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Ответ:
1. Таблицы истинности
a) \( B \land (A \lor B) \)
| A | B | \( A \lor B \) | \( B \land (A \lor B) \) |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 |
б) \( A \land (\overline{B} \lor B) \)
| A | B | \( \overline{B} \) | \( \overline{B} \lor B \) | \( A \land (\overline{B} \lor B) \) |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 |
в) \( B \land (A \lor B \lor C) \)
| A | B | C | \( A \lor B \lor C \) | \( B \land (A \lor B \lor C) \) |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 |
г) \( \overline{A \land B \lor \overline{C}} \)
| A | B | C | \( \overline{C} \) | \( A \land B \) | \( A \land B \lor \overline{C} \) | \( \overline{A \land B \lor \overline{C}} \) |
| 0 | 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 |
| 1 | 1 | 1 | 0 | 1 | 1 | 0 |
