Consider the following premises. For all x, x is a nurse or x is a taxi driver. For all x, if x were a nurse, then x is listening to a song. For all x, x will not listen to a song. Can we infer the following from them? If we can, name the inference rule being used: Sarah is a taxi driver or Barbara is cooking.
 From the fact that for all x, if x were a nurse, then x is listening to a song, and that for all x, x will not listen to a song we can infer that for all x, x is not a nurse via universal modus tollens. From the fact that for all x, x is a nurse or x is a taxi driver, and that for all x, x is not a nurse we can infer that for all x, x is a taxi driver via universal disjunctive syllogism. From the fact that for all x, x is a taxi driver we can infer that Sarah is a taxi driver via universal instantiation. Finally, from the fact that Sarah is a taxi driver we can infer that Sarah is a taxi driver or Barbara is cooking via addition. Therefore, the answer is yes.