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