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Консультация № 178411
15.05.2010, 17:39
45.00 руб.
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Здравствуйте, уважаемые Эксперты. Помогите пожалуйста решить следующую задачу:
Построить таблицу истинности булевой функции
Построить СДНФ, СКНФ, найти минимальную ДНФ.
Построить таблицу истинности булевой функции
Построить СДНФ, СКНФ, найти минимальную ДНФ.
Обсуждение
17.05.2010, 00:54
общий
это ответ
Здравствуйте, Свиридов Алексей Владимирович.
x|y=¬(x⋀y)
x→y=¬x∨y
Значит, (x|¬y)→(y⨁z)=(x⋀y)∨(y⨁z)
y⨁z=y⋀¬z∨¬y ⋀z
(x⋀y)∨(y⋀¬z)∨(¬y ⋀z)
По полученной дизъюнктивной форме легко построить таблицу истинности.
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
СДНФ для этой функции будет ¬x¬yz∨¬xy¬z∨x¬yz∨xy¬z∨xyz.
Знаки конъюнкции для удобства пропущены.
Для получения СКНФ берем все наборы, где значения функции равны 0, в дизъюнкты входят отрицания значений аргументов
СКНФ - (x∨y∨z)(x∨¬y∨¬z)(¬x∨y∨z)(¬x∨y∨¬z)
x|y=¬(x⋀y)
x→y=¬x∨y
Значит, (x|¬y)→(y⨁z)=(x⋀y)∨(y⨁z)
y⨁z=y⋀¬z∨¬y ⋀z
(x⋀y)∨(y⋀¬z)∨(¬y ⋀z)
По полученной дизъюнктивной форме легко построить таблицу истинности.
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
СДНФ для этой функции будет ¬x¬yz∨¬xy¬z∨x¬yz∨xy¬z∨xyz.
Знаки конъюнкции для удобства пропущены.
Для получения СКНФ берем все наборы, где значения функции равны 0, в дизъюнкты входят отрицания значений аргументов
СКНФ - (x∨y∨z)(x∨¬y∨¬z)(¬x∨y∨z)(¬x∨y∨¬z)
Форма ответа
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