Tabli cya i stinnosti matematichna tablicya sho shiroko vikoristovuyetsya u matematichnij logici zokrema v algebri logiki chislenni vislovlen dlya obchislennya znachen bulevih funkcij Pid logichnoyu funkciyeyu takozh logichnoyu operaciyeyu u comu vipadku rozumiyetsya funkciya u kotroyi znachennya zminnih parametriv funkciyi i znachennya samoyi funkciyi virazhayut logichnu istinnist Napriklad v dvoznachnij logici voni mozhut prijmati znachennya istina abo hiba t r u e displaystyle true abo f a l s e displaystyle false 1 displaystyle 1 abo 0 displaystyle 0 Tablichne zadannya funkcij zustrichayetsya ne tilki v logici ale dlya logichnih funkcij tablici viyavilisya osoblivo zruchnimi i z pochatku 20 stolittya za nimi zakripilasya cya specialna nazva Zmist 1 Tablici istinnosti dlya osnovnih logichnih operacij 2 Vikoristannya 3 Div takozh 4 Literatura 5 PosilannyaTablici istinnosti dlya osnovnih logichnih operacij RedaguvatiA displaystyle mathbf A nbsp Zaperechennya A displaystyle mathbf lnot A nbsp Tavtologiya displaystyle top nbsp Protirichchya displaystyle bot nbsp 0 1 1 01 0 1 0A displaystyle mathbf A nbsp B displaystyle mathbf B nbsp Kon yunkciya AND A B displaystyle A land B nbsp Diz yunkciya OR A B displaystyle A lor B nbsp Viklyuchna diz yunkciya XOR A B displaystyle A oplus B nbsp Ekvivalentnist XNOR A B displaystyle A leftrightarrow B nbsp Implikaciya A B displaystyle A rightarrow B nbsp Obernena implikaciya A B displaystyle A leftarrow B nbsp Shtrih Shefera NAND A B displaystyle A B nbsp Strilka Pirsa NOR A B displaystyle A downarrow B nbsp 0 0 0 0 0 1 1 1 1 11 0 0 1 1 0 0 1 1 00 1 0 1 1 0 1 0 1 01 1 1 1 0 1 1 1 0 0alternativne poznachennya A B displaystyle AB nbsp A B displaystyle A B nbsp A B displaystyle A underline lor B nbsp A B displaystyle A overline underline lor B nbsp A B displaystyle A overline land B nbsp A B displaystyle A overline lor B nbsp Vikoristannya RedaguvatiZ vikoristannyam tablic istinnosti mozhna obchisliti znachennya deyakih logichnih viraziv formul cherez znachennya argumentiv sho vhodyat v nih a takozh dovesti ekvivalentnist dvoh formul Napriklad Logichna ekvivalentnist p q p q displaystyle p rightarrow q lnot p lor q nbsp p displaystyle p nbsp q displaystyle q nbsp p displaystyle lnot p nbsp p q displaystyle lnot p lor q nbsp p q displaystyle p rightarrow q nbsp 0 0 1 1 10 1 1 1 11 0 0 0 01 1 0 1 1Z ciyeyi tablici oderzhuyemo sho viraz p q displaystyle p to q nbsp ye ekvivalentnim p q displaystyle neg p lor q nbsp Za dopomogoyu tablic istinnosti mozhna dovoli prosto dovesti sho deyaki formuli ye tavtologiyami tobto prijmayut znachennya Istina pri bud yakih znachennyah argumentiv Napriklad p q r p q p q p r p q p r 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 1 displaystyle begin array c c c c c c c p amp q amp r amp p lor q amp neg p lor q amp p to r amp neg p lor q to p to r hline 1 amp 1 amp 1 amp 1 amp 0 amp 1 amp 1 1 amp 1 amp 0 amp 1 amp 0 amp 0 amp 1 1 amp 0 amp 1 amp 1 amp 0 amp 1 amp 1 1 amp 0 amp 0 amp 1 amp 0 amp 0 amp 1 0 amp 1 amp 1 amp 1 amp 0 amp 1 amp 1 0 amp 1 amp 0 amp 1 amp 0 amp 1 amp 1 0 amp 0 amp 1 amp 0 amp 1 amp 1 amp 1 0 amp 0 amp 0 amp 0 amp 1 amp 1 amp 1 hline end array nbsp Div takozh RedaguvatiMatematichna logika Algebra logiki Chislennya vislovlen Matematichni tabliciLiteratura RedaguvatiAnellis Irving H 2012 Peirce s Truth functional Analysis and the Origin of the Truth Table History and Philosophy of Logic 33 87 97 doi 10 1080 01445340 2011 621702 Posilannya RedaguvatiHazewinkel Michiel red 2001 Truth table Matematichna enciklopediya Springer ISBN 978 1 55608 010 4 Cya stattya potrebuye dodatkovih posilan na dzherela dlya polipshennya yiyi perevirnosti Bud laska dopomozhit udoskonaliti cyu stattyu dodavshi posilannya na nadijni avtoritetni dzherela Zvernitsya na storinku obgovorennya za poyasnennyami ta dopomozhit vipraviti nedoliki Material bez dzherel mozhe buti piddano sumnivu ta vilucheno veresen 2023 Otrimano z https uk wikipedia org w index php title Tablici istinnosti amp oldid 40329942
