Translate the following inference to logic notation: There is at least one x for which if x_9 were a bartender, then x_9 is a nurse. For all x, x_9 will not read a book. For all x, x_9 is a nurse if and only if x_9 will read a book. For all x, if x_9 were a carpenter, then x_9 is a bartender. Therefore there is at least one x for which x_9 is not a carpenter.
exists x: P(x) -> Q(x). forall x: ~R(x). forall x: Q(x) <-> R(x). forall x: S(x) -> P(x). Therefore exists x: ~S(x).