Consider the following premises. For all y, y will write a letter. Can we infer the following from them? There is at least one x_1 for which x_1 will write a letter or x_1 will listen to a song.
 From the fact that for all y, y will write a letter we can infer that William is writing a letter. From the fact that William is writing a letter we can infer that there is at least one x_1 for which x_1 will write a letter. Finally, from the fact that there is at least one x_1 for which x_1 will write a letter we can infer that there is at least one x_1 for which x_1 will write a letter or x_1 will listen to a song. Therefore, the answer is yes.