## Thinking Mathematically (6th Edition)

Use letters to represent each simple statement in the argument. p: We close the door. q: There is less noise. Express the premises and conclusion symbolically as: \frac{\begin{align} & p\to q \\ & q \\ \end{align}}{\therefore p}\ \ \ \ \ \ \frac{\begin{align} & \text{If we close the door, then there is less noise}\text{.} \\ & \text{There is less noise}\text{.} \\ \end{align}}{\therefore \text{We closed the door}\text{.}} The argument is in the form of Fallacy of the Converse. So, the argument is invalid.