhuib ib ybdf ybdf bgsbc bgsbc tbdpb hmhbkbn

Pjiusn1 Hnsbikbd (p ‾ q) ― (¬p \ q) q) bebi bebibc bc ljrhuib bdf tneb tnebk k bgsbc bg\sbc, hbk b tmrebpbt tmrebpbt subtu ndtmrprmtbsn £ ybdf hmdfbkngbtkbd £ ((p ‾ ybd q)f ― (¬p q)) q),)hbkb 8 L. ]dtu ]d tuk k hmhpmrhuebc hmhpmrhuebc,, hnsbikbd hnsbikbd B  B 1 8 p ‾ q ebd G 1 8 ¬p \ q. 8 £ £(G), Hmdfndfbt £ ,(B ―u G£)(B 8) 8 L tmpb tm km kmhudf kmhu dfknd kndbd bd, ybntu ybnt (B U pbt ebtdkmt £tn(G (kb G )£8(B) L, Ɨbtbu ((B B ) hbkb 8 L ekntb bd hmhninkn £ (G ( G ) 8 eub U. ]dtuk hmhpmrhuebc kntb hnsbikbd £ln (B) 8 U ebd £ln (G) 8 L, smrtb £7 ( B ) 8 L ebd £7 ( G ) 8 U .

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

72 / 50

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

]dtu ]d tuk k kbsu kbsus s £ln, kntb hmhninkn £ln (B (B)) 8 U ebd £ln ( G ) 8 L. 2

Ebrn £ln ( G ) 8 £ln (¬p \ q) q) 8 L enpmrjimc £ln ( ¬p) 8 £ln (q) 8 L, bkngbtdyb (p)) 8 U. Ebrn cbsni cbsni ndn ndn enebpbt enebpbt £ln (p ‾ q) 8 L. £ln (p

7

Cbi nd ndnn gmrtmdtbdfb gmrtmdtbdfbd d emdfb emdfbd d bsuhsn bsuhsn gbcwb gbcwb £ln (B (B)) 8 £ln (p ‾ q) 8 U udtuk kbsus £ln.

]dtu ]d tuk k kbsu kbsus s £7, kntb hmhninkn £7 (B) 8 L ebd £7 ( G ) 8 U . 2

Ebrn £7 ( B ) 8 £7 (p ‾ q) 8 L enpmrjimc £7 (p) 8 U ebd £7 (q) 8 L, bkngbtdyb £7 (¬p (¬p)) 8 L. Ebrn cbsni ndn ndn enebpb enebpbtt £7 (¬ (¬p p \ q) 8 L.

7

Cbi nd ndnn gmrtmdtbdfb gmrtmdtbdfbd d emdfb emdfbd d bsuhsn bsuhsn gbcwb gbcwb £7 (G ) 8 £7 (¬p \ q) 8 U udtuk kbsus £7.

Aben tnebk beb ndtmrprmtbsn £ ybdf hmdfbkngbtkbd £ ((p ‾ Emdfb Em dfbd d emhnknbd (p ( p ‾ q) ― (¬p \ q) gmrsnlbt bgsbc.

q) ― (¬ (¬p p \ q)) 8 L.

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

77 / 50

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

Ibtncbd Uudaukkbd gbcw Uudaukkbd gbcwb b ¬ (p K q K v K s) ‾ (¬p \ ¬q \ ¬v \ ¬s) bebibc ljrhuib ljrhuib ybdf ybdf bgsbc bg sbc tbdpb hmhbkbn tbgmi tbgmi kmgmdbrbd kmgmdbrbd.. Pjiusn1 ¬q \ ¬v ¬v \ ¬s) bebi bebibc bc ljrhuib ybdf ybdf tnebk tnebk Hnsbikbd ¬ (p K q K v K s) ‾ (¬p \ ¬q bgsbc bg sbc,, hbkb tmrebpb tmrebpbtt subtu ndtmrpr ndtmrprmtbsn mtbsn £ smcnd smcndff ffb b £ ( ¬ ( p K q K v K s ) ‾ ( ¬p \ ¬q \ ¬v \ ¬s ) ) 8 L. ]dtuk ]dtu k hmhpmrhuebc hmhpmrhuebc,, hnsbikbd hnsbikbd B  B 1 8 ¬ (p K qK v K s) ebd G 1 8 ( ¬p \ ¬q \ ¬v \ ¬s) . Hmdfndfbt £ (B ‾ G ) 8 L tmpbt kmtnkb £ (B (B) 8 U ebd £ (G) 8 L, enpmrjimc 2

