Translate the following inference to logic notation: There is at least one x for which if x_12 were excited, then x_12 is a politician. For all x, x_12 is excited. For all x, x_12 is a cashier. For all x, if x_12 were a politician, then x_12 is a nurse. Therefore there is at least one x for which x_12 is a nurse.
exists x: P(x) -> Q(x). forall x: P(x). forall x: R(x). forall x: Q(x) -> S(x). Therefore exists x: S(x).