Translate the following inference to logic notation: For all x, if x cooks, then x is a scientist. For all x, if x were a scientist, then x is cooking. For all x, x will drink water. For all x, if x listens to a song, then x is cooking. For all x, if x drinks water, then x is listening to a song. Therefore for all x, x is a scientist.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: R(x). forall x: S(x) -> P(x). forall x: R(x) -> S(x). Therefore forall x: Q(x).