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Can anyone help me out on this boolean algebra simplification...im not sure with my answer.

X’YZ + XY’Z’ + X’Y’Z’ + XY’Z + XYZ my answer is x'yz+y'z'+xz but badly not sure of it! can you check thnks in advance

I am assuming the "()" with "'" means the over-score above the variables

joash
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1 Answers1

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\begin{align} XY'Z' + X'Y'Z' &= (X+X')Y'Z' \qquad &\mbox{distributivity}\\ &= Y'Z' \qquad &\mbox{ since } X' + X = 1\\ XY'Z + XYZ &= Y'XZ + YXZ \qquad &\mbox{commutativity}\\&= (Y'+Y)XZ \qquad &\mbox{distributivity}\\&= XZ \qquad &\mbox{ since }Y' + Y = 1\end{align}

So your answer is correct.

Weaam
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