我如何简化（扩展）这个布尔表达式？

Question

表达式 - (A OR B OR C OR D) AND (!B AND !D)

我知道对于分配 属性，它认为 (a OR b) AND (c OR d) = (a AND c) OR (a AND d) OR (b AND c) or (b AND d) 但我不确定如果第二组有 AND

它会如何工作

答案中的步骤会有所帮助。

Answer 1

也许是这样的？

  (A OR B OR C OR D) AND (!B AND !D)
= (A OR B OR C OR D) AND !(B OR D)
= ((A OR C) OR (B OR D)) AND !(B OR D)
= ((A OR C) AND !(B OR D)) OR ((B OR D) AND !(B OR D))
= (A OR C) AND !(B OR D) OR false
= (A OR C) AND !(B OR D)

这似乎是最小的，因为每个变量出现一次并且没有明显的矛盾或重言式。