Consider the Boolean expression \(X = \overline{(A+B).C}\) over Boolean variables A, B, and C. Which one of the following Boolean expressions is equivalent to the given Boolean expression X?
\[ X=\overline{(A+B)\,C} \] \[ \text{By De Morgan’s law:}\quad \overline{(A+B)\,C}=\overline{(A+B)}+\overline{C} \] \[ \overline{(A+B)}=\overline{A}\,\overline{B} \;\;\Rightarrow\;\; X=\overline{A}\,\overline{B}+\overline{C} \] \[ \boxed{\,X=\overline{C}+\overline{A}\,\overline{B}\,} \]
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