1. **State the problem:** We need to analyze the logical argument about the party shutdown using rules of inference and evaluate its validity. 2. **Identify propositions:** - Let $P$: The neighbors contacted law enforcement. - Let $Q$: The volume of the music was excessive. - Let $R$: The party was shut down. 3. **Given information:** - Neighbors did not contact law enforcement: $\neg P$. - Volume was not excessive: $\neg Q$. - If absence of loud music ($\neg Q$) were sufficient to justify shutdown ($R$), then neighbors would have contacted police ($P$). Symbolically: $\neg Q \to P$. 4. **Logical structure:** - Premise 1: $\neg P$ (neighbors did not contact police). - Premise 2: $\neg Q \to P$ (if no loud music, then neighbors contacted police). 5. **Apply Modus Tollens:** - From $\neg Q \to P$ and $\neg P$, infer $\neg \neg Q$, which simplifies to $Q$. - This means the volume was excessive. 6. **Conclusion about shutdown:** - Since $\neg Q \to R$ (absence of loud music justifies shutdown) is given as a conditional, and $\neg Q$ is false (volume was excessive), the condition for shutdown is not met. - Therefore, the party was not shut down: $\neg R$. 7. **Evaluate validity:** - The argument uses correct inference rules (Modus Tollens). - The conclusion $\neg R$ logically follows from the premises. **Final answer:** The argument is valid; the party was not shut down because the volume was excessive and neighbors did not contact police, consistent with the premises.