Consider the following premises. For all x, x is excited or x is not a nurse. For all x, if x were excited, then x is a janitor. There is at least one x for which x will listen to a song or x is a nurse. For all x, if x listens to a song, then x is a janitor. Can we infer the following from them? There is at least one x for which x is a janitor.
 From the fact that for all x, x is excited or x is not a nurse we can infer that for all x, if x were a nurse, then x is excited. From the fact that for all x, if x were a nurse, then x is excited, and that for all x, if x were excited, then x is a janitor we can infer that for all x, if x were a nurse, then x is a janitor. Finally, from the fact that for all x, if x listens to a song, then x is a janitor, that for all x, if x were a nurse, then x is a janitor, and that there is at least one x for which x will listen to a song or x is a nurse we can infer that there is at least one x for which x is a janitor. Therefore, the answer is yes.