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