Заполните таблицу истинности для логического выражения \(K = M \lor B \land \overline{(M \land C)}\).

Конечно, давай заполним таблицу истинности для логического выражения \(K = M \lor B \land \overline{(M \land C)}\). Вот шаги, которые мы выполним: 1. Вычислим \(M \land C\). 2. Вычислим \(\overline{(M \land C)}\). 3. Вычислим \(B \land \overline{(M \land C)}\). 4. Вычислим \(M \lor (B \land \overline{(M \land C)})\), что и есть \(K\). Давай построим таблицу: | M | B | C | M ∧ C | ‾(M ∧ C) | B ∧ ‾(M ∧ C) | K = M ∨ (B ∧ ‾(M ∧ C)) | |---|---|---|-------|--------|--------------|---------------------------| | 0 | 0 | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 0 | 1 | 0 | 0 | | 0 | 1 | 0 | 0 | 1 | 1 | 1 | | 0 | 1 | 1 | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | 1 | 0 | 1 | | 1 | 0 | 1 | 1 | 0 | 0 | 1 | | 1 | 1 | 0 | 0 | 1 | 1 | 1 | | 1 | 1 | 1 | 1 | 0 | 0 | 1 | **Разъяснение по строкам:** * **Строка 1 (M=0, B=0, C=0):** * \(M \land C = 0 \land 0 = 0\) * \(\overline{(M \land C)} = \overline{0} = 1\) * \(B \land \overline{(M \land C)} = 0 \land 1 = 0\) * \(K = M \lor (B \land \overline{(M \land C)}) = 0 \lor 0 = 0\) * **Строка 2 (M=0, B=0, C=1):** * \(M \land C = 0 \land 1 = 0\) * \(\overline{(M \land C)} = \overline{0} = 1\) * \(B \land \overline{(M \land C)} = 0 \land 1 = 0\) * \(K = M \lor (B \land \overline{(M \land C)}) = 0 \lor 0 = 0\) * **Строка 3 (M=0, B=1, C=0):** * \(M \land C = 0 \land 0 = 0\) * \(\overline{(M \land C)} = \overline{0} = 1\) * \(B \land \overline{(M \land C)} = 1 \land 1 = 1\) * \(K = M \lor (B \land \overline{(M \land C)}) = 0 \lor 1 = 1\) * **Строка 4 (M=0, B=1, C=1):** * \(M \land C = 0 \land 1 = 0\) * \(\overline{(M \land C)} = \overline{0} = 1\) * \(B \land \overline{(M \land C)} = 1 \land 1 = 1\) * \(K = M \lor (B \land \overline{(M \land C)}) = 0 \lor 1 = 1\) * **Строка 5 (M=1, B=0, C=0):** * \(M \land C = 1 \land 0 = 0\) * \(\overline{(M \land C)} = \overline{0} = 1\) * \(B \land \overline{(M \land C)} = 0 \land 1 = 0\) * \(K = M \lor (B \land \overline{(M \land C)}) = 1 \lor 0 = 1\) * **Строка 6 (M=1, B=0, C=1):** * \(M \land C = 1 \land 1 = 1\) * \(\overline{(M \land C)} = \overline{1} = 0\) * \(B \land \overline{(M \land C)} = 0 \land 0 = 0\) * \(K = M \lor (B \land \overline{(M \land C)}) = 1 \lor 0 = 1\) * **Строка 7 (M=1, B=1, C=0):** * \(M \land C = 1 \land 0 = 0\) * \(\overline{(M \land C)} = \overline{0} = 1\) * \(B \land \overline{(M \land C)} = 1 \land 1 = 1\) * \(K = M \lor (B \land \overline{(M \land C)}) = 1 \lor 1 = 1\) * **Строка 8 (M=1, B=1, C=1):** * \(M \land C = 1 \land 1 = 1\) * \(\overline{(M \land C)} = \overline{1} = 0\) * \(B \land \overline{(M \land C)} = 1 \land 0 = 0\) * \(K = M \lor (B \land \overline{(M \land C)}) = 1 \lor 0 = 1\) Таблица истинности заполнена.