Consider the following premises. For all x_15, x_15 is not a carpenter. For all x_15, if x_15 works, then x_15 is a carpenter. Michael is writing a letter if and only if David is working. Can we infer the following from them? Michael is writing a letter.
 From the fact that for all x_15, if x_15 works, then x_15 is a carpenter, and that for all x_15, x_15 is not a carpenter we can infer that for all x_15, x_15 will not work. From the fact that for all x_15, x_15 will not work we can infer that David is not working. Finally, from the fact that Michael is writing a letter if and only if David is working, and that David is not working we can infer that Michael is not writing a letter, which contradicts that Michael is writing a letter. Therefore, the answer is no.