Translate the following inference to logic notation: For all x, z is not a politician. There is at least one x for which if z were a politician, then z is a doctor. For all x, z is a doctor if and only if z is a politician. For all x, if z plays tennis, then z is a doctor. Therefore there is at least one x for which z will not play tennis.
forall x: ~P(x). exists x: P(x) -> Q(x). forall x: Q(x) <-> P(x). forall x: R(x) -> Q(x). Therefore exists x: ~R(x).