A Boolean Algebra simplification problem

Question

XY + (YZX)' + YZ

So above I have this boolean expression I have done the work out and I got 1. I was wondering if that was the correct answer or did I miss a step.

Answer 1

Let $X,Y,Z$ be subsets of $A$.

Then checking whether the expression equals $1$ comes to the same as checking that:$$(X\cap Y)\cup(Y\cap Z\cap X)^{\complement}\cup(Y\cap Z)=A$$or equivalently:$$A\subseteq(X\cap Y)\cup(Y\cap Z\cap X)^{\complement}\cup(Y\cap Z)$$It is not really difficult to verify this statement.

Answer 2

Using

Reduction

$P'+PQ=P'+Q$

We get:

$XY+(YZX)'+YZ= XY + Y' + Z' + X' +YZ=X+Y'+Z'+X'+Z=(X+X')+(Z+Z')+Y=1+1+Y=1$