1. The problem is to verify the logical equivalence: $$\sim p \vee q \equiv \sim(p \wedge q)$$ using a truth table. 2. Start by listing all possible truth values for $p$ and $q$. 3. Compute $p \wedge q$ for each combination. 4. Compute $\sim(p \wedge q)$ by negating the result of step 3. 5. Compute $\sim p$ by negating $p$. 6. Compute $\sim p \vee q$ using the results of step 5 and $q$. 7. Compare the columns for $\sim p \vee q$ and $\sim(p \wedge q)$ to confirm they are the same. Truth table: | $p$ | $q$ | $p \wedge q$ | $\sim(p \wedge q)$ | $\sim p$ | $\sim p \vee q$ | |-----|-----|--------------|--------------------|----------|----------------| | T | T | T | F | F | T | | T | F | F | T | F | F | | F | T | F | T | T | T | | F | F | F | T | T | T | From the table, the columns for $\sim p \vee q$ and $\sim(p \wedge q)$ match exactly. Therefore, the logical equivalence $$\sim p \vee q \equiv \sim(p \wedge q)$$ is true.