Informatics. Conversion logic kab zauv

Qhov kev thov ua hauj lwm yuav tsum xyuas nyob rau hauv kom meej lo lus nug txia zajlus kom kab zauv. Nyob rau hauv tas li ntawd, peb xav kom koj coj ib tug luv luv kawg rau logic, uas yuav hais txog qhov yooj yim cov kev cai thiab cov tswv yim. Hloov cov zajlus kom kab zauv - nws yog ib tug heev nyuab cov txheej txheem, yog hais tias tsis paub nrog tag nrho cov nuances ntawm cov kev kawm.

Informatics Hoob no yuav zoo li yooj yooj yim thiab muab Library, Yog hais tias koj ua tib zoo nyeem no tsab xov xwm thiab kawm txog cov kev cai thiab kev cai ntawm transformation, daws teeb meem, thiab yog nqus tau schemes. Peb muaj rau pib txoj cai tam sim no.

logic ntawm science

Basic logic - qhov no yog nej ib tug yooj yim, rau qhov nws yog sau li ntawd, ntau phau ntawv. Qhov tsab xov xwm yuav sib tham txog cov kev qhia tswj cov kev cai ntawm transformation ntawm cov zajlus kom kab zauv, uas yog, cov ntaub ntawv yog lub feem ntau cos thiab concentrated. Nws yog tsim nyog los xav txog qhov ntau muaj txiaj ntsim xam technologies thiab lub tsev schemes.

Yuav pib nrog dab tsi logic thiab zoo li cas yog nws rau? Nws yog ib qho tseem ceeb yuav tau nco ntsoov hais tias qhov no yog ib tug science uas tshuaj xyuas cov ntaub ntawv thiab cov hau kev ntawm kev xav. Txhua yam uas peb pom tau, hnov los yog tsis, raws li cov kev cai lij choj. Peb pov pob los ntawm ib tug qhov siab - nws yeej ib txwm yoov cia li raug cov kev cai ntawm physics. Brew rau thaum sawv ntxov kas fes, ntxiv qab zib thiab qhuav tshuaj instantly yaj nyob rau hauv dej, raws li txoj cai ntawm physics. Peb yog nyob rau hauv kev sib tham nrog cov phooj ywg, qhia lawv cov kev npaj: "Yog hais tias kuv zoo tiv thaiv kev ua hauj lwm, koj tau txais cov diploma", "kuv tsis tau mus txog ntawm lub tsheb, raws li nws kho." Yog tsis muaj noticing, peb muaj tag nrho cov ntawm peb tej lus, nws yog los ntawm logic thiab nws cov kev cai. Yog li ntawd yog vim li cas science yog qhov logic? Ntawm cov hoob kawm, kev paub txog nws cov kev cai, koj yuav tsum tau los yog txiav txim lub sij hawm ntawm ib qho kev vim hais tias lawv tsis tas yuav ua ntawm random thiab yuav raug.

Txawm tias kev xav yog nej ib tug complex txheej txheem, txawm li cas los, nws yuav tsum tau muab faib mus rau hauv ib co Cheebtsam, los yog es, rau hauv daim ntawv (nrog rau cov kev pab uas muaj ib qho kev qhia ntawm kev xav):

• tswv yim;
• cov nqe lus;
• kev xav;
• pov thawj.

Peb kuj muaj rau koj mus rau cov zajlus kom zog thiab txia zajlus kom kab zauv. Cov ntaub ntawv siv tshuab yuav ua tau rau koj muaj kev lom zem thiab yooj yim heev kawm, yog tias koj nyeem qhov tsab xov xwm kom zoo zoo.

zajlus kom zog

Tam sim no peb muaj mus ntsib nrog tus logic zog. Feem ntau nyob rau hauv lub pib ntawm lub unified lub xeev ntsuam xyuas nyob rau hauv Part B thoob plaws paub tab rau converting logic kab zauv rau hauv hais txog zauv Team sib. Lawv yuav tsis tau solved tsis paub txog ntawm lub logic zog.

