Consider the following premises. If it is late, then Charles is a taxi driver. For all z_2, if z_2 were a taxi driver, then z_2 is writing a letter. Charles is writing a letter if and only if it is late. Can we infer the following from them? If Charles writes a letter, then Charles is a taxi driver.
 From the fact that for all z_2, if z_2 were a taxi driver, then z_2 is writing a letter we can infer that if Charles were a taxi driver, then Charles is writing a letter. From the fact that Charles is writing a letter if and only if it is late we can infer that if Charles writes a letter, then it is late. Finally, from the fact that if Charles writes a letter, then it is late, and that if it is late, then Charles is a taxi driver we can infer that if Charles writes a letter, then Charles is a taxi driver. Therefore, the answer is yes.