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