Yuav ua li cas yog lub ntsiab hauj lwm ntawm no science? Ntawm cov hoob kawm, txoj kev tshawb no ntawm cov zajlus kom kab zauv (ob txoj thiab yooj yim). Yuav ua li cas yog ib tug yooj yim lub taub Tawvv? Los ntawm cov phiajcim zoo tib yam, uas yog vim lub ligaments, uas yog lub npe hu ua zog.

Tag nrho cov muaj tsib cords:

• inversion (ie, negation, los ntawm kev siv no muaj nuj nqi, koj yuav tau txais cov ntawv qhia, contrary rau qhov no: Kuv mus rau qhov tsos hnub no - hnub no kuv yuav tsis mus rau qhov tsos);
• disjunction (qhov no muaj nuj nqi yog feem ntau xa mus rau raws li cov zajlus kom tas li ntawd, nyob rau hauv thiaj li yuav ua kom nws ntshiab, muab ib tug piv txwv yooj yim ntawm lub neej: "Yog hais tias kuv muaj ib tug mob taub hau los yog lub plab, ces kuv yuav tsis mus rau lub tsev kawm ntawv" - qhov no qhia yog muaj tseeb, yog tias coj mus rau hauv tus account tsawg kawg yog ib tug ntawm cov uas yuav tsum tau );
• tau (feem ntau xa mus rau raws li ib tug muaj kuab ua lej khu: "Yog hais tias kuv mam li ntxuav tais diav thiab ua zaj lus qhia, ces mus rau ib tug taug kev nrog cov phooj ywg" - qhov no qhia yuav muaj tseeb yog tias ob tug mob yog npaum li cas mus rau hauv tus account);
• lub implication (nyob rau hauv lub logic ntawm no muaj nuj nqi no yog hu ua los ntawm cov nram qab no, hmoov tsis, nws yog tsis yooj yim sua los qhia lub neej qhov teeb meem no; cuav muaj nuj nqi yuav tsum yog ib yam dab tsi xav ua tab sis ho tsis ua hauj lwm, nyob rau hauv lwm tus neeg mob, cov nuj nqi yuav tsis muaj tseeb);
• equivalence (los yog koob pheej ntawm lawv yog hais tias tus ob nqe lus no muaj tseeb los yog cuav, qhov tshwm sim uas peb tau txais qhov tseeb).

Nws yog ib qho tseem ceeb kom nco ntsoov tias nyob rau hauv computer science, tej yam yooj yim qhia yog denoted los ntawm ib tug capital tsab ntawv ntawm lub Latin niam ntawv. Tom ntej no, nws yog tsim nyog los nco ntsoov qhov tseeb lub rooj rau txhua muaj nuj nqi. Thov nco ntsoov tias nws tsis yog tsim nyog los cim es yuav tsuas to taub txog cov kev khiav dej num.

qhov tseeb cov lus

tau

Tus thawj qhia (A)	Qhov thib ob qhia (B)	Tshwm (C)
L	L	L
thiab	L	L
L	thiab	L
thiab	thiab	thiab

disjunction

A	Cov	C
L	L	L
thiab	L	thiab
L	thiab	thiab
thiab	thiab	thiab

inversion

A	Cov
thiab	L
L	thiab

implication

A	Cov	C
L	L	thiab
thiab	L	L
L	thiab	thiab
thiab	thiab	thiab

equivalence

A	Cov	C
L	L	thiab
thiab	L	L
L	thiab	L
thiab	thiab	thiab

Nyob rau hauv tas li ntawd, nws yog ib qho tseem ceeb rau koj nco ntsoov qhov tseeb hais tias cov lus dag nyob rau hauv lub logic qhia los ntawm tus xov tooj 0, thiab muaj tseeb qhia - lub tus nab npawj 1. yooj yim rau koj, koj yuav thov tau thiab ntxiv rau los yog rho tawm kos npe rau. Xyuam xim rau lub fact tias cov tsis muaj tseeb thiab yeej muaj tseeb qhia nyob rau hauv lub tswv yim ntxhuav cim nrog cov tsiaj ntawv "L" thiab "kuv" feem.

tsev

Ua ntej cov tswv yim mus rau lub hloov dua siab tshiab ntawm cov zajlus kom kab zauv yuav tsum tau raws li lawv tus kheej siv. Tej compound los yog, raws li tau hais tias ua ntej lawm, complex qhia muaj ob qhov chaw:

• nqi uas yog denoted los ntawm cov tsiaj ntawv ntawm lub Latin tsiaj ntawv;
• Tej yam tshwm sim uas qhia muaj nuj nqi thiab muaj kev cob cog rau txhua lwm yam yooj yim cov kab zauv.

