Khoos phib tawj science: qhov tseeb lub rooj. Constructing tseeb ntxhuav

Niaj hnub no peb tham txog qhov kev kawm hu ua science. Qhov tseeb cov lus, ntau yam ntawm kev khiav dej num, qhov kev txiav txim ntawm tua - cov no yog cov peb lus nug yooj yim uas peb yuav sim mus nrhiav cov lus teb nyob rau hauv tsab xov xwm.

Feem ntau cov Hoob no yog qhia nyob rau hauv high school, tiam sis muaj ntau cov tub ntxhais kawm yog qhov ua rau to taub yuam kev ntawm ib co nta. Thiab yog hais tias koj yuav mus mob siab kuv lub neej, nws cia li yuav tsis ua li cas tsis muab ib zaug xwb lub xeev ntsuam xyuas nyob rau hauv computer science. Qhov tseeb cov lus, hloov complex kab zauv, qhov kev txiav txim logic teeb meem - nws muaj peev xwm ua tau raws li tag nrho cov pib. Peb tam sim no xav txog nyob rau hauv ntau yam no lub npe thiab pab koj tau txais ntau tshaj cov khoom rau cov tub ntxhais.

lub logic ntawm cov kev kawm

Yuav ua li cas hom ntawm kev kawm - computer science? Qhov tseeb lub rooj - yuav ua li cas los tsim kom tau nws? Yog vim li cas science yog qhov logic? Rau tag nrho cov nqe lus nug no, peb yuav teb nrog koj tam sim no.

Cov ntaub ntawv siv tshuab - nws yog ib tug heev fascinating kev kawm. Nws yuav tsis tau yooj yim nyob rau hauv lub neej niaj hnub, vim hais tias txhua yam uas nyob ib ncig peb, ib txoj kev los sis lwm, txog rau lub computer.

Fundamentals ntawm logic ntawm science yog theem nrab tsev kawm ntawv cov xib fwb nyob rau hauv qhov kev kawm no. Tseeb ntxhuav, kev siv, simplifying kab zauv - tag nrho cov no yuav tsum piav qhia rau tus xib fwb ntawm lub computer science. Qhov no science yog tsim nyog kiag li nyob rau hauv peb lub neej. Saib zoo, txhua yam yog kev kawm rau tej kev cai lij choj. Koj cog pob, nws ya mus li, tab sis, ces poob rov qab mus rau lub ntiaj teb, nws yog vim hais tias ntawm cov kev cai ntawm physics thiab cov rog ntawm lub ntiajteb txawj nqus. Niam cooks lub kua zaub thiab ntxiv ntsev. Yog vim li cas thaum peb noj, peb tsis tuaj nyob rau hauv lub grain? Heev tsuas, lub ntsev yaj nyob rau hauv dej, kev kawm rau cov kev cai ntawm Science News for KIDS.

Tam sim no xyuam xim rau txoj kev uas koj tham.

• "Yog hais tias kuv yuav mus coj koj tus miv rau ib tug Veterinary lub tsev kho mob, nws yog yuav tsum tau txhaj tshuaj tiv thaiv."
• "Hnub no yog ib tug heev nyuaj hnub, vim hais tias koj yuav tsum mus saib."
• "Kuv tsis xav mus rau lub tsev kawm ntawv, vim hais tias hnub no yuav yog ib lub colloquium", thiab hais txog.

Txhua yam koj hais, nco ntsoov mus ua raws li cov kev cai ntawm logic. Qhov no siv tau ob qho tib si rau ua lag ua luam thiab mus tus phooj ywg kev sib tham. Nws yog vim li no nws yog tsim nyog los nkag siab txog cov kev cai ntawm logic, tsis txhob ua nyob hauv random, thiab tso siab tau nyob rau hauv lub sij hawm ntawm cov txheej xwm.

zog

Nyob rau hauv thiaj li yuav ua qhov tseeb lub rooj rau lub tswv yim ua hauj lwm koj yuav tsum tau paub lub logic zog. Yuav ua li cas yog nws? Logic muaj nuj nqi muaj ib co tsiaj, uas yog cov nqe lus (muaj tseeb los yog cuav), thiab cov nqi ntawm cov nuj nqi rau nws tus kheej yuav tsum tau muab peb cov lus teb rau lo lus nug: "Qhov qhia yog muaj tseeb los yog cuav."

Tag nrho cov kab zauv muaj cov nram qab qhov tseem ceeb:

• Yeej muaj tseeb los yog cuav.
• T los yog F.
• 1 los yog 0.
• Plus los yog rho tawm.

