Consider the following premises. It is raining or David is playing a game. For all x, x will not play a game. It is not raining or Mary is an astronaut. If Jessica were an office clerk, then Mary is not an astronaut. Can we infer the following from them? Jessica is not an office clerk.
 From the fact that for all x, x will not play a game we can infer that David is not playing a game. From the fact that it is raining or David is playing a game, and that it is not raining or Mary is an astronaut we can infer that David is playing a game or Mary is an astronaut. From the fact that David is playing a game or Mary is an astronaut, and that David is not playing a game we can infer that Mary is an astronaut. Finally, from the fact that if Jessica were an office clerk, then Mary is not an astronaut, and that Mary is an astronaut we can infer that Jessica is not an office clerk. Therefore, the answer is yes.