Sau ib qho kev qhia nyob rau hauv cov lus ntawm algebra ntawm logic? Yuav kom ua li no, koj yuav tsum tau ua ob peb yam:

• muab tag nrho hais rau tej yam yooj yim cov kab zauv;
• cov tsiaj ntawv txhais cov ntsiab;
• highlight qhov link ntawm tej yam yooj yim cov kab zauv;
• sau lub resulting qhia nrog tus cim tshwj xeeb ntawm lub algebra ntawm logic.

Peb qhia tau xav txog ib tug piv txwv yooj yim: (Z * F = 5, los yog Z * F = 4) thiab (Z * F yog tsis sib npaug zos rau 5 los yog Z * F yog tsis sib npaug zos rau 4). Nws yog tsim nyog los hloov rau lub zog 2. Tom qab hais tias, peb tau txais cov kev qhia (4 los yog 5 = 4 = 4) thiab (4 yog tsis sib npaug zos rau 5 los sis 4 yog tsis sib npaug zos rau 4). Tom qab lub lag luam, peb yuav tsum ntsiab qhov qhia thiab cov kev sib raug zoo ntawm lawv, yuav tsum tau npaj raws li nram no: (Z los yog F) thiab (tsis Z los yog F). Tom qab ntawd, peb yuav tsum tau hloov no cov ntaubntawv povthawj siv, hloov lub qhov tseem ceeb nqe lus. Nyob rau hauv cov ntaub ntawv uas, yog hais tias tus qhia yog muaj tseeb, ces nws yog tsim nyog los hloov 1, txwv tsis pub - 0. Peb tau txais: G = 1 thiab 1. Tom qab qhov tsim nyog suav, peb muab tau cov kev tshwm sim: G = 1, uas yog ib tug complex qhia yog muaj tseeb.

kev cai

Tam sim no peb caw koj mus xav txog qhov kev cai ntawm logic thiab cov zajlus kom kab zauv transformation cai. Nws yog ib qho tseem ceeb hais tias tej zajlus kom qhia yuav tsum hloov dua siab tshiab mus rau lwm lub siv cov kev cai ntawm logic. Tam sim no peb muaj ib tug los ze zog saib tag nrho kaum tus cai.

Thawj rau peb daim ntawv teev - lub "txoj cai ntawm ob negation." Hais tias yog, qhov qhia "tsis (tsis A)" yuav tsum tau qhov qhia txog "A".

Communicative txoj cai yog nyob rau hauv kev kawm txog zauv, nco ntsoov nws yooj yim heev. A + B = B + A, A * B = B * A.

Sib koom ua ke txoj cai - (D + E) + F = (D + F) + E, tib txoj cai siv rau cov zajlus kom sib npaug.

Faib txoj cai - nws yog ib lub tsev qhib parenthesis. Piv txwv li: (A + B) * C = (A * C) + (B * C).

De Morgan txoj kev cai: tsis muaj (A + B) = * Nea Neuve, tsis (A * B) + = Hea Hnpl, Hea AimplikatsiyaV = + B, tsis (AimplikatsiyaV) = A * Neuve.

Idempotency: X + X = C los yog C = C *.

constants Exception: X = 1 + 1 + X 0 = X; X * 1 = X, X * 0 = 0.

Tom ntej no peb xaiv raws li txoj cai ntawm contradiction, los ntawm cov nram qab no, peb yuav hais tias cov nram qab no kab zauv: V * = 0 Neuve.

Lub logic yog thiab haum txoj cai, uas nyob rau hauv kev xyaum raws li nram no: C + (C * D) = C los yog C * (C + D) = C.

Nws tseem ceeb heev kom nco ntsoov zajlus kom kab zauv hloov dua siab tshiab txoj cai zam: (P * E) + (HEC * E) = E los yog (C + E) * (HEC + E) = E.

