Consider the following premises. For all x_5, if x_5 listens to a song, then x_5 is a politician. For all x_5, x_5 is a politician or x_5 is not rich. There is at least one x_5 for which x_5 is a cashier or x_5 is rich. For all x_5, if x_5 were a cashier, then x_5 is listening to a song. Can we infer the following from them? For all x_5, x_5 is not a politician.
 From the fact that for all x_5, if x_5 were a cashier, then x_5 is listening to a song, and that for all x_5, if x_5 listens to a song, then x_5 is a politician we can infer that for all x_5, if x_5 were a cashier, then x_5 is a politician. From the fact that for all x_5, x_5 is a politician or x_5 is not rich we can infer that for all x_5, if x_5 were rich, then x_5 is a politician. Finally, from the fact that for all x_5, if x_5 were a cashier, then x_5 is a politician, that for all x_5, if x_5 were rich, then x_5 is a politician, and that there is at least one x_5 for which x_5 is a cashier or x_5 is rich we can infer that there is at least one x_5 for which x_5 is a politician, which contradicts that For all x_5, x_5 is not a politician. Therefore, the answer is no.