Translate the following inference to logic notation: For all x, if x_4 drinks water, then x_4 is sad. There is at least one x for which x_4 is not sad. For all x, if x_4 writes a letter, then x_4 is working. For all x, if x_4 works, then x_4 is drinking water. For all x, if x_4 were sad, then x_4 is drinking water. Therefore there is at least one x for which x_4 will not write a letter.
forall x: P(x) -> Q(x). exists x: ~Q(x). forall x: R(x) -> S(x). forall x: S(x) -> P(x). forall x: Q(x) -> P(x). Therefore exists x: ~R(x).