Consider the following premises. There is at least one x_4 for which x_4 is not a writer. For all x_4, if x_4 were happy, then x_4 is a writer. For all x_4, x_4 is a writer if and only if x_4 is happy. Can we infer the following from them? For all x_4, x_4 is happy.
 From the fact that for all x_4, x_4 is a writer if and only if x_4 is happy we can infer that for all x_4, if x_4 were a writer, then x_4 is happy. From the fact that for all x_4, if x_4 were happy, then x_4 is a writer, and that for all x_4, if x_4 were a writer, then x_4 is happy we can infer that for all x_4, x_4 is happy if and only if x_4 is a writer. Finally, from the fact that for all x_4, x_4 is happy if and only if x_4 is a writer, and that there is at least one x_4 for which x_4 is not a writer we can infer that there is at least one x_4 for which x_4 is not happy, which contradicts that For all x_4, x_4 is happy. Therefore, the answer is no.