Translate the following inference to logic notation: For all x, if x_8 takes a plane, then x_8 is not writing a letter. For all x, if x_8 plays tennis, then x_8 is drinking water. For all x, x_8 will write a letter. For all x, if x_8 takes a plane, then x_8 is playing tennis. There is at least one x for which if x_8 drinks water, then x_8 is taking a plane. Therefore there is at least one x for which x_8 will not play tennis.
forall x: P(x) -> ~Q(x). forall x: R(x) -> S(x). forall x: Q(x). forall x: P(x) -> R(x). exists x: S(x) -> P(x). Therefore exists x: ~R(x).