Consider the following premises. For all x_6, x_6 is a server. For all x_6, x_6 will write a letter or x_6 will play a game. For all x_6, if x_6 writes a letter, then x_6 is not a server. Can we infer the following from them? Patricia is playing a game.
 From the fact that for all x_6, if x_6 writes a letter, then x_6 is not a server, and that for all x_6, x_6 is a server we can infer that for all x_6, x_6 will not write a letter. From the fact that for all x_6, x_6 will write a letter or x_6 will play a game, and that for all x_6, x_6 will not write a letter we can infer that for all x_6, x_6 will play a game. Finally, from the fact that for all x_6, x_6 will play a game we can infer that Patricia is playing a game. Therefore, the answer is yes.