Consider the following premises. Patricia is not making tea. It is overcast if and only if Patricia is making tea. If it is overcast, then Patricia is making tea. If it is not overcast, then William is a sailor. Can we infer the following from them? If we can, name the inference rule being used: William is a sailor.
 From the fact that it is overcast if and only if Patricia is making tea we can infer that if Patricia makes tea, then it is overcast via biconditional elimination. From the fact that if Patricia makes tea, then it is overcast, and that if it is overcast, then Patricia is making tea we can infer that Patricia is making tea if and only if it is overcast via biconditional introduction. From the fact that Patricia is making tea if and only if it is overcast, and that Patricia is not making tea we can infer that it is not overcast via biconditional elimination. Finally, from the fact that if it is not overcast, then William is a sailor, and that it is not overcast we can infer that William is a sailor via modus ponens. Therefore, the answer is yes.