Consider the following premises. There is at least one x_8 for which x_8 will write a letter if and only if x_8 is a cashier. For all x_8, x_8 is sad if and only if x_8 will write a letter. Can we infer the following from them? For all x_8, the fact that x_8 were sad does not imply that x_8 is a cashier.
 From the fact that there is at least one x_8 for which x_8 will write a letter if and only if x_8 is a cashier we can infer that there is at least one x_8 for which if x_8 writes a letter, then x_8 is a cashier. Finally, from the fact that for all x_8, x_8 is sad if and only if x_8 will write a letter we can infer that for all x_8, if x_8 were sad, then x_8 is writing a letter, which contradicts that For all x_8, the fact that x_8 were sad does not imply that x_8 is a cashier. Therefore, the answer is no.