1. **Problem Statement:** Construct a truth table for the compound proposition $(p \lor q) \lor r$. 2. **Step 1:** List all possible truth values for variables $p$, $q$, and $r$. Since each variable can be either true (T) or false (F), and there are 3 variables, we have $2^3=8$ rows. 3. **Step 2:** Compute $p \lor q$ for each combination. 4. **Step 3:** Compute $(p \lor q) \lor r$ using the results from Step 2 and values of $r$. 5. **Truth Table:** | $p$ | $q$ | $r$ | $p \lor q$ | $(p \lor q) \lor r$ | |-----|-----|-----|------------|---------------------| | F | F | F | F | F | | F | F | T | F | T | | F | T | F | T | T | | F | T | T | T | T | | T | F | F | T | T | | T | F | T | T | T | | T | T | F | T | T | | T | T | T | T | T | 6. **Explanation:** The logical OR operation $\lor$ is true if at least one operand is true. 7. Hence, $(p \lor q) \lor r$ is true if at least one of $p$, $q$, or $r$ is true. **Final answer:** The truth table above shows all truth values for the compound proposition.