Consider the following premises. Susan is not writing a letter. For all x_3, if x_3 were happy, then x_3 is writing a letter. For all x_3, if x_3 writes a letter, then x_3 is happy. Can we infer the following from them? Susan is happy.
 From the fact that for all x_3, if x_3 writes a letter, then x_3 is happy, and that for all x_3, if x_3 were happy, then x_3 is writing a letter we can infer that for all x_3, x_3 will write a letter if and only if x_3 is happy. From the fact that for all x_3, x_3 will write a letter if and only if x_3 is happy we can infer that Susan is writing a letter if and only if Susan is happy. Finally, from the fact that Susan is writing a letter if and only if Susan is happy, and that Susan is not writing a letter we can infer that Susan is not happy, which contradicts that Susan is happy. Therefore, the answer is no.