Consider the following premises. David is working or Sarah is listening to a song. David is working if and only if Sarah is a politician. For all y, if y listens to a song, then y is a politician. Can we infer the following from them? If we can, name the inference rule being used: Sarah is not a politician.
 From the fact that for all y, if y listens to a song, then y is a politician we can infer that if Sarah listens to a song, then Sarah is a politician via universal instantiation. From the fact that David is working if and only if Sarah is a politician we can infer that if David works, then Sarah is a politician via biconditional elimination. Finally, from the fact that if David works, then Sarah is a politician, that if Sarah listens to a song, then Sarah is a politician, and that David is working or Sarah is listening to a song we can infer that Sarah is a politician via disjunction elimination, which contradicts that Sarah is not a politician. Therefore, the answer is no.