离散二元运算分配律的例题

假设我们有三个布尔变量 A、B 和 C，那么分配律可以表示为：

- A AND (B OR C) = (A AND B) OR (A AND C)
- A OR (B AND C) = (A OR B) AND (A OR C)

下面我们来看一个例题：

假设有三个布尔变量 A、B 和 C，其值分别为 A=1，B=0，C=1。计算以下两个表达式的值：

- A AND (B OR C)
- (A AND B) OR (A AND C)

根据分配律，这两个表达式的值应该相等。

首先计算 A AND (B OR C)：

- B OR C = 0 OR 1 = 1
- A AND (B OR C) = 1 AND 1 = 1

然后计算 (A AND B) OR (A AND C)：

- A AND B = 1 AND 0 = 0
- A AND C = 1 AND 1 = 1
- (A AND B) OR (A AND C) = 0 OR 1 = 1

因此，我们可以得出结论，A AND (B OR C) = (A AND B) OR (A AND C) = 1。