Construct a truth table for the given statement. \[ p \leftrightarrow \sim q \] Fill in the truth table. \begin{tabular}{|c|c|c|c|} \hline $\mathbf{p}$ & $\mathbf{q}$ & $\sim \mathbf{q}$ & \multicolumn{2}{|c|}{$\mathbf{p} \leftrightarrow \sim \mathbf{q}$} \\ \hline$T$ & $T$ & $\square$ & $\square$ \\ \hline$T$ & $F$ & $\square$ & $\square$ \\ \hline$F$ & $T$ & $\square$ & \\ \hline$F$ & $F$ & $\square$ & \\ \hline \end{tabular}

Step 1 ：Construct a truth table for the given statement \(p \leftrightarrow \sim q\).

Step 2 ：Fill in the truth table. The truth table is a way to represent the logical values of a statement based on the possible values of its variables. In this case, we have two variables, p and q.

Step 3 ：The symbol \(\sim\) represents the logical NOT operation, which inverts the value of the variable it is applied to. The symbol \(\leftrightarrow\) represents the logical biconditional operation, which is true if both variables have the same value and false otherwise.

Step 4 ：To fill in the truth table, we need to calculate the value of \(\sim q\) for each possible value of q, and then calculate the value of \(p \leftrightarrow \sim q\) for each possible combination of p and \(\sim q\).

Step 5 ：The completed truth table is: \[\begin{tabular}{|c|c|c|c|} \hline \(\mathbf{p}\) & \(\mathbf{q}\) & \(\sim \mathbf{q}\) & \multicolumn{2}{|c|}{\(\mathbf{p} \leftrightarrow \sim \mathbf{q}\)} \\ \hline \(T\) & \(T\) & \(F\) & \(F\) \\ \hline \(T\) & \(F\) & \(T\) & \(T\) \\ \hline \(F\) & \(T\) & \(F\) & \(T\) \\ \hline \(F\) & \(F\) & \(T\) & \(F\) \\ \hline \end{tabular}\]

Step 6 ：\(\boxed{\text{Final Answer: The completed truth table is:}}\) \[\begin{tabular}{|c|c|c|c|} \hline \(\mathbf{p}\) & \(\mathbf{q}\) & \(\sim \mathbf{q}\) & \multicolumn{2}{|c|}{\(\mathbf{p} \leftrightarrow \sim \mathbf{q}\)} \\ \hline \(T\) & \(T\) & \(F\) & \(F\) \\ \hline \(T\) & \(F\) & \(T\) & \(T\) \\ \hline \(F\) & \(T\) & \(F\) & \(T\) \\ \hline \(F\) & \(F\) & \(T\) & \(F\) \\ \hline \end{tabular}\]