Translate the following inference to logic notation: For all x, x_18 is not a politician. There is at least one x for which if x_18 were a musician, then x_18 is playing tennis. For all x, x_18 is a nurse if and only if x_18 will play tennis. For all x, x_18 is a politician if and only if x_18 is a musician. For all x, if x_18 plays tennis, then x_18 is a musician. Therefore there is at least one x for which x_18 is not a nurse.
forall x: ~P(x). exists x: Q(x) -> R(x). forall x: S(x) <-> R(x). forall x: P(x) <-> Q(x). forall x: R(x) -> Q(x). Therefore exists x: ~S(x).