1. The problem asks for the truth table entries for the column $\overline{C}$, which is the NOT operation applied to the variable $C$. 2. The NOT operation in Boolean algebra inverts the value: if $C=0$, then $\overline{C}=1$; if $C=1$, then $\overline{C}=0$. 3. Given the values of $C$ in the truth table rows as $[0,1,0,1,0,1,0,1]$, we apply the NOT operation to each: $$\overline{C} = [1,0,1,0,1,0,1,0]$$ 4. This matches the provided column vector for $\overline{C}$. 5. Writing the answer as an 8-row, single-column matrix: $$\begin{bmatrix}1\\0\\1\\0\\1\\0\\1\\0\end{bmatrix}$$ This completes the solution for the first question.