Consider the following premises. For all x_6, if x_6 were a taxi driver, then x_6 is writing a letter. For all x_6, if x_6 makes tea, then x_6 is a taxi driver. David is sleeping or Jessica is making tea. If David sleeps, then Jessica is writing a letter. Can we infer the following from them? Jessica is writing a letter.
 From the fact that for all x_6, if x_6 makes tea, then x_6 is a taxi driver, and that for all x_6, if x_6 were a taxi driver, then x_6 is writing a letter we can infer that for all x_6, if x_6 makes tea, then x_6 is writing a letter. From the fact that for all x_6, if x_6 makes tea, then x_6 is writing a letter we can infer that if Jessica makes tea, then Jessica is writing a letter. Finally, from the fact that if David sleeps, then Jessica is writing a letter, that if Jessica makes tea, then Jessica is writing a letter, and that David is sleeping or Jessica is making tea we can infer that Jessica is writing a letter. Therefore, the answer is yes.