7 0

£ ( G ) 8 £ (¬p \ ¬q ¬q \ ¬v ¬ v \ ¬s ¬ s ) 8 L, bkngbtdyb £ ((¬ ¬p) 8 £ (¬ ( ¬q) 8 £ (¬ ( ¬v ) 8 £ (¬ ( ¬s ) 8 L, sm smcn cndf dffb fb enpmrjimc enpmrjimc £ (p ( p) 8 £ (q ( q) 8 £ (v ( v) 8 £ (s ( s) 8 U . B ) 8 £ (¬ ( ¬ (p K q K v K s) s ) ) 8 L.  Bkngb  Bkn gbtd tdy yb £ (p ( p K q K v K s) 8 U , smcndffb £ ((B Cbsni djhjr (7) gmrtmdtbdfbd emdfbd bsuhsn £ (B (B)) 8 U ybdf kntb hninkn. hninkn.

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

Aben tnebk tnebk hudfknd hudfknd beb beb ndtmrpr ndtmrprmtbsn mtbsn £ ybdf bdf hmdfbkngbt hmdfbkngbtkbd kbd ¬ v \ ¬ s ) ) 8 L. £ ( ¬ ( p K q K v K s ) ‾ ( ¬p \ ¬q \ ¬v Emdfbd emhnknbd Emdfbd emhnknbd ¬ (p K q K v K s) ‾ (¬p \ ¬q \ ¬v \ ¬s) bebibc ljrhuib ljrhuib ybdf ybdf bgsbc.

70 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pnl Pnlbt-snl bt-snlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn Gmrebs Gmrebsbrk brkbd bd Pmhbdtnkd Pmhbdtnkdyb yb

Ibtncbd _mrnksb _mrn ksb bpbkb bpbkbc c ljrh ljrhuib-ljrhuib uib-ljrhuib gmrnk gmrnkut ut g gmrsnl mrsnlbt bt bgsb bgsbc c (vbine (vbine ) , tmrpmducn (sbtnslnbgim) (sbtns lnbgim),, kjdtrbenksn, btbu hmrup hmrupbkb bkbd d `jdtndfmd`y `jdtndfmd`y.. 2

(p ‾ q \ p ‾ v) ― (p ‾ q K v )

7

( p K q \ ¬ v ) ‾ (¬ (p ― v) K ¬q)

0

=

( ( ¬p K q) K (v ‾ p ) K ( v ‾ s ) K ( s ‾ t ) ) ‾ t ((p ‾ q)K(¬p ‾ v) K (v ‾ s) s))) ‾ (¬q ‾ s) ((p ‾ q )K (v ‾ s) K ( ¬p ‾ ¬s)) ‾ (v ‾ q)

<

p q ‾ (p K ¬q) \ (¬p K q)

5

6 3

p q ‾ (p \ q) K (¬p K ¬q) p q ‾ ¬ (p ― q)

>

¬ (p ― q) ― (p K ¬q) \ (¬p K q)

2?

(p \ q) K ( ¬p K ¬q) ― (p K ¬q) \ ( ¬p K q)

75 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pkm Pkmhb hb Ljrhuib (H (Hbt btmr mrnn Pupimhmd), Pupimh md), Kjdsmku Kjdsmkumds mdsnn Ijfns, Ijfn s, ebd Kmsmtb Kmsmtbrbbd rbbd Ijfnkb

Gbcbsbd

2

Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ljrhuib Ijfnkb Ijfnkb _rjpj _rjpjsnsn snsn

7

Pnlbt Pnl bt-s -snlnlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn _rjpjsnsn Gmre Gmrebsb bsbrkbd rkbd Pmhbd Pmhbdtnkdy tnkdyb b

0

Pkmh Pk mhb b Ljrhuib (Hb (H btmr tm rn Pupimhmd), Kjdsmkumd Kjdsmkumdsn sn Ijfns, ebd Kmsmtbrb Kmsmtbrbbd bd Ijfnkb

