Translate the following inference to logic notation: For all x, if x_7 were a nurse, then x_4 is cooking. For all x, x_7 will not make tea or x_7 is a nurse. For all x, x_7 will make tea or x_7 is rich. For all x, if x_7 were rich, then x_4 is cooking. Therefore there is at least one x for which x_4 will cook.
forall x: P(x) -> Q(x). forall x: ~R(x) or P(x). forall x: R(x) or S(x). forall x: S(x) -> Q(x). Therefore exists x: Q(x).