1. ## Boolean algebra problem

Hello,
I need to prove that this expression is correct (in boolean algebra) and I can't figure out how.
WXY'Z'+XYZ+WY'Z'+WXZ=XYZ+WY'(X+Z')
Can anyone help me?

2. ## Re: Boolean algebra problem

What do you mean by a correct expression and what can you use in a proof? Can you use truth tables?

3. ## Re: Boolean algebra problem

I need to prove that the expression is true and I cannot use truth tables. I need manipulate the expression with rules like DeMorgen sentence for example so both sides of the expression will be equal

4. ## Re: Boolean algebra problem

Working on the right-hand side,
\begin{align*}
xyz+wy'(x+z')&= xyz+wxy'+wy'z'\\ &=xyz+wxy'(z+z')+wy'z'\\ &=xyz+wxy'z+wxy'z'+wy'z'.
\end{align*}
Now, working on the left-hand side,
\begin{align*}
wxy'z'+xyz+wy'z'+wxz &=wxy'z'+xyz+wy'z'+wx(y+y')z\\ &=wxy'z'+xyz+wy'z'+wxyz+wxy'z\\ &=wxy'z'+xyz(1+w)+wy'z'+wxy'z\\ &=wxy'z'+xyz+wy'z'+wxy'z
\end{align*}

5. ## Re: Boolean algebra problem

Thank you very much!