Consider the following premises. There is at least one x_8 for which x_8 is sad if and only if x_8 will write a letter. For all x_8, x_8 will write a letter if and only if x_8 will work. For all x_8, x_8 will not work. Can we infer the following from them? There is at least one x_8 for which x_8 is not sad.
 From the fact that there is at least one x_8 for which x_8 is sad if and only if x_8 will write a letter we can infer that there is at least one x_8 for which if x_8 were sad, then x_8 is writing a letter. From the fact that for all x_8, x_8 will write a letter if and only if x_8 will work, and that for all x_8, x_8 will not work we can infer that for all x_8, x_8 will not write a letter. Finally, from the fact that there is at least one x_8 for which if x_8 were sad, then x_8 is writing a letter, and that for all x_8, x_8 will not write a letter we can infer that there is at least one x_8 for which x_8 is not sad. Therefore, the answer is yes.