5

Cukuh-cukuh Cukuhcukuh Mkunvbi Mkunvbimdsn mdsnIjfn Ijfnkb kb

7= / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

7< / 50

 

Pkm Pkmhb hb Ljrhuib (H (Hbt btmr mrnn Pupimhmd), Pupimh md), Kjdsmku Kjdsmkumds mdsnn Ijfns, Ijfn s, ebd Kmsmtb Kmsmtbrbbd rbbd Ijfnkb

Pkmhb Lj Ljrhu rhuib ib (Hbt (Hbtmr mrnn Pu Pupi pimh mhmd md)) Hmibiun tbgmi tbgmi kmg kmgmd mdbr brbd bd,, knt ntb b ebpbt hmincbt gbcw gbcwb b kmtnfb ljrhuib gmrnk gmr nkut ut hmrupbkbd hmrupbkb d ljrhuib ybdf bgsbc bgsbc11 2  B 18 p \ ¬p ln 7  B 1 8 q \ ¬q 7 0  B 0 1 8 (p ‾ q) \ ¬ (p ‾ q) Umrincbtt gbcw Umrincb gbcwb b kmtnfb ljrhuib en btb btbs s hmhninkn hmhninkn gmdtuk ybdf bdf ’smrupb‘.  Bfbr tnebk  Bf tnebk pmr pmriu iu tnfb tnfb kbin kbin hmhg hmhguk ukttnkbd nkbd kmbgsbcbd tnfb tnfb ljr ljrhu huib ib tmrsm tmrsmgu gut, t, kntb ebpbt hmhb hmhbkbn kbn skmhb kmhb ljrhuib B \ ¬ B . _beb B ln enbhgn hgni p smgbfbn B, pbeb B 7 enbhgn hgni q smgbfbn B, ebd pbeb B0 enbhgni p ‾ q smgbfb smgbfbnn B. B. Ljrhuib B ln , B 7 , ebd B0 yb ybdf df enpmrjimc enpmrjimc emd emdfb fbd d hmdffbdtn hmdffbdtn B hmdaben hmdaben ljrhuib ljrhuib ljrhuib b dybtb/ dybtb / kbinhbt dybtb dybtb (ndstbd`m) ebrn skmhb tmrt tm rtmd mdtu tu ensmgut smgb smgbfb fbnn ljrhui ljrh lj rhu uib B \ ¬B. ¬B .  Bpbg  Bp bgninib b skmhb ljrh ljrhui uib b B \ ¬B ¬ B tmrguktn bgsbc, hbkb smtnbp ljrh ljrhui uib b dybt dybtb b ebrn ebrn

skm sk mhb ljrhuib ljrhuib ndn ndn aufb bgsbc bgsbc.. LNL UmiUmi-]) ]) HQN ((LNL

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

76 / 50

 

Pkm Pkmhb hb Ljrhuib (H (Hbt btmr mrnn Pupimhmd), Pupimh md), Kjdsmku Kjdsmkumds mdsnn Ijfns, Ijfn s, ebd Kmsmtb Kmsmtbrbbd rbbd Ijfnkb

Ibtncbd Uudaukkbd gbcw Uudaukkbd gbcwb b ljrhuib-l ljrhuib-ljrhui jrhuib b gmrnkut1 gmrnk ut1 2 ¬ ( p K q ) ‾ ¬p \ ¬q 7

¬(pKqKvKs) ‾ ¬(pKq)\¬(vKs)

0

¬ ( p K q K v K s K t K u ) ‾ ¬ (p K q K v) v) \ ¬ (s K t K u) u)

bebibc ljrhuib-ljrhuib bebibc ljrhuib-ljrhuib ybd ybdf f bgsbc bgsbc.. Pjiusn1 _mrcbtnk _mrc btnkbd bd gbcwb smtnbp ljrhuib ljrhuib en btbs ebpbt enpbdebdf smgb smgbfb fbnn ljrh ljrhuib uib emdfb emdfbd d skmhb¬ skmhb ¬ (B K G) ‾ ¬B \ ¬G. _be beb b ljrhui ljrhuib b pmrtbhb pmrtbhb B 8 p ebd ebd G 8 q, pbeb pbeb ljrhuib kmeub B 8 p K qeb qebd G 8 v K s, smrtb pbeb ljrhuib tmrbkcnr B 8 pK qK v ebd G 8 s K t K u. u.  Bkngb  Bkn gbtd tdy yb, udtuk udtuk hmhg hmhgu uktn ktnkbd kbd gbcwb kmtn kmtnfb fb ljrh ljrhui uib b en btbs bgsbc hbkb kntb `ukup hmdudaukkbd gbcwb skmhb ljrhuib ¬ ( B K G) ‾ ¬B \ ¬G aufb bgsbc. _mhgu _m hguktn ktnbd bd ebpb ebpbtt enib enibkukb kukbd d emdfbd hmtj hmtjem em lbisnlnk lbisnlnkbsn. bsn.

