1. **Problem Statement:** Construct the truth table for the compound proposition $p \to \neg q$. 2. **Identify variables:** The proposition involves two variables: $p$ and $q$. 3. **List all possible truth values for $p$ and $q$:** Since both $p$ and $q$ can be either True (T) or False (F), we have four combinations: - $p = T, q = T$ - $p = T, q = F$ - $p = F, q = T$ - $p = F, q = F$ 4. **Compute $\neg q$ (not $q$):** - If $q = T$, then $\neg q = F$ - If $q = F$, then $\neg q = T$ 5. **Compute $p \to \neg q$ (implication):** Recall that $p \to r$ (if $p$ then $r$) is false only when $p$ is True and $r$ is False; otherwise, it's True. Evaluate for each row: - $p=T$, $\neg q=F$: $T \to F = F$ - $p=T$, $\neg q=T$: $T \to T = T$ - $p=F$, $\neg q=F$: $F \to F = T$ - $p=F$, $\neg q=T$: $F \to T = T$ 6. **Summarize results in truth table:** | $p$ | $q$ | $\neg q$ | $p \to \neg q$ | | :-: | :-: | :-------: | :-------------: | | T | T | F | F | | T | F | T | T | | F | T | F | T | | F | F | T | T | **Final answer:** The truth table above fully describes $p \to \neg q$.