Translate the following inference to logic notation: For all x, x_9 will write a letter if and only if x_9 is a nurse. There is at least one x for which if x_9 works, then x_9 is writing a letter. For all x, if x_9 were an office clerk, then x_9 is working. For all x, x_9 is not a nurse. Therefore there is at least one x for which x_9 is not an office clerk.
forall x: P(x) <-> Q(x). exists x: R(x) -> P(x). forall x: S(x) -> R(x). forall x: ~Q(x). Therefore exists x: ~S(x).