Translate the following inference to logic notation: For all x, z will cook. For all x, z is sad if and only if z is a nurse. For all x, if z were a nurse, then z is not cooking. For all x, if z plays squash, then z is sad. Therefore for all x, z will not play squash.
forall x: P(x). forall x: Q(x) <-> R(x). forall x: R(x) -> ~P(x). forall x: S(x) -> Q(x). Therefore forall x: ~S(x).