Translate the following inference to logic notation: For all x, y is a bartender. For all x, if y were a bartender, then y is an astronaut. For all x, y is a cashier or y is not an astronaut. Therefore for all x, y is a cashier.
forall x: P(x). forall x: P(x) -> Q(x). forall x: R(x) or ~Q(x). Therefore forall x: R(x).