I have this boolean equation:
X'Y'+XY+X'Y=X'+Y
I want to prove it.
Now I was wondering if I can rearrange this equation, if I could, so I can factor out the other side; tell me if this is allowed. I haven't seen anything to say I could in my textbook:
X'Y'+XY+X'Y
X'Y'+X'Y+XY see now I move the X'Y to the left
X'(Y+Y')+XY
X'+X'Y+XY
X'+Y(X'+X)
X'+Y
Am I doing it right? I've been trying this equation in other ways and haven't been able to prove it otherwise.
Almost all of your rearrangements are correct, except it is not clear how you get from $X'(Y+Y')+XY$ to $X'+X'Y+XY$. I would write your argument like this: $$\begin{split}X'Y'+XY+X'Y&=X'Y'+X'Y+XY\\ &=X'(Y'+Y)+XY\\ &=X'(1)+XY\\ &=X'+XY\\ &=(X'+X)(X'+Y)\\ &=(1)(X'+Y)\\ &=X'+Y.\end{split}$$