## Thinking Mathematically (6th Edition)

Use letters to represent each simple statement in the argument. p: Metro rail system is in operation. q: There are traffic delays. Express the premises and conclusion symbolically as: \frac{\begin{align} & \sim p\to q \\ & \sim q \\ \end{align}}{\therefore p}\ \ \ \ \ \ \frac{\begin{align} & \text{If a metro rail system is not in operation, there are traffic delays}\text{.} \\ & \text{Over the past year there have been no traffic delays}\text{.} \\ \end{align}}{\therefore \text{Over the past year a metro rail system has been in operation}\text{.}} The argument is in the form of Contra-positive Reasoning. Thus, the argument is valid.