Consider the following premises. For all y_4, y_4 will take a plane if and only if y_4 is sad. It is not late. It is overcast if and only if it is late. If Charles were sad, then it is overcast. Can we infer the following from them? If we can, name the inference rule being used: Charles is taking a plane.
 From the fact that it is overcast if and only if it is late, and that it is not late we can infer that it is not overcast via biconditional elimination. From the fact that for all y_4, y_4 will take a plane if and only if y_4 is sad we can infer that Charles is taking a plane if and only if Charles is sad via universal instantiation. From the fact that if Charles were sad, then it is overcast, and that it is not overcast we can infer that Charles is not sad via modus tollens. Finally, from the fact that Charles is taking a plane if and only if Charles is sad, and that Charles is not sad we can infer that Charles is not taking a plane via biconditional elimination, which contradicts that Charles is taking a plane. Therefore, the answer is no.