Apol 2

March 14, 2023 | Author: Anonymous | Category: N/A
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^uhstë` >/>9 - Qnkj`kïmj` Bûgjk` M` Shon > - chdjmjçøhs prhbjojmnrhs cn Nubn 8 Bûgjkn c`s Yrhcjknc`s (prhcjkntjvn) ndjron-sh quh<   ‒K`o` n bûgjkn quh trntn nphmns cns pr`p`sjçøhs sjmgubnrhs ê onjs sjopbhs quh n quh trntn tnoaêo k`o k`mlumt`s ch `alht`s, `s nut`rhs prhdhrjrno shpnrnr ` hstuc` cn Bûgjkn ho cn nubn 8, nmnbjsh ns nbthrmntjvns h nssjmnbh n nbthrmntjvn k`o n rhsp`stn K@QQHSN M`tn< >9.9

 N

nphmns ` jtho J hstî k`rrht`

A

nphmns ` jtho JJ hstî k`rrht`

K

`s jthms J h JJ hstë` k`rrht`s

&

T`kì nkhrt`u!

Shxt` cn Nubn 8 - Shon > chdjmjçøhs prhbjojmnrhs (pg. ;)

C

`s jthms J h JJ hstë` jmk`rrht`s

^uhstë` 1/>9 - Qnkj`kïmj` Bûgjk` @ kîbkub` ch prhcjknc`s, nprhshmtnc` h chdjmjc` m` Shon 1 cn Nubn 8 k`o` ‒uon hxthmsë` c` kîbkub` pr`p`sjkj`mnb quh trntn ch prhcjknc`s, `u pr`p`sjçøhs qunmtjdjkncns‟ trnz quh n bjmgungho d`ronb cn bûgjkn ch prhcjknc`s ê onjs hxprhssjvn quh n cn bûgjkn pr`p`sjkj`mnb, p`js nbêo c`s sïoa`b`s (k`mhktjv`s) bûgjk`s ~, ], v, -= h 2-=, ns dûroubns aho-d`roncns (dad) cn bûgjkn ch prhcjknc`s së` k`op`stns p`r<   Ch nk`rc` k`o ` k`mthüc` ojmjstrnc` m` Shon 1 cn Nubn 8, qunjs së` `s k`op`mhmths cns dûroubns aho-d`roncns (dad) cn bûgjkn ch prhcjknc`s, nbêo c`s sïoa`b`s (k`mhktjv`s) cn bûgjkn pr`p`sjkj`mnb0  Nmnbjsh ns nbthrmntjvns h nssjmnbh n nbthrmntjvn k`o n rhsp`stn K@QQHSN M`tn< >9.9

 N

A

Mhgnçë`, K`mlumçë`, Cjslumçë`, Cjslumçë`, Jopbjknçë` h Aj-jopbjknçë` @alht`s, Yrhcjknc`s, K`mhktjv`s, Tnrjîvhjs Tnrjîvhj s h ^unmtjdjknc`rhs

&

T`kì nkhrt`u!

Shxt` Nubn 8 - Shon< 1 ‛ nbdnaht` cn bûgjkn ch prhcjknc`s (pg. 8)

K

Mhgnçë Mhgn çë`, `, K`m K`mlu lumç mçë` ë`,, Cjsl Cjslum umçë çë`, `, K`mcjkj`mnb h Ajk`mcjkj`mnb

C

Më`, H, @u Më`, @u,, [h. [h..h .hmt mtë` ë` h [h [h h s` s`oh ohmt mth h sh

^uhstë` ;/>9 - Qnkj`kïmj` Bûgjk` K`o` chskrjt` m`s [bjchs cn Nubn 3, "Xon pr`p`sjçë` Y (p, q, r, ...) jopbjkn b`gjknohmth muon pr`p`sjçë` ^ (p, q, r, ...) sh ^ (p, q, r, ...) ê vhrcnchjrn (T) t`cns ns vhzhs quh Y (p, q, r, ...) ê vhrcnchjrn. Mhstns k`mcjçøhs, hskrhvh-sh quh Y (p, q, r.... r....)) ^ (p, q, r, ...), quh sh bì< Y jopbjkn ho ^."   K`msjchrn-sh hmtë` quh n jopbjknçë` bûgjkn hmtrh cuns cncns dûroubns pr`p`sjkj`mnjs `k`rrh qunmc`<

 Nssjmnbh n nbthrmntjvn K@QQHS K@QQHSN N M`tn< >9.9

 N

qunmc` mns rhsphktjvns tnahbnsvhrcnchs, bjmen n bjmen mns k`bumns rhsubtnc`, më` k`mk`rrh sjoubtnmhnohmth ho vhrcnchdnbsjcnch, mhstn `rcho.

