Consider the following premises. For all x_5, if x_5 were a writer, then x_5 is a nurse. For all x_5, if x_5 were happy, then x_5 is a carpenter. For all x_5, x_5 is happy. For all x_5, if x_5 were a carpenter, then x_5 is a writer. Can we infer the following from them? For all x_5, x_5 is a nurse.
 From the fact that for all x_5, if x_5 were happy, then x_5 is a carpenter, and that for all x_5, if x_5 were a carpenter, then x_5 is a writer we can infer that for all x_5, if x_5 were happy, then x_5 is a writer. From the fact that for all x_5, if x_5 were happy, then x_5 is a writer, and that for all x_5, x_5 is happy we can infer that for all x_5, x_5 is a writer. Finally, from the fact that for all x_5, if x_5 were a writer, then x_5 is a nurse, and that for all x_5, x_5 is a writer we can infer that for all x_5, x_5 is a nurse. Therefore, the answer is yes.