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pkm Pkmhb hb Ljrhuib (H (Hbt btmr mrnn Pupimhmd), Pupimh md), Kjdsmku Kjdsmkumds mdsnn Ijfns, Ijfn s, ebd Kmsmtb Kmsmtbrbbd rbbd Ijfnkb

Kjds Kj dsmk mkum umds dsnn Ijfns ebd ebd Kmsmtbr Kmsmtbrbbd bbd Ijfnkb Emlndnsn

Hnsbikbd B ebd ebd G bebibc bebibc eub eub ljrhuib ijfn ijfnkb kb prjpjs prjpjsnsn nsn11 Ljrhuib B ebd G enkbtbkbd smtbrb btbu mkunvbi mkunvbimd md (ijfn`bii (ijfn`biiy y mqunvbimd mqunvbimdt) t) an  ankb kb ljrhuib  B ― G hmrupbkbd tbutjijfn. Cbi ndn entuinskbd emdfbd B emdfbd B ö G btbu btbu B  B m G . dsn ijfns (ij (ijfn fn`b `bii `jdsmqumd `jdsmqumd`m) `m) ebrn B ankb Ljrhuib G enkbtbk enkbtbkbd bd smg smgbf bfbn bn kjdsmkum kjdsmkumdsn ljrhuib  B ‾ G hmrupbkbd tbutjijfn. Cbi ndn entuinskbd emdfbd B emdfbd B ↗ G . ]dtuk ]dtu k hmdudaukkbd kjdsmkum kjdsmkumds dsnn ijfns hbupud hbupud kmsmtb kmsmtbrbb rbbd d ijfnkb bdtbr bdtbr eub ljrhuib, ljrhui b, hb hbkb kb kntb knt b ebpbt1 ebpbt1 hmdffudbk hmdff udbkbd bd tbgmi tbgmi kmgmdbr kmgmdbrbrb brbd d hmdff hmd ffudb udbkbd kbd cukuh-cukuh mkunvbimdsn mkunvbimdsn ijfnkb

73 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pkm Pkmhb hb Ljrhuib (H (Hbt btmr mrnn Pupimhmd), Pupimh md), Kjdsmku Kjdsmkumds mdsnn Ijfns, Ijfn s, ebd Kmsmtb Kmsmtbrbbd rbbd Ijfnkb

@jdtjc Kjd Kjdsm smku kumd mdsn sn Ijfn Ijfns s (2)

Ibtncbd Uudaukkbd gbcw gbcwb (( ((p p ‾ q) K p) ↗ q. Pjiusn1 emdfb emdfbd d tbgmi kmgmdbrbd kmgmdbrbd bkbd entud entudauk aukkb kbd d gbcwb gbcwb ((p ‾ bebi be bibc bc tbutjijfn, tbutjijfn, tnda tn dabu bu gbcw gbcwb b

q) K p) ‾ q

p U U

q U L

p‾ q U L

(p ‾ q) K p U L

((p ‾ q )K p ) ‾ q U U

L L

U L

U U

L L

U U

Kjdsmkumdsn ijfns ((p ‾ q) K p) ↗ q aufb endbhbkbd smgbfbn hjeus pjdm pjdmds ds (engbcbs (engb cbs imgnc ibda ibdaut ut pbeb gbcb gbcbsb sbd d ndlmrmds ndlmrmdsn). n).

0? / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pkm Pkmhb hb Ljrhuib (H (Hbt btmr mrnn Pupimhmd), Pupimh md), Kjdsmku Kjdsmkumds mdsnn Ijfns, Ijfn s, ebd Kmsmtb Kmsmtbrbbd rbbd Ijfnkb

@jdtjc Kjd Kjdsm smku kumd mdsn sn Ijfn Ijfns s (7)

Ibtncbd Uudaukkbd gbcw gbcwb (( ((p p ‾ q) K ¬q) ↗ ¬p. Pjiusn1 emdfb emdfbd d tbgmi kmgmdbrbd kmgmdbrbd bkbd entud entudauk aukkb kbd d gbcwb gbcwb ((p ‾ bebi be bibc bc tbutjijfn, tbutjijfn, tnda tn dabu bu gbcw gbcwb b

q) K ¬q) ‾ ¬p

p U U

q U L

¬p L L

¬q L U

p‾ q U L

(p ‾ q) K ¬q L L

((p ‾ q) K ¬q) ‾ ¬p U U

L L

U L

U U

L U

U U

L U

U U

Kjdsmkumdsn ijfns ((p ‾ q) K ¬q) ↗ ¬p aufb endbhbkbd smgbfbn hjeus tjiimds (engbcbs (engb cbs imgnc ibda ibdaut ut pbeb gbcb gbcbsb sbd d ndlmrmds ndlmrmdsn). n).

02 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Pkm Pkmhb hb Ljrhuib (H (Hbt btmr mrnn Pupimhmd), Pupimh md), Kjdsmku Kjdsmkumds mdsnn Ijfns, Ijfn s, ebd Kmsmtb Kmsmtbrbbd rbbd Ijfnkb

@jdtjc @jdtj c Kmsmt Kmsmtb brb rbbd bd Ijf Ijfnkb nkb (2)

Ibtncbd Uudauk Uud aukkbd kbd gbcwb gbcwb p ‾ q ö ¬p \ q. Pjiusn1 emdfb emdfbd d tbgm tbgmii kmgmdbrbd kmgmdbrbd bkbd entud entudau aukk kkbd bd gbcwb gbcwb (p ‾ bebi be bibc bc tbutjijfn, tbutjijfn, tnda tn dabu bu gbcw gbcwb b

q) ― (¬p \q)

p U U

q U L

¬p L L

p‾ q U L

¬p \ q U L

(p ‾ q) ― (¬p \ q) q) U U

L L

U L

U U

U U

U U

U U

_mrcbtnkbd _mrcbtnk bd gbcwb p ‾ q ebd ¬p \ q hmhn hmhnink inknn dnibn dnibn kmgmdb kmgmdbrbd rbd ybdf ybdf sbhb sbhb pbeb smtnbp smtnb p gbrn gbrns s tbgmi tbgmi kmgmd kmgmdbr brbd bd en btbs.

07 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

00 / 50

 

Pkm Pkmhb hb Ljrhuib (H (Hbt btmr mrnn Pupimhmd), Pupimh md), Kjdsmku Kjdsmkumds mdsnn Ijfns, Ijfn s, ebd Kmsmtb Kmsmtbrbbd rbbd Ijfnkb

@jdtjc @jdtj c Kmsmt Kmsmtb brb rbbd bd Ijf Ijfnkb nkb (7)

Ibtncbd Uudaukkbd gbcwb ¬ (p K q) ö ¬p \ ¬q. Pjiusn1 Pjiu sn1 emdf emdfbd bd tbgmi tbgmi kmgmdbrb kmgmdbrbd d bkbd bkbd entud entudauk aukkbd kbd gbcw gbcwb b ¬ (p K q) ― ¬p \ ¬q bebi be bibc bc tbutjijfn, tbutjijfn, tnda tndabu bu gbcw gbcwb b p U U

q U L

¬p L L

¬q L U

pKq U L

¬ (p K q) L U

¬p \ ¬q L U

¬ (p K q) ― ¬p \ ¬q U U

L L

U L

U U

L U

L L

U U

U U

U U

_mrcbtnkbd gbcwb gbcwb ¬ (p K q) ebd ¬p \ ¬q hmhni hmhninkn nkn dnibn kmgmd kmgmdbrb brbd d ybdf sbhb sbhb pbeb pbeb smtnbp gbrn gbrns s tbgmi tbgmi kmgmdbrbd kmgmdbrbd en btbs. btbs. Kmsmtbrb Kmsmtbrbbd bd ¬ (p K q) ö ¬p \ ¬q aufb Hjrfbd bd.. ennstnibckbd smgbfbn cukuh Em Em Hjrf

