Consider the following premises. For all y, y will not work. For all y, y will work or y will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is listening to a song or it is cloudy.
 From the fact that for all y, y will work or y will listen to a song, and that for all y, y will not work we can infer that for all y, y will listen to a song via universal disjunctive syllogism. From the fact that for all y, y will listen to a song we can infer that Jennifer is listening to a song via universal instantiation. Finally, from the fact that Jennifer is listening to a song we can infer that Jennifer is listening to a song or it is cloudy via addition. Therefore, the answer is yes.