Translate the following inference to logic notation: For all x, x_8 will cook if and only if x_8 will play tennis. For all x, x_8 is not a doctor. For all x, x_8 will play tennis if and only if x_8 is a writer. For all x, x_8 will cook if and only if x_8 is a doctor. Therefore for all x, x_8 is not a writer.
forall x: P(x) <-> Q(x). forall x: ~R(x). forall x: Q(x) <-> S(x). forall x: P(x) <-> R(x). Therefore forall x: ~S(x).