布尔简化-为什么(A+NOT(B.C)).(B+NOT(B.C))

Question

这是方程式的答案，但我不明白为什么。请帮忙！

Answer 1

如果逐个应用布尔代数定律，则解决方案是一个直接结果：

1. de Morgan定理：由OR连接在一起的两项的补码与由AND连接的两项补码相同，反之亦然(即NOT(A + B) = NOT(A) * NOT(B)和NOT(A * B) = NOT(A) + NOT(B)(
2. 交换律：用AND或OR连接两个独立项的顺序并不重要
3. 补码定律：一个项与其补码与AND相连，分别等于0，而OR等于1(即A * NOT(A) = 0和A + NOT(A) = 1(
4. 废止定律：与AND和0相连的项等于0，与OR和1相连的项=1(即A * 0 = 0和A + 1 = 1(
5. 恒等定律：由AND与1连接或由OR与0连接的项等于其自身(即A * 1 = A和A + 0 = A(

(还有更多，但这里不需要(

适用于你的学期：

(A + NOT(B*C))        * (B + NOT(B*C))        * (C + NOT(B*C)) 
[with 1.]   = (A + NOT(B) + NOT(C)) * (B + NOT(B) + NOT(C)) * (C + NOT(B) + NOT(C))
[with 2.]   = (A + NOT(B) + NOT(C)) * (B + NOT(B) + NOT(C)) * (C + NOT(C) + NOT(B))
[with 3.]   = (A + NOT(B) + NOT(C)) * (1          + NOT(C)) * (1          + NOT(B))      
[with 4.]   = (A + NOT(B) + NOT(C)) *  1                    *  1      
[with 5.]   = (A + NOT(B) + NOT(C))  
[with 1.]   = (A + NOT(B*C))