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Таблица истинности ONLINE
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Таблица истинности для функции ¬P∧(P≡(Q∨¬(R∨¬Q))):
Промежуточные таблицы истинности:¬Q: R∨(¬Q): | R | Q | ¬Q | R∨(¬Q) | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 |
¬(R∨(¬Q)): | R | Q | ¬Q | R∨(¬Q) | ¬(R∨(¬Q)) | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 0 | 1 | 0 |
Q∨(¬(R∨(¬Q))): | Q | R | ¬Q | R∨(¬Q) | ¬(R∨(¬Q)) | Q∨(¬(R∨(¬Q))) | | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 0 | 0 | | 1 | 0 | 0 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | 0 | 1 |
P≡(Q∨(¬(R∨(¬Q)))): | P | Q | R | ¬Q | R∨(¬Q) | ¬(R∨(¬Q)) | Q∨(¬(R∨(¬Q))) | P≡(Q∨(¬(R∨(¬Q)))) | | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
¬P: (¬P)∧(P≡(Q∨(¬(R∨(¬Q))))): | P | Q | R | ¬P | ¬Q | R∨(¬Q) | ¬(R∨(¬Q)) | Q∨(¬(R∨(¬Q))) | P≡(Q∨(¬(R∨(¬Q)))) | (¬P)∧(P≡(Q∨(¬(R∨(¬Q))))) | | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
Общая таблица истинности:| P | Q | R | ¬Q | R∨(¬Q) | ¬(R∨(¬Q)) | Q∨(¬(R∨(¬Q))) | P≡(Q∨(¬(R∨(¬Q)))) | ¬P | ¬P∧(P≡(Q∨¬(R∨¬Q))) | | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности: | P | Q | R | F | | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 0 |
F сднф = ¬P∧¬Q∧¬R ∨ ¬P∧¬Q∧R Логическая cхема:
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности: | P | Q | R | F | | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 0 |
F скнф = (P∨¬Q∨R) ∧ (P∨¬Q∨¬R) ∧ (¬P∨Q∨R) ∧ (¬P∨Q∨¬R) ∧ (¬P∨¬Q∨R) ∧ (¬P∨¬Q∨¬R) Логическая cхема:
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