&

T`kì nkhrt`u! [bjch ;/>9 Nubn ; Jopbjknçë`

Xon pr`p`sjçë` Y (p, q, r, ...) jopbjkn b`gjknohmth muon pr`p`sjçë` ^ (p, q, r, ...) sh ^ (p, q, r, ...) ê vhrcnchjrn (T) t`cns ns vhzhs quh Y (p, q, r, ...) ê vhrcnchjrn. Mhstns k`mcjçøhs, hskrhvh-sh quh Y (p, q, r....) ^ (p, q, r, ...), quh sh bì< Y jopbjkn ho ^.  N jopbjknçë` bûgjkn hmtrh cuns cncns dûroubns pr`p`sjkj`mnjs qunmc` mns rhsphktjvns tnahbnsvhrcnchs, bjmen n bjmen mns k`bumns rhsubtnc`, më` k`mk`rrh sjoubtnmhnohmth ho vhrcnchdnbsjcnch, mhstn `rcho.

A

qunmc` qunm c` ` k`m k`mlu lumt mt` ` rhs rhsp` p`st stn n cns cns tnahbns-vhrcnchs ê mub`.

K

qunmc` qunm c` ns tn tnah ahbn bnss-vh vhrc rcnc nchs hs th tho o k`o k`o` ` k`mlumt` rhsp`stn D pnrn t`cns bjmens.

C

qunmc` qunm c` ns ns tn tnah ahbn bns-v s-vhr hrcn cnch chss tho tho ` k`mlumt` rhsp`stn ho t`cns bjmens Thrcnchjr` h Dnbs` nbthrmncnohmth.

H

qunmc` qunm c` ns dû dûro roub ubns ns pr pr`p `p`s `sjk jkj` j`mn mnjs js së së` ` jgunjs.

^uhstë` 3/>9 - Qnkj`kïmj` Bûgjk` [hgumc` n chdjmjçë` ch Hqujvnbìmkjn bûgjkn (Nubn 3), chdjmj-sh quh uon pr`p`sjçë` Y ê b`gjknohmth hqujvnbnmth `u nphmns hqujvnbh n uon pr`p`sjçë` ^ sh<  Nssjmnbh n nbthrmntjvn K@QQHS K@QQHSN N M`tn< >9.9

 N

Ns tnahbns vhrcnch chstns cuns pr`p`sjçøhs së` cjdhrhmths

A

Y h ^ së` së` rh rhpr prhs hshm hmtn tncn cnss p`r p`r tn tnah ahbn bn vhrcnch cjdhrhmths

K

Ns tnahbns vhrcnch chstns cuns pr`p`sjçøhs së` jcìmtjkns

&

C

T`kì nkhrt`u!

Y h ^ më` më` së së` ` rhp rhprh rhsh shmt mtnc nc`s `s p` p`r  r  tnahbns vhrcnch

^uhstë` 8/>9 - Qnkj`kïmj` Bûgjk`  N jopbjknçë` cns Yr`p`sjçøhs p h q, k`o ns pr`p`sjçøhs k`op`stns (p ] q) (p v q), mhstn `rcho, së` k`msjchrncns jopbjknçë` bûgjkn  ho qunb c`s khmîrj`s0

M`tn< >9.9

 N

hmtë` (p ] q) k`mtrncjçë`.

(p v q) ghrn uon

hmtë` (p ] q)

(p v q) ghrn uon

A tnut`b`gjn. B`g`, (p ] q)

&

(p v q)

T`kì nkhrt`u!

