## Thinking Mathematically (6th Edition)

Let$p$be: All houses meet the hurricane code. Let$q$be: None of them are destroyed by a category 4 hurricane. The form of the premises is, \begin{align} & \underline{\begin{align} & p\to q \\ & \\ & \sim q \\ \end{align}}\ \ \ \ \ \underline{\begin{array}{*{35}{l}} \begin{align} & \text{If all houses meet the hurricane code, } \\ & \text{then none of them are destroyed by a category 4 hurricane}\text{.} \\ \end{align} \\ \text{Some houses were destroyed by Andrew, a category 4 hurricane}\text{.} \\ \end{array}} \\ & \ \therefore \ \ ?\ \ \ \ \ \ \ \ \ \ \text{Therefore, } \\ \end{align} The conclusion $\sim p$ is valid because it forms the contrapositive reasoning of a valid argument, when it follows the given premises. The conclusion translates as, some houses meet the hurricane code.Therefore, the valid conclusion from the provided premises is, some houses meet the hurricane code.