Construct a truth table for the statement $q \rightarrow(p \vee r)$. \begin{tabular}{|c|c|c|c|c|} \hline$p$ & $q$ & $r$ & $p \vee r$ & $q \rightarrow(p \vee r)$ \\ \hline$T$ & $T$ & $T$ & $\square$ & $\square$ \\ \hline \end{tabular}

Step 1 ：Construct a truth table for the statement \(q \rightarrow(p \vee r)\).

Step 2 ：Calculate the truth values of \(p \vee r\) and \(q \rightarrow(p \vee r)\) for all possible combinations of truth values of \(p\), \(q\), and \(r\).

Step 3 ：The logical OR operation \(p \vee r\) is true if either \(p\) or \(r\) is true.

Step 4 ：The logical implication \(q \rightarrow(p \vee r)\) is false only if \(q\) is true and \((p \vee r)\) is false, otherwise it is true.

Step 5 ：Generate all possible combinations of truth values for \(p\), \(q\), and \(r\). The combinations are: \((T, T, T), (T, T, F), (T, F, T), (T, F, F), (F, T, T), (F, T, F), (F, F, T), (F, F, F)\).

Step 6 ：Calculate the truth values of \(p \vee r\) for each combination. The values are: \(T, T, T, T, T, F, T, F\).

Step 7 ：Calculate the truth values of \(q \rightarrow(p \vee r)\) for each combination. The values are: \(T, T, T, T, T, F, T, T\).

Step 8 ：\(\boxed{\text{Final Answer: The truth table for the statement } q \rightarrow(p \vee r) \text{ is:}}\)

Step 9 ：\begin{tabular}{|c|c|c|c|c|}\hline p & q & r & p \vee r & q \rightarrow(p \vee r) \\ \hline T & T & T & T & T \\ \hline T & T & F & T & T \\ \hline T & F & T & T & T \\ \hline T & F & F & T & T \\ \hline F & T & T & T & T \\ \hline F & T & F & F & F \\ \hline F & F & T & T & T \\ \hline F & F & F & F & T \\ \hline \end{tabular}