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Cukuh-cukuh MkunvbimdsnIjfnkb

Gbcbsbd

2

Ndtmrprmtbsn ebd Pmhbdtnk Ljrhuib Ljrhuib Ijfnkb Ijfnkb _rjpj _rjpjsnsn snsn

7

Pnlbt Pnl bt-s -snlnlbt bt Ljrhuib Ijfnkb Ijfnkb _rjpjsnsn _rjpjsnsn Gmre Gmrebsb bsbrkbd rkbd Pmhbd Pmhbdtnkdy tnkdyb b

0

Pkmh Pk mhb b Ljrhuib (Hb (H btm tmrrn Pupimhmd), Kjdsmkumd Kjdsmkumdsn sn Ijfns, ebd Kmsm Kmsmtbrb tbrbbd bd Ijfnkb

5

Cukuh-cukuh Cukuhcukuh Mkunvbi Mkunvbimdsn mdsnIjfn Ijfnkb kb

05 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Cukuh-cukuh MkunvbimdsnIjfnkb

Mkunv Mku nvbim bimds dsnn Ijf Ijfnkb nkb ybd bdf f Hmingbtkbd ¬, ¬ , K, eb ebd d\

pK U ö p p\ L ö p

Pnlbtt nemd Pnlb nemdtn tntb tbs s

p\ U ö U pK L ö L p\pö p pKpö p ¬ ( ¬p) ö p

Pnlbt ejhn jhndbsn bsn

p \ q ö q\ p p K q ö qK p

Pnlbt ne nemh mhpj pjtm tmd d Pnlbt dm dmfbsn fbdeb Pnlbt Pn lbt kjhutb kjhutbtn tnl  l 

0= / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

0< / 50

 

Cukuh-cukuh MkunvbimdsnIjfnkb

(pKq)Kv ö pK(qKv) (p\q)\v ö p\(q\v) p\(qKv) ö (p\q)K(p\v) pK(q\v) ö (pKq)\(pKv) ¬ (p K q) ö ¬p \ ¬q ¬ (p \ q) ö ¬p K ¬q p\(pKq) ö p pK(p\q) ö p p\ ¬ ¬p pöU pK ¬ ¬p pöL

Pnlbt bsjs bsjsnb nbtn tnl  l  Pnlbt Pn lbt enstrngut enstrngutnl  nl  Cukuh EmHj Em Hjrfb rfbd d Pnlbt Pnl bt bgsjr bgsjrps psnn (pmdy (pmdymrb mrbpbd pbd)) Pnlbt dmfbsn

Gmrebs Gmre bsbr brkbd kbd snlbt snlbt bsjsnbtnl, bsjsnbtnl, hbkb tbdeb kurudf pbe pbeb b ljrhuib (p K q) K v, p K (q K v), v), (p \ q) \ v, hbupu hbupud d p \ (q \ v) v ) ebpbt ebpbt encnib encnibdfkbd dfkbd e ebd bd entuins smg smgbfbn p K q K v (udtuk gmdtuk gmdtuk kjdaudf kj daudftnl) tnl) ebd p \ q \ v (udtuk gmdtuk gmdtuk ensaudftnl ensa udftnl). ).

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Cukuh-cukuh MkunvbimdsnIjfnkb

Mknvbimdsn Mknvbimd sn Ijfnkb Ijfnkb ybdf ybdf Hmingbtk Hmingbtkbd bd ‾

ebd ―

p ‾ qö ¬p\q p ‾ q ö ¬q ‾ ¬p ¬ (p ‾ q) ö p K ¬q (p ‾ q) K (p ‾ v) ö p ‾ (q K v ) (p ‾ v) K (q ‾

v) ö (p K q ) ‾ v

(p ‾ v) \ (q ‾

v) ö (p \ q ) ‾ v

(p ‾ q) \ (p ‾ v) ö p ‾ (q \ v ) p ― q ö (p ‾ q)K(q ‾ p) p ― q ö ¬p ― ¬q p ― q ö (p K q) \ ( ¬p K ¬q) ¬ (p ― q) ö p ― ¬q

06 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Cukuh-cukuh MkunvbimdsnIjfnkb

_mhguktnbd Mkunvbim Mkunvbimdsn dsn emd emdfb fbd d Cukuh Mkunv Mkunvbim bimdsn dsn ( 2) Ibtncbd