Ntawm no, muab nyiam mus rau ib tug txoj kev uas yog ntau yooj yim rau koj. Nyob rau hauv thiaj li yuav ua ib qhov tseeb cov lus, peb yuav tsum tau sau tag nrho cov ob peb ua ke ntawm cov tsiaj ntawv. Lawv tus xov tooj yog xam los ntawm cov mis: 2 mus rau lub hwj chim n. Cov tshwm sim ntawm xam - lub xov tooj uas tau ob peb ua ke ntawm lub nce mus nce los n nyob rau hauv cov mis qhia tus xov tooj ntawm cov tsiaj ntawv nyob rau hauv lub mob. Yog hais tias cov kev qhia muaj ib tug ntau ntawm cov tsiaj ntawv, koj siv tau cov tswvyim rau koj tus kheej los yog ua rau ib tug me me rooj nrog tus erection ntawm ob mus rau lub hwj chim.

Tag nrho logic zog yog xya los yog bonds txuas qhov qhia:

• Npaug (tau).
• Tsis tas li ntawd (disjunction).
• Corollary (implication).
• Equivalence.
• Inversion.
• Sheffer stroke.
• Pierce xub.

Tus thawj lag luam, uas muaj tuaj nyob rau hauv daim, yog hu ua "cov zajlus kom sib npaug." Nws yuav tsum tau muab sau graphically nyob rau hauv daim ntawv ntawm ib tus inverted lub zuam, tej yam tshwm sim & los yog *. Cov kauj ruam thib ob nyob rau hauv peb daim ntawv teev - zajlus kom tas li ntawd, graphically qhia raws li ib tug zuam +. Lub implication yog ib zajlus kom tsim nyog tau, qhia los ntawm ib tug xub taw los ntawm lub tej yam kev mob nyob rau hauv qhov kev tshawb nrhiav. Equivalence yog denoted los ntawm ob-txoj kev xub, cov nuj nqi muaj ib tug yeej muaj tseeb tus nqi xwb nyob rau hauv tus neeg mob ntawm code ob qhov tseem ceeb coj ib tug nqi ntawm "1" los yog "0". Inversion yog ib zajlus kom negation. Sheffer stroke muaj nuj nqi no yog hu ua, uas tsis muaj txoj kev tau thiab cov zajlus kom tsis - muaj nuj nqi, negating lub disjunction.

Basic binary zog

Zajlus kom tseeb rooj yuav pab tau nrhiav tau ib lo lus teb rau qhov teeb meem, tab sis koj yuav tsum nco ntsoov rau hauv lub rooj ntawm binary zog. Nyob rau hauv seem no, lawv yuav tsum tau muab.

Tau (npaug). Yog hais tias ob tug kab zauv uas muaj tseeb, qhov tshwm sim uas peb tau txais qhov tseeb, nyob rau hauv tag nrho cov lwm tus neeg mob peb tau txais ib cov lus dag.

Nws zoo li ib lub rooj, koj paub, ces muaj yog tsis muaj yuav tsum tau coj nws mus rau tag nrho cov qauv. Nyob rau hauv daim duab saum toj koj yuav saib tau nyob rau hauv tej rooj plaub, qhov tshwm sim yog sib npaug zos rau ib tug.

Tshwm - pw rau tom cov zajlus kom tas li ntawd peb tsuas yog nyob rau hauv rooj plaub ob cuav inputs.

Cov zajlus kom tsim nyog tau ntawm ib tug tsis muaj tseeb tshwm sim thaum tus mob no yeej muaj tseeb, raws li ib tug yuav tau txais - ib tug dag. Koj muaj peev xwm muab ib qho piv txwv ntawm lub neej: "Kuv xav mus yuav qab zib, tab sis hauv lub khw twb kaw," yog li ntawd, lub qab zib thiab tsis yuav.

Equivalence yog muaj tseeb xwb nyob rau hauv cov ntaub ntawv ntawm tib yam tswv yim tseem ceeb. Hais tias yog, thaum nkawg "0, 0" los yog "1, 1".

Nyob rau hauv cov ntaub ntawv ntawm inversion tag nrho cov elementary, Yog hais tias lub tswv yim yog ib tug yeej muaj tseeb qhia, nws yog hloov dua siab tshiab rau tsis muaj tseeb, thiab vice versa. Nyob hauv daim duab koj yuav pom li cas nws yog qhia graphically.

Schiffer bar cov zis yuav muaj ib tug tsis muaj tseeb tshwm sim yog hais tias muaj ob tiag tiag kab zauv.

