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Таблица истинности ONLINE
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Таблица истинности для функции (X1∧X2∧X3)≡¬X2∧(X1∨X3|(¬X2|¬X3)):
Промежуточные таблицы истинности:X1∧X2: (X1∧X2)∧X3: | X1 | X2 | X3 | X1∧X2 | (X1∧X2)∧X3 | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | 0 | | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 1 | 0 | 0 | | 1 | 0 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | 0 | | 1 | 1 | 0 | 1 | 0 | | 1 | 1 | 1 | 1 | 1 |
¬X2: ¬X3: (¬X2)|(¬X3): | X2 | X3 | ¬X2 | ¬X3 | (¬X2)|(¬X3) | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 1 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | 1 |
X3|((¬X2)|(¬X3)): | X3 | X2 | ¬X2 | ¬X3 | (¬X2)|(¬X3) | X3|((¬X2)|(¬X3)) | | 0 | 0 | 1 | 1 | 0 | 1 | | 0 | 1 | 0 | 1 | 1 | 1 | | 1 | 0 | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 | 1 | 0 |
X1∨(X3|((¬X2)|(¬X3))): | X1 | X3 | X2 | ¬X2 | ¬X3 | (¬X2)|(¬X3) | X3|((¬X2)|(¬X3)) | X1∨(X3|((¬X2)|(¬X3))) | | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
(¬X2)∧(X1∨(X3|((¬X2)|(¬X3)))): | X2 | X1 | X3 | ¬X2 | ¬X2 | ¬X3 | (¬X2)|(¬X3) | X3|((¬X2)|(¬X3)) | X1∨(X3|((¬X2)|(¬X3))) | (¬X2)∧(X1∨(X3|((¬X2)|(¬X3)))) | | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
((X1∧X2)∧X3)≡((¬X2)∧(X1∨(X3|((¬X2)|(¬X3))))): | X1 | X2 | X3 | X1∧X2 | (X1∧X2)∧X3 | ¬X2 | ¬X2 | ¬X3 | (¬X2)|(¬X3) | X3|((¬X2)|(¬X3)) | X1∨(X3|((¬X2)|(¬X3))) | (¬X2)∧(X1∨(X3|((¬X2)|(¬X3)))) | ((X1∧X2)∧X3)≡((¬X2)∧(X1∨(X3|((¬X2)|(¬X3))))) | | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
Общая таблица истинности:| X1 | X2 | X3 | X1∧X2 | (X1∧X2)∧X3 | ¬X2 | ¬X3 | (¬X2)|(¬X3) | X3|((¬X2)|(¬X3)) | X1∨(X3|((¬X2)|(¬X3))) | (¬X2)∧(X1∨(X3|((¬X2)|(¬X3)))) | (X1∧X2∧X3)≡¬X2∧(X1∨X3|(¬X2|¬X3)) | | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности: | X1 | X2 | X3 | F | | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 |
F сднф = ¬X1∧¬X2∧X3 ∨ ¬X1∧X2∧¬X3 ∨ ¬X1∧X2∧X3 ∨ X1∧X2∧¬X3 Логическая cхема:
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности: | X1 | X2 | X3 | F | | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 |
F скнф = (X1∨X2∨X3) ∧ (¬X1∨X2∨X3) ∧ (¬X1∨X2∨¬X3) ∧ (¬X1∨¬X2∨¬X3) Логическая cхема:
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