1. **State the problem:** Construct a truth table for the compound proposition $ (p \lor q) \lor r $. 2. **List all possible truth values for $p$, $q$, and $r$: Since each can be true (T) or false (F), there are $2^3 = 8$ combinations:** $$\begin{array}{ccc} p & q & r \\ \hline T & T & T \\ T & T & F \\ T & F & T \\ T & F & F \\ F & T & T \\ F & T & F \\ F & F & T \\ F & F & F \end{array}$$ 3. **Calculate $p \lor q$ for each row:** - $p \lor q$ is true if at least one of $p$ or $q$ is true, false otherwise. 4. **Calculate $(p \lor q) \lor r$ for each row:** - This is true if at least one of $p \lor q$ or $r$ is true, false otherwise. 5. **Complete truth table:** $$\begin{array}{cccccc} p & q & r & p \lor q & (p \lor q) \lor r \\ \hline T & T & T & T & T \\ T & T & F & T & T \\ T & F & T & T & T \\ T & F & F & T & T \\ F & T & T & T & T \\ F & T & F & T & T \\ F & F & T & F & T \\ F & F & F & F & F \end{array}$$ **Final answer:** The truth table above shows the values of $ (p \lor q) \lor r $ for all possible truth values of $p$, $q$, and $r$.