Consider the following premises. Sarah is listening to a song or it is snowing. If Mary were a politician, then Sarah is listening to a song. If Sarah listens to a song, then Mary is a politician. Mary is not a politician. Can we infer the following from them? If we can, name the inference rule being used: It is snowing.
 From the fact that if Mary were a politician, then Sarah is listening to a song, and that if Sarah listens to a song, then Mary is a politician we can infer that Mary is a politician if and only if Sarah is listening to a song via biconditional introduction. From the fact that Mary is a politician if and only if Sarah is listening to a song, and that Mary is not a politician we can infer that Sarah is not listening to a song via biconditional elimination. Finally, from the fact that Sarah is listening to a song or it is snowing, and that Sarah is not listening to a song we can infer that it is snowing via disjunctive syllogism. Therefore, the answer is yes.