Consider the following premises. Elisabeth is a scientist if and only if Jessica is playing a game. If it is sunny, then Jessica is playing a game. For all x_3, x_3 is not a scientist. Can we infer the following from them? It is not sunny.
 From the fact that for all x_3, x_3 is not a scientist we can infer that Elisabeth is not a scientist. From the fact that Elisabeth is a scientist if and only if Jessica is playing a game, and that Elisabeth is not a scientist we can infer that Jessica is not playing a game. Finally, from the fact that if it is sunny, then Jessica is playing a game, and that Jessica is not playing a game we can infer that it is not sunny. Therefore, the answer is yes.