14. Заполните таблицу истинности выражения: (¬A ∧ ¬B ∨ C) ∧ D.

Таблица истинности для выражения (¬A ∧ ¬B ∨ C) ∧ D: | A | B | C | D | ¬A | ¬B | ¬A ∧ ¬B | (¬A ∧ ¬B) ∨ C | ((¬A ∧ ¬B) ∨ C) ∧ D | |---|---|---|---|----|----|---------|---------------|-------------------| | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | Решение: Выражение (¬A ∧ ¬B ∨ C) ∧ D истинно, только если (¬A ∧ ¬B ∨ C) истинно И D истинно. (¬A ∧ ¬B ∨ C) истинно, если (¬A ∧ ¬B) истинно ИЛИ C истинно. (¬A ∧ ¬B) истинно, если ¬A истинно И ¬B истинно. Ответ: | A | B | C | D | ((¬A ∧ ¬B) ∨ C) ∧ D | |---|---|---|---|-------------------| | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 1 | | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 1 | | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | 0 | | 1 | 0 | 0 | 1 | 0 | | 1 | 0 | 1 | 0 | 0 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | | 1 | 1 | 0 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | 1 |