1. The problem asks to represent the statement "he is unhealthy only if he is dirty" using logical statements involving $p$ and $q$. 2. Given: - $p$: He is healthy - $q$: He is neat 3. "He is unhealthy" is the negation of $p$, so it is $\neg p$. 4. "He is dirty" is the negation of $q$, so it is $\neg q$. 5. The phrase "only if" means implication: "A only if B" translates to $A \Rightarrow B$. 6. Therefore, "he is unhealthy only if he is dirty" translates to: $$\neg p \Rightarrow \neg q$$ 7. Looking at the options: - A. $\neg p \Rightarrow \neg q$ (matches our expression) - B. $\neg p \Rightarrow q$ - C. $p \Rightarrow \neg q$ - D. $\neg q \Rightarrow \neg p$ 8. The correct representation is option A. **Final answer:** A. $\neg p \Rightarrow \neg q$