Question: Given that (A cdot B=0) and (A+B=1), use algebraic manipulation to prove that [(A+C) cdot(bar{A}+B) cdot(B+C)=B cdot C]

Given that \(A \cdot B=0\) and \(A+B=1\), use algebraic manipulation to prove that

\[(A+C) \cdot(\bar{A}+B) \cdot(B+C)=B \cdot C\]

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