[bjch ;/>9 Nubn ;. Jopbjknçë`

Xon pr`p`sjçë` Y (p, q, r, ...) jopbjkn b`gjknohmth muon pr`p`sjçë` ^ (p, q, r, ...) sh ^ (p, q, r, ...) ê vhrcnchjrn (T) t`cns ns vhzhs quh Y (p, q, r, ...) ê vhrcnchjrn. Mhstns k`mcjçøhs, hskrhvh-sh quh Y (p, q, r....) ^ (p, q, r, ...), quh sh bì< Y jopbjkn ho ^.  N jopbjknçë` bûgjkn hmtrh cuns cncns dûroubns pr`p`sjkj`mnjs qunmc` mns rhsphktjvns tnahbnsvhrcnchs, bjmen n bjmen mns k`bumns rhsubtnc`, më` k`mk`rrh sjoubtnmhnohmth ho vhrcnchdnbsjcnch, mhstn `rcho.

K

hmtë` (p ] q)

(p v q) ghrn uon

k`mtjmgìmkjn.

C

hmtë` (p ] q) (p v q) më` ê uon pr`p`sjçë` vîbjcn pnrn hsth nrguohmt`.

^uhstë` 4/>9 - Qnkj`kïmj` Bûgjk` Bhjn ` thxt`< ...ns kbnsshs ch dûroubns pr`p`sjkj`mnjs së` knrnkthrjzncns phbn ‒d`ron hstruturnb‟, jst` ê, phbns hstruturns - Yîgjmn >8, Qnkj`kïmj` Bûgjk` ^unmtjtntjv` - Yr`dª Ynubn Drnmkjs Ahmhvjchs, NXBN >. K`msjchrnmc` ` thxt` c` hmumkjnc` h `s k`mthüc`s na`rcnc`s ho snbn h m` onthrjnb ch np`j`, nssjmnbh T pnrn n(s) chdjmjçøhs ch Dûroubn pr`p`sjkj`mnb THQCNCHJQN[ h D pnrn ns DNB[N[. J. ( ) ‒N dûroubn pr`p`sjkj`mnb ê k`op`stn p`r uo ümjk` `phrnc`r bûgjk`‟. JJ. ( ) ‒Xon dûroubn pr`p`sjkj`mnb ê uo k`mlumt` `u sêrjh djmjtn ch thro`s k`mstjtuïcn ch phb` ohm`s uo `phrnc`r bûgjk` quh jmkjcn s`arh n` ohm`s uon pr`p`sjçë` sjopbhs k`op`mhmth‟. JJJ. ( ) ‒dûroubn pr`p`sjkj`mnb ê n rhbnçë` hmtrh ns bhtrns c` nbdnaht` h `s `phrnc`rhs prjoîrj`s pr joîrj`s onthoîtjk`s ch ncjçë`, suatrnçë`, oubtjpbjknçë` h cjvjsë`‟. JT.. ( ) ‒K`mlumt` ch `phrnc`rhs onthoîtjk`s quh JT ntuno s`arh `s müohr`s h vnrjîvhjs bûgjkns, quh jmkjcho s`arh `s rhsubtnc`s cns `phrnçøhs‟.

 Nssjmnbh n shquìmkjn k`rrhtn< M`tn< >9.9

 N

D, D, D, T, T, T

A

T, T, T, T

K

D, D, T, D

C

D, T, D, D

&

T`kì nkhrt`u!

K@QQHSN ‛ Nphmns n K@QQHSN nbthrmntjvn JJ ê k`rrhtn k`o` nprhshmtnc` m` knpïtub` 3.> ‛ QHBNÇØH[ HMSQH K@MHKSJT@[ BÛGJK@[ H @[ @YHQNC@QH[ BÛGJK@[ ‛ [uaknpïtub` 3.>.> CHDJMJÇË@, Qnkj`kïmj` Bûgjk` ^unmtjtntjv` Yr`dª Ynubn Drnmkjs Ahmhvjchs,  NXBN >, Yîgjmn >8). Ns chonjs së` jmk`rrhtns

^uhstë` 7/>9 - Qnkj`kïmj` Bûgjk`  N Cupbn Cupbn Mhgnçë` nprhshmtncn mn tnahbn ch Hqujvnbìmkjns M`tîvhjs ([bjch 3/>9 cn nubn 4) ê rhprhshmtncn K@QQHSNOHMSH K@QQHSNOHMSH p`r qunb cns nbthrmntjvns0 M`tn< >9.9

 N

~q -= ~Y

A

^~q 2-= p~Y

K

~Y -= ~Y

C

~~Y 2?= Y

&

T`kì nkhrt`u!

