Translate the following inference to logic notation: For all x, if x_5 were a nurse, then x_5 is cooking. For all x, x_5 is a nurse. For all x, if x_5 were happy, then x_5 is taking a plane. For all x, if x_5 cooks, then x_5 is happy. Therefore for all x, x_5 will take a plane.
forall x: P(x) -> Q(x). forall x: P(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). Therefore forall x: S(x).