Consider the following premises. There is at least one y for which y is a scientist. For all y, y is a musician. For all y, y is a musician if and only if y is a cashier. Can we infer the following from them? If we can, name the inference rule being used: For all y, either y is a scientist or y is a cashier are not true.
 From the fact that for all y, y is a musician if and only if y is a cashier we can infer that for all y, if y were a musician, then y is a cashier via universal biconditional elimination. From the fact that for all y, if y were a musician, then y is a cashier, and that for all y, y is a musician we can infer that for all y, y is a cashier via universal modus ponens. Finally, from the fact that there is at least one y for which y is a scientist, and that for all y, y is a cashier we can infer that some scientists are cashiers via existential conjunction, which contradicts that For all y, either y is a scientist or y is a cashier are not true. Therefore, the answer is no.