Translate the following inference to logic notation: For all x, x_12 will work and x_12 is rich. For all x, x_12 will write a letter if and only if x_12 is a nurse. For all x, if x_12 were a nurse, then x_12 is not working. For all x, if x_12 were a nurse, then x_12 is writing a letter. Therefore for all x, x_12 will not write a letter.
forall x: P(x) and Q(x). forall x: R(x) <-> S(x). forall x: S(x) -> ~P(x). forall x: S(x) -> R(x). Therefore forall x: ~R(x).