Consider the following premises. For all x_7, x_7 will play a game if and only if x_7 is rich. Richard is a mechanic. If Linda plays a game, then Richard is not a mechanic. Can we infer the following from them? Linda is not rich.
 From the fact that for all x_7, x_7 will play a game if and only if x_7 is rich we can infer that Linda is playing a game if and only if Linda is rich. From the fact that if Linda plays a game, then Richard is not a mechanic, and that Richard is a mechanic we can infer that Linda is not playing a game. Finally, from the fact that Linda is playing a game if and only if Linda is rich, and that Linda is not playing a game we can infer that Linda is not rich. Therefore, the answer is yes.