1. **State the problem:** Determine which pairs of statements are logically equivalent. 2. **Recall logical equivalences:** - The negation of a conjunction: $$\neg (P \wedge Q) \equiv \neg P \vee \neg Q$$ (De Morgan's Law). - The contrapositive of an implication: $$P \to Q \equiv \neg Q \to \neg P$$. 3. **Analyze Pair I:** - Statement 1: "It is not true that both you have pneumonia and I got flu" translates to $$\neg (P \wedge Q)$$ where $P$ = "you have pneumonia" and $Q$ = "I got flu". - Statement 2: "Either you have no pneumonia or I have no flu" translates to $$\neg P \vee \neg Q$$. - By De Morgan's Law, $$\neg (P \wedge Q) \equiv \neg P \vee \neg Q$$. - Therefore, Pair I statements are logically equivalent. 4. **Analyze Pair II:** - Statement 1: "Joe tells you that he is an engineer and he studied in Mapua" translates to $$P \wedge Q$$ where $P$ = "Joe is an engineer" and $Q$ = "Joe studied in Mapua". - Statement 2: "If Joe is lying, then Joe is not an engineer or he did not study in Mapua" translates to $$\neg (P \wedge Q) \to (\neg P \vee \neg Q)$$. - The contrapositive of $$P \wedge Q$$ is not the same as the implication given. - Statement 2 is a conditional statement about Joe lying implying $$\neg P \vee \neg Q$$, which is not logically equivalent to Statement 1. - Therefore, Pair II statements are not logically equivalent. 5. **Conclusion:** Only Pair I statements are logically equivalent. **Final answer:** Option B