1. The problem asks to express the given logical propositions involving p, q, and r as English sentences. 2. Recall the meanings: - $p$: You have the fever. - $q$: You miss the final examination. - $r$: You pass the course. 3. Also recall logical symbols: - $\sim$ means NOT (negation). - $\leftrightarrow$ means if and only if (biconditional). - $\to$ means implies (conditional). - $\lor$ means OR (disjunction). 4. Now translate each: (i) $\sim q \leftrightarrow r$ means "You do not miss the final examination if and only if you pass the course." (ii) $q \to \sim r$ means "If you miss the final examination, then you do not pass the course." (iii) $(p \to \sim r) \lor (q \to \sim r)$ means "Either if you have the fever, then you do not pass the course, or if you miss the final examination, then you do not pass the course." (iv) $r \to \sim q$ means "If you pass the course, then you do not miss the final examination." (v) $\sim p \to \sim q$ means "If you do not have the fever, then you do not miss the final examination." Final answers: (i) You do not miss the final examination if and only if you pass the course. (ii) If you miss the final examination, then you do not pass the course. (iii) Either if you have the fever, then you do not pass the course, or if you miss the final examination, then you do not pass the course. (iv) If you pass the course, then you do not miss the final examination. (v) If you do not have the fever, then you do not miss the final examination.