Uudaukkb kkbd gbcwb p K q ‾ v ö p ‾ (q ‾ v) hmd hmdffudbkb dbkbd d cukuh-c cukuh-cuk ukuh uh mkunvbimdsn mkunvb imdsn ybd ybdf f beb. Pjiusn1 p K q‾ v

ö ö ö ö ö

(p K q) ‾ v ¬ (p K q) \ v (¬p \ ¬q) ¬q) \ v ¬p \ (¬q (¬q \ v) ¬p \ (q ‾ v)

(gmrebsbrkbd prmsmemds K ebd ‾ ) (mkunvbimdsn B ‾ G ö ¬ B \ G ) (gmrebsbrkbd cukuh Em Hjrfb rfbd) (gmrebsbrkbd snlbt lbt bs bsjsnbtnl \) (mkunvbimdsn ¬ B \ G ö  B ‾ G )

ö

p‾

(mkunvbimdsn ¬ B \ G ö  B ‾ G )

(q ‾ v)

Mkunvbimdsn skm skmhb hb ljrhuib ljrhuib B ‾ G ö ¬ B \ G ebpbt enguktnkbd enguktnk bd emdf emdfbd bd huebc huebc emdf em dfbd bd hmtjem lbis lbisnlnk nlnkbsn bsn tmrcbebp tmrcbebp kmbgsb kmbgsbcb cbd d sk skmh mhb b ljrhuib ljrhuib (B ‾ G ) ― (¬B \ G) . Pnlb Pn lbtt mkun kunvbimdsn p K q ‾ v ö p ‾ (q ‾ v) aufb aufb enns ennstn tnib ibck ckbd bd smgbfbn snlbt

03 / 50

mkspjrtbsn.. mkspjrtbsn HQN ((LNL LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

0> / 50

 

Cukuh-cukuh MkunvbimdsnIjfnkb

_mhguktnbd Mkunvbim Mkunvbimdsn dsn emd emdfb fbd d Cukuh Mkunv Mkunvbim bimdsn dsn ( 7)

Ibtncbd Uudaukkbd gbcw gbcwb b ¬ (p \ ( ¬p K q)) q) ) ebd ebd ¬p K ¬q mkunvbim mkunvbimd d hmd hmdff ffud udbk bkbd bd cukuh-cukuh mkunvbimd mkunvbimdsn sn ybd ybdf f beb. Pjiusn1 ¬ (p \ ( ¬p K q))

ö ö ö ö ö ö ö

¬pK¬(¬pKq) ¬p K ( ¬ ( ¬ p ) \ ¬q ) ¬ p K (p \ ¬ q ) ( ¬p K p) \ (¬p K ¬q) L \ ( ¬ p K ¬q ) (¬pK¬q)\L ¬p K¬q

(gmrebsbrkbd cukuh Em Hjrfbd) (gmrebsbrkbd Hjrfbd) (gmrebsbrkbd (gmreb sbrkbd cukuh Em Hjrfbd) Hjrfbd) (gmrebsbrkbd snlbt snl bt dmfb dmfbsn sn fbdeb) (gmr (g mreb ebsb sbrkb rkbd d snlb snlbtt enst enstrng rngutn utnl) l) (gmrebsbrkbd snlbt dmfbsn) (gmr (g mreb ebsb sbrkb rkbd d snlb snlbtt kjh k jhutb utbtnl tnl)) (gmr (g mreb ebsb sbrkb rkbd d snlbt nemdtntbs) nemdtntbs)

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

5? / 50

 

Cukuh-cukuh MkunvbimdsnIjfnkb

_mhguktnbd _mhguk tnbd Kmbg Kmbgsb sbcb cbd d emd emdfb fbd d Cuk Cukuh uh Mkunvbim Mkunvbimdsn dsn (2) Ibtncbd Uudaukkbd gbc gbcw wb (p K q) ‾ (p \ q) bebibc bebibc ljrhuib ybdf ybdf bgsb bgsbc c (vbin vb ine) e) emdf emdfbd bd hmhbkbn cukuh-cukuh cukuh-cukuh mkunvbimdsn ybdf ybdf beb. Pjiusn1  Bkb  B kbd d en entu tuda daukk ukkbd bd gbcwb (p K q) ‾ (p \ q) mkunvbimd emdfbd U. (p K q) ‾ (p \ q )