Nyob rau hauv cov ntaub ntawv ntawm cov zajlus kom tsis muaj nuj nqi yuav tsum muaj tseeb xwb nyob rau hauv rooj plaub yog hais tias tus tswv yim peb muaj xwb tsis muaj tseeb kab zauv.

Nyob rau hauv dab tsi thiaj li yuav ua zajlus kom ua hauj lwm

Nco ntsoov tias qhov kev siv ntawm qhov tseeb ntxhuav thiab simplification ntawm kab zauv yog tau tsuas yog thaum qhov tseeb kev txiav txim ntawm kev ua hauj lwm. Nco ntsoov ib theem zuj zus nyob rau hauv uas lawv yuav tsum tau nqa tawm, nws yog ib qho tseem ceeb heev kom tau qhov tseeb tshwm sim.

• zajlus kom negation;
• npaug;
• Tsis tas li ntawd;
• kev tshawb nrhiav;
• equivalence;
• tsis kam muab kev npaug (Sheffer stroke);
• tsis kam muab ntxiv (xub Pierce).

Piv txwv li №1

Peb tam sim no qhia tau xav txog cov piv txwv ntawm constructing ib qhov tseeb lub rooj rau lub 4 zog. Koj yuav tsum paub nyob rau hauv uas tus neeg mob F = 0 nyob rau hauv kab zauv: Nea + B + C * D

Lo lus teb rau qhov hauj lwm no yuav tsum yog tus hloov lwm lub tsev ntawm lub nram qab no ob peb ua ke: "1, 0, 0, 0", "1, 0, 0, 1" thiab "1, 0, 1, 0". Raws li koj tau pom, ua rau hauv lub rooj heev tsuas qhov tseeb. Ib zaug dua kuv xav kos koj cov xim rau cov kev txiav txim ntawm cov kev ua. Nyob rau hauv lub cov ntaub ntawv, nws yog raws li nram no:

1. Cov inversion ntawm cov thawj yooj yim qhia.
2. Cov tau ntawm lub thib peb thiab thib plaub kab zauv.
3. Disjunction thib ob qhia nrog rau cov kev tshwm sim ntawm yav dhau los laij.

Piv txwv li №2

Tam sim no peb saib lwm txoj hauj lwm uas yuav tsum tau rau kev tsim kho ntawm ib tug qhov tseeb lub rooj. Laij (piv txwv raug coj los ntawm lub tsev kawm ntawv cov hoob kawm) tej zaum yuav muaj cov zajlus kom muaj teeb meem raws li siv. Ib tug nyuag saib ib tug ntawm lawv. Koj Vanya txhaum ntawm tub sab tub nyiag lub pob, yog tias koj paub li nram qab no:

• Yog hais tias Vanya tsis txhob ua tub sab los yog tub sab tub nyiag Peter, ces Sergei koom nyob rau hauv lub tub sab tub nyiag.
• Yog hais tias Ivan yog tsis muaj txim txhaum, thiab Sergei tsis txhob ua tub sab hauv lub pob.

Peb paub cov cim: Kuv - Ivan nyiag lub pob; P - Peter nyiag; C - Sergei nyiag.

Nyob rau hauv no, peb yuav ua tau kab zauv: F = ((nei + R) implication C) * (nei implication HEC). Peb yuav tsum tau cov kev xaiv, nyob qhov twg cov nuj nqi yuav siv sij hawm qhov tseeb tus nqi. Tom ntej no, tsim ib lub rooj, vim hais tias qhov no muaj nuj nqi yog li ntau li ntau 7 txiav txim, nws yuav tsum tau rho. Peb yuav tsum tau tsuas yog los ntawm lub tswv yim cov ntaub ntawv thiab kev soj ntsuam.

Nco ntsoov tias nyob rau hauv qhov teeb meem no peb muaj, es tsis txhob "0" cim thiab "1" siv cov ntxiv thiab rho tawm. Nws kuj siv tau thiab. Peb txaus siab nyob rau hauv ib tug ua ke, nyob qhov twg F = +. Tom qab cais lawv, peb yuav kos cov nram qab no xaus: Vanya koom nyob rau hauv lub tub sab ntawm lub pob, raws li nyob rau hauv tag nrho cov mob qhov twg F yuav siv sij hawm tus nqi +, thiab muaj ib tug zoo nqi.

Piv txwv li №3

Tam sim no peb muab rau koj mus nrhiav tus naj npawb ntawm cov ob peb ua ke thaum F = 1. Cov kab zauv raws li nram no: F = Nea + B * A + Neuve. A rooj ntawm qhov tseeb:

A: 4 ua ke.