Translate the following inference to logic notation: For all x, if x_5 were a lawyer, then x_5 is a scientist. For all x, if x_5 were a scientist, then x_5 is a lawyer. For all x, x_5 is not a lawyer. For all x, if x_5 works, then x_5 is a scientist. Therefore for all x, x_5 will not work.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: ~P(x). forall x: R(x) -> Q(x). Therefore forall x: ~R(x).