Consider the following premises. Linda is not cooking. If it is not cloudy, then William is a mechanic. If Linda cooks, then it is cloudy. If it is cloudy, then Linda is cooking. Can we infer the following from them? If we can, name the inference rule being used: William is not a mechanic.
 From the fact that if Linda cooks, then it is cloudy, and that if it is cloudy, then Linda is cooking we can infer that Linda is cooking if and only if it is cloudy via biconditional introduction. From the fact that Linda is cooking if and only if it is cloudy, and that Linda is not cooking we can infer that it is not cloudy via biconditional elimination. Finally, from the fact that if it is not cloudy, then William is a mechanic, and that it is not cloudy we can infer that William is a mechanic via modus ponens, which contradicts that William is not a mechanic. Therefore, the answer is no.