# How to simplify Boolean expressions using Boolean rules and theorems [closed]

$$T=(ABC(BC)')'$$ How to simplify the Boolean expression using Boolean rules and theorem

## closed as off-topic by jvdhooft, JonMark Perry, Shailesh, Claude Leibovici, The Dead LegendOct 20 '17 at 11:38

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• Welcome to MSE. It will be more likely that you will get an answer if you show us that you made some effort. – José Carlos Santos Oct 20 '17 at 9:17
• (ABC(BC)')' =A'B'C'(BC'') =A'B'C'(BC) =A'B'C'+ABC+A'BC =A'(B'C'+BC)+ABC =A'(B+C)+ ABC – shasha Oct 20 '17 at 9:27

$T=(abc(bc)')'=(abc(b'+c'))'=(a(bb')c+ab(cc'))'=(0+0)'=0$
since $xy=yx$, $(xy)'=x'+y'$ and $xx'=0$ $\forall x,y$
Edit : The result is $(0+0)' = 1$