Yog hais tias koj saib nyob rau hauv kev nthuav dav ntawm thiab nco ntsoov tag nrho cov kev cai nyob rau hauv seem no, cov teeb meem nrog rau cov transformation yuav tsis tshwm sim. Attendance tseem ceeb yog qhov kev txiav txim ntawm tua. Muab qhov khoom ntau xim rau kom muab faib rau kev khiav dej num ntawm kev txiav txim - yog tus yuam sij rau qhov tseeb tov ntawm qhov teeb meem.

Cov kev cai thiab kev cai ntawm transformation thiab simplification, qhov kev txiav txim ntawm cov kev ua, piv txwv

Zajlus kom txoj cai lij choj thiab cov kev cai rau converting zajlus kom kab zauv uas yooj yim heev kom nco ntsoov. Yog hais tias koj tsis ntseeg qhov tseeb ntawm txawm ib tug ntawm lawv, ces mus saib rau koj tus kheej. Ua li no, koj yuav tsum siv 10 feeb ntawm koj lub sij hawm thiab ua qhov tseeb lub rooj rau ib lub teb.

Tam sim no peb qhia mus xav txog cov kev cai ntawm logic thiab pom kev cai ntawm cov zajlus kom kab zauv nrog tej piv txwv. Qhov no yog tsim nyog nyob rau hauv thiaj li yuav kom kho tus tau txais kev txawj ntse. Them kev mloog kom qhov kev txiav txim theem zuj zus.

Peb yuav muab: C + (HEC * E). Nws yog tsim nyog los piv cov kev qhia. Tus thawj tshaj plaws uas peb muaj los qhib qhov nkhaus. Tom qab ntawd peb tau lub nram qab no qhia: (C + HEC) * (C + E). Nws yuav tsum tau muab sau tseg tam sim ntawd hais tias cov zajlus kom tas li ntawd ntawm ob opposite nqe lus muab rau peb qhov tseeb. Yuav ua li cas peb tau txais raws li ib tug tshwm sim ntawm: 1 * (C + E). Dua qhib lub nkhaus: (1 * C) + (1 + E). Tam sim no ib zaug dua peb nco ntsoov cov kev cai thiab tau txais ib qho lus teb: C + E.

Raws li koj twb pom, txhua yam yog yooj yim heev. Yuav kom daws tau cov teeb meem no yuav tsum nco ntsoov cov kev cai uas tau teev tseg nyob rau hauv lub yav dhau los seem. Peb muaj rau koj tsiv mus daws tau logic teeb meem, raws li qhov no ua hauj lwm yog ib tug me ntsis ntau tham yav dhau los.

Lub rooj sib tham txoj kev sib tw

Peb tau ntsib nrog cov qauv rau kev kawm hu ua "logic", lub transformation ntawm cov zajlus kom kab zauv, peb luv luv saib cov kev cai uas tau teev tseg. Cov feem ntau nyuaj paub tab nrog cov kev npaj ntawm cov zajlus kom kab zauv - qhov no ua hauj lwm. Nws yog ib qho tseem ceeb yuav tau nco ntsoov hais tias lawv muaj peev xwm yuav daws tau nrog kev pab los ntawm cov lus sib cav, cov conversion qhia los yog lub rooj txoj kev. Peb qhia tau xav txog ib tug ntawm lawv nyob rau hauv kom meej.

Peb cov tub hluas (Cyril, Anton thiab pob txha) twb nyob rau hauv tib lub chav tsev. Mam li nco dheev Niam tawm ntawm lub chav ua noj los hnov lub suab ntawm cov tawg khob. Nws khiav mus rau nws cov tub thiab hais tias, "Leej twg ua li no?" Cov lus teb yog raws li nram no: Kirill hais tias lub khob tau tawg tsis muaj cov pob txha, thiab Anton; Anton hais tias nws puas tau Kostya es tsis txhob Cyril; Kostya hais tias lub culprit yog tsis Anton. Peb paub tias ib tug neeg tau ib tug ntawm cov tub hluas hais rau nws niam qhov tseeb. Koj yuav tsum tau xyuas seb leej twg broke lub khob.

