Translate the following inference to logic notation: For all x, z is a cashier or z is not a poet. There is at least one x for which z is a poet or z is not excited. For all x, if z were a cashier, then z is excited. Therefore there is at least one x for which if z were excited, then z is a cashier.
forall x: P(x) or ~Q(x). exists x: Q(x) or ~R(x). forall x: P(x) -> R(x). Therefore exists x: R(x) -> P(x).