Consider the following premises. For all x_7, if x_7 drives a car, then x_7 is writing a letter. There is at least one x_7 for which x_7 is poor or x_7 will not write a letter. For all x_7, x_7 will drive a car. Can we infer the following from them? There is at least one x_7 for which x_7 is poor.
 From the fact that there is at least one x_7 for which x_7 is poor or x_7 will not write a letter we can infer that there is at least one x_7 for which if x_7 writes a letter, then x_7 is poor. From the fact that for all x_7, if x_7 drives a car, then x_7 is writing a letter, and that for all x_7, x_7 will drive a car we can infer that for all x_7, x_7 will write a letter. Finally, from the fact that there is at least one x_7 for which if x_7 writes a letter, then x_7 is poor, and that for all x_7, x_7 will write a letter we can infer that there is at least one x_7 for which x_7 is poor. Therefore, the answer is yes.