ö ö ö

¬ (p K q) \ (p \ q) (¬p \ ¬q) ¬q) \ (p \ q) ( ¬p \ p) \ (¬q \ q)

ö

U\U

ö

U

(mkunvbimdsn B ‾ G ö ¬ B \ G ) (gmrebsbrkbd cukuh Em Hjrfbd) (gmre (g mrebs bsbrk brkbd bd snlbt snlbt kjhutbtnl  kjh utbtnl  ebd eb d bsjsnbt bsjsnbtnl nl udtuk \) (gmre (g mrebs bsbrk brkbd bd snlbt snlbt kjhutbtnl  kjh utbtnl  ebd eb d snlbt dmf dmfbsn bsn udtuk udtuk \) (gmreb (gm rebsbrk sbrkbd bd snlbt snlbt ejhndbsn) ejhndbsn)

Ebrn cbsni ndn, kntb ebpbt hmduinskbd (p K q) ↗ (p \q). \ q).

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

 

Cukuh-cukuh MkunvbimdsnIjfnkb

_mhguktnbd _mhguk tnbd Kmbg Kmbgsb sbcb cbd d emd emdfb fbd d Cuk Cukuh uh Mkunvbim Mkunvbimdsn dsn (7)

Ibtncbd Uudauk Uuda ukkb kbd d gbcwb (p ‾ q K v ) ‾ (p ‾ q) bebibc ljrh ljrhui uib b ybdf bgsbc (vbine) (vbine) emdf em dfbd bd hmhbkbn cukuh-cukuh cukuh-cukuh mkunvbimdsn mkunvbimdsn ybdf beb. Pjiusn1  Bkb  B kbd d en entu tuda daukk ukkbd bd gbcwb (p ‾ q K v ) ‾ (p ‾ q) mkun kunvbimd emdfbd U .

ö

(p ‾ q K v ) ‾ (p ‾ q) ¬ (p ‾ q K v ) \ ( p ‾ q)

ö ö ö

¬ ( ¬p \ (q K v)) \ (¬ ( ¬p \ q) q) (¬ (¬p (¬p) K ¬ (q K v)) \ (¬p (¬p \ q) (p K (¬q \ ¬v) ) \ (¬p \ q)

(mkunvbimdsn B ‾ G ö ¬ B \ G ) (mkunvbimdsn B ‾ G ö ¬ B \ G ) (gmrebsbrkbd cukuh Em Hjrfbd) (gmrebsbrkbd cukuh Em Hjrfbd ebd eb d snlbt snlbt dmfb mfbsn fbdeb) fbdeb)

52 / 50

HQN (LNL (LNL UmiUmi-]) ])

Ijfnkb Ijf nkb _rjpjs _rjpjsnsn nsn 7

 Bfustu  Bfu stus-P s-Pmptm mptmhgmr hgmr 7? 7?2> 2>

57 / 50

 

Cukuh-cukuh MkunvbimdsnIjfnkb

ö ö ö ö ö ö ö

(p K ¬q) \ (p K ¬v) \ ( ¬p \ q) (p K ¬q) \ ( ¬p \ q) \ (p K ¬v) ( ¬¬p K ¬q) \ ( ¬p \ q) \ (p K ¬v) ¬ ( ¬p \ q) \ (¬p \ q) \ (p K ¬v) U \ (p K ¬v) (p K ¬ v ) \ U U

Ebrn cbsni cbsni ndn, ndn, knt ntb b ebpbt hmduin hmduinskbd skbd (p ‾

(gmreb (gmr ebsb sbrk rkbd bd snlbt enstrngu enst rngutnl) tnl) (gmr (g mreb ebsb sbrk rkbd bd snlbt kjhutbtnl udtuk \) (gmrebsbrkbd snlbt snl bt dmfb dmfbsn sn fbdeb) (gmreb (gm rebsbrk sbrkbd bd snlbt snlbt Em Hjrfbd) (gmrebsbrkbd (gmreb sbrkbd sn snlb lbtt dmfb dmfbsn) sn) (gmrebsbrkbd snlbt kjhutbtnl udtuk \) \) (gmrebsbrkbd snlbt ejhndbsn) q K v) ↗ (p ‾ q).