Translate the following inference to logic notation: For all x, if z were a janitor, then z is happy. For all x, if z were a janitor, then z is happy. For all x, if z were happy, then z is a janitor. For all x, z is not a janitor. For all x, z is happy if and only if z is a doctor. Therefore for all x, z is not a doctor.
forall x: P(x) -> Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: ~P(x). forall x: Q(x) <-> R(x). Therefore forall x: ~R(x).