Txawj, cov lus teb Cyril thiab Anton nyias hais txawv nyias, raws li zoo li Cyril Kostya. Thiaj li, lawv yuav tsis ob leeg yuav muaj tseeb. Peb ua raws li nram no xaus - Anton thiab Kostya hais qhov tseeb, thiab Cyril yog lub culprit ntawm lub tawg khob. Qhov no txoj kev siv meditation. Tam sim no browsing kev daws rau qhov teeb meem qub, tsuas yog los ntawm txoj kev hloov siab los ntseeg qhia. Yuav pib, peb ua kom paub abbreviations:

• KR - khob tawg Cyril;
• Thiab - lub khob no lawm Anton;
• K - lub perpetrator ntawm tus pob txha.

Tus tub teb hais tias:

• Cyril - lub caj dab, A;
• Anton - Necro, K;
• Kostya - Tsis.

Kev ua kom ib qho kev qhia, yog tias Kostya tau dag, thiab Cyril thiab Anton hais qhov tseeb: HEK * A = 1 thiab K * necro = 1 thiab A = 1. Converting qhia, peb tau txais ib tug contradiction: 0 = 1. Peb assumption yog tsis muaj tseeb, nws yog tsim nyog los xyuas lwm cov kev xav.

Yog hais tias peb hais tsis xav hais tias Cyril tau dag, thiab Anton thiab Kostya hais rau nws niam qhov tseeb, ces cov hauv qab no qhia: K * Nea = 1 thiab K = 1 * Necro thiab Nea = 1. Simplifying cov kev qhia uas peb tau txais KR * * Nea HEK = 1. Qhov no qhia tias peb assumption yog tseeb, tseeb, Cyril tsoo ib khob thiab dag rau kuv niam.

Tabular txoj kev daws

Xam tias yog cov kev cai ntawm logic thiab cov transformation ntawm cov zajlus kom kab zauv, yeej pab peb tiv nrog neeg ua hauj lwm, uas yog nyob rau hauv lub yav dhau los seem. Tam sim no peb qhia mus xav txog qhov tabular txoj kev daws mus rau nram qab no qhov teeb meem.

Dmitry, Anatoly thiab Lyudmila yog kiv cua ntawm koj xov xwm, peb yeej paub hais tias tag nrho cov nyob rau hauv ntau qhov chaw ntawm lub ntiaj teb no thiab muaj ntau yam uas koj nyiam. Txiav txim seb leej twg nyob rau hauv dab tsi nroog thiab dab tsi xav. Cov nram qab no muaj tseeb:

• Dmitri twb tsis tau mus Paris, thiab Lyudmila - nyob rau hauv lub nroog Loos;
• ib tug uas nyob rau hauv Paris, tsis zoo li ib tug yeeb yam;
• ib tug txiv neej uas nyob rau hauv lub nroog Loos, tau suab;
• Lyudmila aversion rau lub neeg dhia tes.

Nyob rau hauv thiaj li yuav daws tau qhov teeb meem, koj yuav tau ua ib lub rooj me me.

Fabkis	Ltalis	United States		vocals	tus neeg dhia tes	movie
			Dmitry
			Anatoly
			Lyudmila

Txuas ntxiv los ntawm koj lub siab tshaj plaws yog xav tau. Txhua yam uas koj tau nyeem nyob rau hauv qhov mob yuav tsum tau xav txog nyob rau hauv lub rooj no. Nyob rau hauv lub chav kawm ntawm sau nws ua clear cov nram qab no:

• Dmitry nyob hauv Rome thiab koom nrog cov suab;
• Anatoly nyob hauv Paris thiab feem ntau tuaj koom lub caij ua si;
• Lyudmila yog ib tug kiv cua loj ntawm xinesmas, uas nyob hauv Tebchaws Meskas.

Them koj qhov kev xav rau qhov tseeb tias qhov tseeb qhia yog cim los ntawm tus xov tooj 1, thiab qhov tsis muaj tseeb yog 0. Thaum sau daim ntawv nrog cov cim no, koj yuav pom cov lus teb rau lo lus nug uas koj nyiam.

Microcircuit

Piv txwv ntawm kev hloov ntawm cov zajlus kom pom, uas peb tau xav, yog txoj hauv kev xub pom zoo. Nyob rau ntawm daim pib ntawm lub xeev kev ntsuam xyuas, tus mob yuav raug muab nyob rau hauv tag nrho hauv daim ntawv ntawm lub microcircuit.

