Consider the following premises. Sarah is writing a letter if and only if it is cold. If it is overcast, then it is cold. Karen is sleeping if and only if Sarah is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: If it is overcast, then Karen is sleeping.
 From the fact that Sarah is writing a letter if and only if it is cold we can infer that if it is cold, then Sarah is writing a letter via biconditional elimination. From the fact that Karen is sleeping if and only if Sarah is writing a letter we can infer that if Sarah writes a letter, then Karen is sleeping via biconditional elimination. From the fact that if it is overcast, then it is cold, and that if it is cold, then Sarah is writing a letter we can infer that if it is overcast, then Sarah is writing a letter via transitivity. Finally, from the fact that if it is overcast, then Sarah is writing a letter, and that if Sarah writes a letter, then Karen is sleeping we can infer that if it is overcast, then Karen is sleeping via transitivity. Therefore, the answer is yes.