Consider the following premises. Mary is not listening to a song. For all x_19, if x_19 were a police officer, then x_19 is listening to a song. Mary is a police officer or it is overcast. Can we infer the following from them? If we can, name the inference rule being used: It is overcast or it is cloudy.
 From the fact that for all x_19, if x_19 were a police officer, then x_19 is listening to a song we can infer that if Mary were a police officer, then Mary is listening to a song via universal instantiation. From the fact that if Mary were a police officer, then Mary is listening to a song, and that Mary is not listening to a song we can infer that Mary is not a police officer via modus tollens. From the fact that Mary is a police officer or it is overcast, and that Mary is not a police officer we can infer that it is overcast via disjunctive syllogism. Finally, from the fact that it is overcast we can infer that it is overcast or it is cloudy via addition. Therefore, the answer is yes.