- Tabela e saktësisë është
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1. 2. 4. IMPLIKACIONI I GJYKIMEVE
- Kur gjykimi i përbërë formohet prej dy gjykimeve tjera me ndihmën e lidhëzës "nëse . . . , atëherë . . .", thuhet se ajo lidhëz e përcakton veprimin logjik që quhet implikacion [1] . Gjykimi që pason pas fjalës "nëse" quhet supozim (hipotezë, premisë), ndërsa gjykimi pas fjalës "atëherë" quhet konkluzion (tezë, pasojë). Kuptohet, hipoteza është fundamenti në të cilën rëndom bazohet konkluzioni. Kështu është rasti, p .sh. në implikacionet :
- p : Nëse n
N, atëherë n2 ;
- q : Nëse a < 0 dhe b < 0, atëherë a • b > 0 ;
- r : Nëse n
5, atëherë (n2 + 5n -1) 7 ;
- s : Nëse x
6, atëherë log (3x2 - 8) 2 .
- P ë r k u f i z i m i 1.2.4.1. - Implikacioni i dy gjykimeve p, q quhet gjykimi p
q (lexo : nëse p, atëherë q ose nga p rrjedh q ose p implikon q), i cili është jo i saktë kur p është i saktë e q jo i saktë.
- Simboli
është shenja e implikacionit. Tabela e saktësisë së implikacionit është:
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v (p q) |
ose më shkurt
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![{\displaystyle \scriptstyle {\Rightarrow }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb5320e9341c58a8f7d0e74df1fb5234f97a19d3) |
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- S h e m b u l l i 5. - Le të jenë gjykimet : p:
1,5 dhe q : 3,14 . Të caktohen saktësisë e implikacioneve :
p q, p![{\displaystyle \scriptstyle {\Rightarrow }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb5320e9341c58a8f7d0e74df1fb5234f97a19d3) q, q p, q![{\displaystyle \scriptstyle {\Rightarrow }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb5320e9341c58a8f7d0e74df1fb5234f97a19d3) p .
- Z g j i d h j e : Meqë v (p)
![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) , v (q) ![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) do të kemi:
v (p q)![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) , v (p![{\displaystyle \scriptstyle {\Rightarrow }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb5320e9341c58a8f7d0e74df1fb5234f97a19d3) q)![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) , v (q p)![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) , v (q![{\displaystyle \scriptstyle {\Rightarrow }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb5320e9341c58a8f7d0e74df1fb5234f97a19d3) p)![{\displaystyle \scriptstyle {=}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0a664fb934fdecbb413b38ad8f5c7abf1932cc) .
- Duhet theksuar se me negacionin, konjuksionin dhe disjunksionin mund të lidhen në mes tyre dy gjykime çfarëdo, plotësisht të pavarura, kurse në implikacionin e gjykimeve vlera e saktësisë së gjykimit të parë mund të influencojë në vlerën e saktësisë së gjykimit tjetër.
- ↑ Nga fjala latine implicatio - gërshetim, thurje.
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