[bjch 3/>9 cn nubn 4

H

~~q 2-= ~p

^uhstë` 5/>9 - Qnkj`kïmj` Bûgjk` [hln n pr`p`sjçë` nanjx`. "[h s`u l`gnc`r, hmtë` s`u a`mjt`. Më` s`u a`mjt`. B`g`, më` s`u l`gnc`r." Srntn-sh ch< M`tn< >9.9

 N

O`cums Y`mhms6

A

O`cums S`bbhms6

&

T`kì nkhrt`u!

 N hxprhssë` sjoaûbjkn ê (p=q)]~q-=~p, h rhsubtn ho tnut`b`gjn.

K

dnbî dn bîkj kjn n cn cn ndj ndjro ronç nçë` ë` c` k` k`ms mshq hquh uhmt mth6 h6

C

dnbî dn bîkj kjn n cn cn mh mhgn gnçë çë` ` c` nm nmth thkh khch chmt mth. h.

^uhstë` :/>9 - Qnkj`kïmj` Bûgjk` M` [bjch 5/>9 cn nubn 4 së` chdjmjc`s Nrguohmt`s. ^unb n nbthrmntjvn quh rhprhshmtn n chdjmjçë` k`rrhtn ch Nrguohmt`s0 M`tn< 9.9

 N

A

Nrguohmt` ê uon rhsp`stn n uon chthrojmncn phrgumtn/quhstj`mnohmt` Xo nrguohmt` ê uon shquìmkjn ch pr`p`sjçøhs hmtrh ns qunjs uon chbns ê n k`mkbusë` h ns chonjs së` prhojssns.

&

[bjch 5/>9 cn nubn 4

K

Nrg rguo uohm hmtt` ê uo uo k`m k`mllum umtt` ch ch shmthmçns utjbjzncns pnrn rhsp`stn n uo chthrojmnc` quhstj`mnohmt`

C

@s nrg nrguo uohm hmt` t`ss tho tho hoan hoansn snoh ohmt mt`, `, ndjrono h k`opr`vno sh ns pr`p`sjçøhs bûgjkns së` tnut`b`gjns, k`mtrncjçë` `u k`mtjmgìmkjn

^uhstë` >9/>9 - Qnkj`kïmj` Bûgjk`  Nprhshmtnc`s h chdjmjc`s m` thon 1.8 cn Nubn 8, `s qunmtjdjknc`rhs së` sïoa`b`s utjbjznc`s ho hxprhssøhs quh qunmtjdjkno (ntrjauho vnb`rhs) n chthrojmnc`s hbhohmt`s c` k`mlumt` h trnmsd`rono uon shmthmçn nahrtn ho pr`p`sjçë` h së` utjbjznc`s pnrn hxprhssnr pr`prjhcnchs quh vnbho pnrn t`c`s `s jmcjvïcu`s c` c`oïmj` `u pnrn nbgums jmcjvïcu`s c` c`oïmj`, rhsphktjvnohmth. Ch nk`rc` k`o ` k`mthüc` ojmjstrnc` m` thon 1.8  cn Nubn 8, qunjs së` `s qunmtjdjknc`rhs0    Nmnbjsh ns nbthrmntjvns h nssjmnbh n nbthrmntjvn k`o n rhsp`stn K@QQHSN M`tn< >9.9

 N A

Mhgnçë`, K`mlumçë`, Cjslumçë` Cjslumçë` umjvhrsnb h hxjsthmkjnb

&

T`kì nkhrt`u!

Shxt` Nubn 8 - Shon< 1.8 ‛ qunmtjdjknc`rhs (pg. :)

K

K`mc K` mcjk jkj` j`mn mnbb h Aj Ajk` k`mc mcjk jkj` j`mn mnbb

C

Jopb Jo pbjk jknç nçë` ë` h hq hquj ujvn vnbì bìmk mkjn jn

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