Consider the following premises. It is cloudy. If it is cloudy, then it is raining. For all x_21, x_21 will play a game and x_21 is bored. Can we infer the following from them? William is playing a game and it is raining.
 From the fact that for all x_21, x_21 will play a game and x_21 is bored we can infer that for all x_21, x_21 will play a game. From the fact that for all x_21, x_21 will play a game we can infer that William is playing a game. From the fact that if it is cloudy, then it is raining, and that it is cloudy we can infer that it is raining. Finally, from the fact that William is playing a game, and that it is raining we can infer that William is playing a game and it is raining. Therefore, the answer is yes.