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Консультация № 186019
Обсуждение
13.05.2012, 21:26
общий
это ответ
Здравствуйте, lightcyber!
По условию
(не поздно И хорошее настроение) [$8594$] (телевизор) [$8594$] (ест).
Известно, что он пришёл не поздно и не ест. Значит хорошего настроения у него быть не может, т.к. в этом случае, по вышесказанному, он бы ел. Значит, если настроение бывает либо хорошим, либо плохим, настроение у него плохое.
По условию
(не поздно И хорошее настроение) [$8594$] (телевизор) [$8594$] (ест).
Известно, что он пришёл не поздно и не ест. Значит хорошего настроения у него быть не может, т.к. в этом случае, по вышесказанному, он бы ел. Значит, если настроение бывает либо хорошим, либо плохим, настроение у него плохое.
14.05.2012, 01:17
общий
14.05.2012, 01:19
Ну так и выше написанное - строгое доказательство. Или имеется в виду, что требуется именно полная таблица истинности для всех четырёх высказываний?
Выше написанное формально:
c = пришёл не поздно,
g = хорошее настроение,
t = телевизор,
e = ест.
Известно, что следующие два высказывания истинны:
(c [$8743$] g) [$8594$] t,
t [$8594$] e.
Таблица истинности для импликации:
.
Т.к. t [$8594$] e истинно и он не ел(e=F), то t=F.
Т.к. истинно (c [$8743$] g) [$8594$] t и t=F, то (c [$8743$] g)=F.
Из таблицы истинности для конъюнкции:
,
и того, что c=T, заключаем, что g=F.
Выше написанное формально:
c = пришёл не поздно,
g = хорошее настроение,
t = телевизор,
e = ест.
Известно, что следующие два высказывания истинны:
(c [$8743$] g) [$8594$] t,
t [$8594$] e.
Таблица истинности для импликации:
.Т.к. t [$8594$] e истинно и он не ел(e=F), то t=F.
Т.к. истинно (c [$8743$] g) [$8594$] t и t=F, то (c [$8743$] g)=F.
Из таблицы истинности для конъюнкции:
,и того, что c=T, заключаем, что g=F.
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