Consider the following premises. It is cold. William is playing tennis. If it is cold, then it is overcast. Can we infer the following from them? If we can, name the inference rule being used: It is not overcast.
 From the fact that it is cold, and that William is playing tennis we can infer that it is cold and William is playing tennis via conjunction. From the fact that it is cold and William is playing tennis we can infer that it is cold via simplification. Finally, from the fact that if it is cold, then it is overcast, and that it is cold we can infer that it is overcast via modus ponens, which contradicts that It is not overcast. Therefore, the answer is no.