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

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

Step 2 ：Fill in the truth table. The logical operator \(\leftrightarrow\) represents logical equivalence, which means the statement is true if both \(q\) and \(\sim p\) are true or both are false. The operator \(\sim\) represents logical negation, which means \(\sim p\) is the opposite of \(p\).

Step 3 ：In the given table, we have \(p\) as True and \(q\) as False. Since \(\sim p\) is the opposite of \(p\), \(\sim p\) will be False. And since \(q\) and \(\sim p\) are not both true or both false, \(q \leftrightarrow \sim p\) will be False.

Step 4 ：\(p = True\)

Step 5 ：\(q = False\)

Step 6 ：\(\sim p = False\)

Step 7 ：\(q \leftrightarrow \sim p = True\)

Step 8 ：The values for \(\sim p\) and \(q \leftrightarrow \sim p\) when \(p\) is True and \(q\) is False are False and True respectively. So, the completed truth table is:

Step 9 ：\begin{tabular}{|c|c|c|c|} \hline \(p\) & \(q\) & \(\sim p\) & \(q \leftrightarrow \sim p\) \\ \hline \(T\) & \(T\) & \(F\) & \(F\) \\ \hline \(T\) & \(F\) & \(F\) & \(T\) \\ \hline \end{tabular}

Step 10 ：\(\boxed{\text{The values for } \sim p \text{ and } q \leftrightarrow \sim p \text{ when } p \text{ is True and } q \text{ is False are False and True respectively.}}\)