Translate the following inference to logic notation: For all x, if x_6 cooks, then x_6 is playing tennis. For all x, if x_6 plays tennis, then x_6 is a doctor. For all x, x_6 will cook or x_6 is not a doctor. Therefore for all x, x_6 will cook if and only if x_6 is a doctor.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: P(x) or ~R(x). Therefore forall x: P(x) <-> R(x).