Nws yog ib qho tseem ceeb kom paub tias tag nrho cov cuab yeej siv tau raws li cov ntsiab lus ntawm lub ntsiab lus, uas yog, tej yam khoom siv uas ua tau ib qho kev ua haujlwm zoo tib yam nkaus xwb.

Peb twb tau sib tham txog tej kev ua ib yam li lub ntsiab lus (zajlus kom sib npaug). Nws yog feem ntau raug cim los ntawm lub cim &. Qhov kev ua no yog qhov tsim nyog rau qhov muaj nqi ntawm ntau qhov tseem ceeb. Nyob rau hauv daim duab koj pom lub tswv yim ntawm cov kev hloov zauv.

Lub disabunction muaj nuj nqi yog tsim nyog rau kev siv lub disabunction ntawm ib co qhov muaj nqis nkag. Thaum sau ib qho kev qhia, txoj haujlwm no feem ntau yog los ntawm lub cim . Daim duab qhia tias lub tswv yim.

Cov kev hloov ua inversion yog ib qho kev hloov ntawm ib qho kev qhia rau qhov kev tawm tsam. Hauv daim duab koj tuaj yeem pom tias lub tswv yim "tsis" zoo li cas.

Piv txwv ntawm simplification formula # 1

Cov cai tswjfwm kev pom zoo ntawm kev hloov ntawm cov zajlus kom qhia yuav tsum tau kho nyob rau hauv kev xyaum. Nws yog nyob rau hauv kev nrhiav lub hom phiaj no, peb thov kom daws tau nws tus kheej ob qho piv txwv ntawm qhov nyuaj thiab sib piv nrog cov txiaj ntsig ntawm seem no ntawm tsab xov xwm.

Yog hais tias koj tseem tsis tau cim cov qauv rau kev hloov cov kab zauv zaj lus, koj tuaj yeem ua koj tus kheej "ceeb toom" me me. Koj yuav pom tias tsis ntev koj yuav tsis saib nws.

Piv txwv: (X + T) * (notX + T) * (M + notT). Tsis txhob sau dig muag, sim daws qhov piv txwv koj tus kheej.

Hauv kev simplification, peb tau txais cov lus hauv qab no: T * (M + neT) = (T * M) + (T * neT) = (T * neM) + 0 = (T + 0) * (M + 0) = T * M

Raws li koj tau pom, los ntawm qhov tsis ntev thiab qhov cumbersome txoj kev qhia peb tau txais luv luv T * M. Yog hais tias koj tsis tau tswj los daws qhov kev piv txwv no rau koj tus kheej, ces rov qab mus rau qhov chaw uas peb xav txog cov kev hloov ntawm cov zajlus, cov dej num.

Piv txwv ntawm kev simplification ntawm lub mis 2

Hauv seem no, peb xav hais tias koj simplify qhov qhia (E + H) * (E + K). Cia peb los soj ntsuam cov kauj ruam kev daws teeb meem. Ua ntej tshaj, peb yuav tsum qhib qhov khawm, nco ntsoov cov kev ua zauv thaum pib. Yog li, peb tau txais cov lus qhia nram qab no: E * E + E * K + H * E + H * K. Tsis tas li ntawd, peb paub tias qhov tshwm sim uas tau tshwm sim muaj EF, peb nco qab txog txoj cai ntawm kev ua haujlwm thiab hloov cov lus cim: E + E * K + H * E + H * K. Cov kauj ruam tom ntej yog los hloov lub tshuab E + E * K, siv lub bracketing ntawm tus E thiab cov cuab yeej: A + 1 = 1. Peb tau txais qhov kev qhia: E + H * E + H * K. Peb mus zoo li cov khoom dhau los thiab nqa tawm ntawm cov nkhaus E. Vim li ntawd, peb tau txais cov lus teb: E + H * K.

Them qhov tseeb tias qhov kev pab tsuas yog zoo nkaus li nyuab thaum xub thawj siab. Kom "nias lawv zoo li cov noob", koj tsuas yog xav kawm cov kev cai lij choj ntawm cov tswv yim.