我如何简化（扩展）此布尔表达式？

Question

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

[我知道具有分配属性，它拥有(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具有AND，它将如何工作

答案中的步骤会有所帮助。

Answer 1

也许是这样？

  (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，因为每个变量只出现一次，并且没有明显的矛盾或重言式。