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