## Thinking Mathematically (6th Edition)

Let$p$be I vacation in Paris. Let$q$be I eat French pastries. Let $r$be I gain weight. The form of the premises is \begin{align} & \underline{\begin{align} & p\to q \\ & q\to r \\ \end{align}}\ \ \ \ \ \underline{\begin{array}{*{35}{l}} \text{If I vacation in Paris, I eat French pastries}\text{.} \\ \text{If I eat French pastries, I gain weight}\text{.} \\ \end{array}} \\ & \ \therefore \ \ ?\ \ \ \ \ \ \ \ \ \ \text{Therefore, } \\ \end{align} The conclusion $p\to r$ is valid because it forms the transitive reasoning of a valid argument when it follows the given premises. The conclusion $p\to r$ translates as follows: If I vacation in Paris, I gain weight. Therefore, the valid conclusion from the provided premises is If I vacation in Paris, I gain weight. The valid conclusion from the provided premises is If I vacation in Paris, I gain weight.