math - Which boolean law is this?

Question

F = XYZ + XYZ' + XY'Z + X'YZ

= (XYZ + XYZ + XYZ) + XYZ' + XY'Z + X'YZ (i don't know what law was used to get this)

I was given some guidance on a question that has been troubling me, but would like to not make this mistake in future. can anyone tell me what law that is above?

Answer 1

这应该很简单......

假设我们有F=X那么我们可以把它写成F=X+X。

这属于Indempotent Law A+A=A

Answer 2

首先，我想稍后再回答您，但请您注意“幂等定律”：-

对于任何布尔变量 a，

a + a = a (Idempotent Law)

接下来，现在回答你的问题。这个解决方案只不过是一种简化最小术语的方法。

F = XYZ + XYZ' + XY'Z + X'YZ

  = (XYZ + XYZ + XYZ) + XYZ' + XY'Z + X'YZ 

  = (XYZ + XYZ') + (XYZ + XY'Z) + (XYZ + X'YZ)

  = XY(Z+Z') + XZ(Y+Y') + YZ(X+X')

  = XY + XZ + YZ.    (Since,  a + a' = 1 ,as per the Complement law)

如此简单，这就是解决这个问题的方法......