Translate the following inference to logic notation: For all x, if x_5 goes running, then x_5 is cooking. There is at least one x for which if x_5 drinks water, then x_5 is running. For all x, x_5 will not take a plane. For all x, x_5 will take a plane if and only if x_5 will cook. Therefore there is at least one x for which x_5 will not drink water.
forall x: P(x) -> Q(x). exists x: R(x) -> P(x). forall x: ~S(x). forall x: S(x) <-> Q(x). Therefore exists x: ~R(x).