Consider the following premises. For all x_2, x_2 will not write a letter or x_2 will listen to a song. For all x_2, x_2 will not climb a mountain. There is at least one x_2 for which x_2 will write a letter or x_2 will climb a mountain. Can we infer the following from them? For all x_2, x_2 will not listen to a song.
 From the fact that there is at least one x_2 for which x_2 will write a letter or x_2 will climb a mountain, and that for all x_2, x_2 will not write a letter or x_2 will listen to a song we can infer that there is at least one x_2 for which x_2 will climb a mountain or x_2 will listen to a song. Finally, from the fact that there is at least one x_2 for which x_2 will climb a mountain or x_2 will listen to a song, and that for all x_2, x_2 will not climb a mountain we can infer that there is at least one x_2 for which x_2 will listen to a song, which contradicts that For all x_2, x_2 will not listen to a song. Therefore, the answer is no.