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Консультация № 121060
31.01.2008, 17:24
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Помогите проверить на тожд. равенство путем ан. превращений.
С помощью построения таблички ист. получаеться (тожд. равные), а так - тупик.
¬(а∧c → ¬ (а → b)) = a∧b∧c
И если можно с поисанием законов.
БОЛЬШОЕ СПАСИБО!
С помощью построения таблички ист. получаеться (тожд. равные), а так - тупик.
¬(а∧c → ¬ (а → b)) = a∧b∧c
И если можно с поисанием законов.
БОЛЬШОЕ СПАСИБО!
Обсуждение
Неизвестный
01.02.2008, 02:06
общий
это ответ
Здравствуйте, skynet!
∨ ¬ → ∧
Что было понятно, распишем действия по скобкам
а → b = ¬а ∨ b
¬(¬а ∨ b) = а ∧ ¬b (применили закон де моргана)
а∧c → а ∧ ¬b = ¬(а∧c) ∨ а∧¬b = ¬а ∨ ¬c ∨ а∧¬b
далее используем тождество х ∨ ¬х∧у = х ∨ у, где в качестве х выступает ¬а, в качестве у ¬b и получаем
¬а ∨ ¬c ∨ ¬b
Ну а ¬(¬а ∨ ¬c ∨ ¬b) = a∧b∧c (закон де моргана)
∨ ¬ → ∧
Что было понятно, распишем действия по скобкам
а → b = ¬а ∨ b
¬(¬а ∨ b) = а ∧ ¬b (применили закон де моргана)
а∧c → а ∧ ¬b = ¬(а∧c) ∨ а∧¬b = ¬а ∨ ¬c ∨ а∧¬b
далее используем тождество х ∨ ¬х∧у = х ∨ у, где в качестве х выступает ¬а, в качестве у ¬b и получаем
¬а ∨ ¬c ∨ ¬b
Ну а ¬(¬а ∨ ¬c ∨ ¬b) = a∧b∧c (закон де моргана)
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