Translate the following inference to logic notation: For all x, if x_6 were a server, then x_6 is not cooking. For all x, x_6 will cook. For all x, x_6 is a server or x_6 will drink water. There is at least one x for which if x_6 drinks water, then x_6 is fast. Therefore there is at least one x for which x_6 is fast.
forall x: P(x) -> ~Q(x). forall x: Q(x). forall x: P(x) or R(x). exists x: R(x) -> S(x). Therefore exists x: S(x).