Translate the following inference to logic notation: For all x, if x_6 were a politician, then z_1 is a doctor. For all x, x_6 is a politician. For all x, if x_6 were a lawyer, then z_1 is a doctor. Therefore there is at least one x for which z_1 is a doctor.
forall x: P(x) -> Q(x). forall x: P(x). forall x: R(x) -> Q(x). Therefore exists x: Q(x).