1. The problem is to construct a truth table for the compound proposition $p \wedge \neg p$. 2. First, list all possible truth values for $p$. Since $p$ is a simple proposition, it can be either true (T) or false (F). 3. Next, compute $\neg p$, the negation of $p$. This flips the truth value of $p$. 4. Finally, compute $p \wedge \neg p$, which is true only when both $p$ and $\neg p$ are true simultaneously. | $p$ | $\neg p$ | $p \wedge \neg p$ | |-----|----------|-------------------| | T | F | F | | F | T | F | Since $p$ and $\neg p$ can never be true together, $p \wedge \neg p$ is always false.