Consider the following premises. For all x_11, x_11 is a taxi driver or x_11 will not write a letter. For all x_11, x_11 will listen to a song if and only if x_11 is a taxi driver. For all x_11, x_11 will not listen to a song. There is at least one x_11 for which x_11 will write a letter or x_11 is poor. Can we infer the following from them? There is at least one x_11 for which x_11 is poor.
 From the fact that for all x_11, x_11 will listen to a song if and only if x_11 is a taxi driver, and that for all x_11, x_11 will not listen to a song we can infer that for all x_11, x_11 is not a taxi driver. From the fact that for all x_11, x_11 is a taxi driver or x_11 will not write a letter we can infer that for all x_11, if x_11 writes a letter, then x_11 is a taxi driver. From the fact that for all x_11, if x_11 writes a letter, then x_11 is a taxi driver, and that for all x_11, x_11 is not a taxi driver we can infer that for all x_11, x_11 will not write a letter. Finally, from the fact that there is at least one x_11 for which x_11 will write a letter or x_11 is poor, and that for all x_11, x_11 will not write a letter we can infer that there is at least one x_11 for which x_11 is poor. Therefore, the answer is yes.