Consider the following premises. If Thomas writes a letter, then Thomas is a writer. It is not snowing. For all y, if y were a writer, then y is a carpenter. It is snowing if and only if Thomas is a writer. For all y, if y were a carpenter, then y is writing a letter. Can we infer the following from them? Thomas is not writing a letter.
 From the fact that for all y, if y were a writer, then y is a carpenter, and that for all y, if y were a carpenter, then y is writing a letter we can infer that for all y, if y were a writer, then y is writing a letter. From the fact that for all y, if y were a writer, then y is writing a letter we can infer that if Thomas were a writer, then Thomas is writing a letter. From the fact that if Thomas writes a letter, then Thomas is a writer, and that if Thomas were a writer, then Thomas is writing a letter we can infer that Thomas is writing a letter if and only if Thomas is a writer. From the fact that it is snowing if and only if Thomas is a writer, and that it is not snowing we can infer that Thomas is not a writer. Finally, from the fact that Thomas is writing a letter if and only if Thomas is a writer, and that Thomas is not a writer we can infer that Thomas is not writing a letter. Therefore, the answer is yes.