Consider the following premises. For all x_10, if x_10 works, then x_10 is writing a letter. Thomas is working or Thomas is not writing a letter. Can we infer the following from them? If is not true that Thomas is writing a letter if and only if Thomas is working.
 From the fact that for all x_10, if x_10 works, then x_10 is writing a letter we can infer that if Thomas works, then Thomas is writing a letter. From the fact that Thomas is working or Thomas is not writing a letter we can infer that if Thomas writes a letter, then Thomas is working. Finally, from the fact that if Thomas writes a letter, then Thomas is working, and that if Thomas works, then Thomas is writing a letter we can infer that Thomas is writing a letter if and only if Thomas is working, which contradicts that If is not true that Thomas is writing a letter if and only if Thomas is working. Therefore, the answer is no.