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