Consider the following premises. For all y_2, y_2 is a scientist if and only if y_2 will write a letter. There is at least one y_2 for which if y_2 were sad, then y_2 is writing a letter. For all y_2, if y_2 writes a letter, then y_2 is sad. Can we infer the following from them? For all y_2, the fact that y_2 were sad does not imply that y_2 is a scientist.
That contradicts the premises. Therefore the answer is no.