Consider the following premises. For all x_8, x_8 will write a letter or x_8 is a mechanic. For all x_8, x_8 will write a letter if and only if x_8 is sad. For all x_8, x_8 is not sad. Can we infer the following from them? For all x_8, x_8 is a mechanic or x_8 will listen to a song.
 From the fact that for all x_8, x_8 will write a letter if and only if x_8 is sad, and that for all x_8, x_8 is not sad we can infer that for all x_8, x_8 will not write a letter. From the fact that for all x_8, x_8 will write a letter or x_8 is a mechanic, and that for all x_8, x_8 will not write a letter we can infer that for all x_8, x_8 is a mechanic. Finally, from the fact that for all x_8, x_8 is a mechanic we can infer that for all x_8, x_8 is a mechanic or x_8 will listen to a song. Therefore, the answer is yes.