Discussion
The logic expression \(\bar{A}BC + \bar{A}\bar{B}C + AB\bar{C} + A\bar{B}\bar{C}\) can be simplified to
Answer: A
The expression simplifies to \(A\) XOR \(C\).
Group the terms in pairs that differ only in \(B\):
\[ \begin{aligned} \bar{A}C(B + \bar{B}) + A\bar{C}(B + \bar{B}) &= \bar{A}C + A\bar{C} \\ &= A \oplus C \end{aligned} \]
The output is 1 exactly when \(A\) and \(C\) differ, whatever \(B\) is. \(A\) AND \(\bar{C}\) keeps only the second pair of terms. The output is not constant: with \(A = C = 0\) every term is 0, and with \(A = 0, C = 1\) the first term is 1, so neither 0 nor 1 is right.
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