Consider the following premises. If Joseph were curious, then John is working. If John works, then Patricia is writing a letter. If it is cold, then Joseph is curious. It is cold if and only if Patricia is writing a letter. Can we infer the following from them? If it is cold, then Patricia is writing a letter.
 From the fact that if it is cold, then Joseph is curious, and that if Joseph were curious, then John is working we can infer that if it is cold, then John is working. Finally, from the fact that if it is cold, then John is working, and that if John works, then Patricia is writing a letter we can infer that if it is cold, then Patricia is writing a letter. Therefore, the answer is yes.