Translate the following inference to logic notation: For all x, if x_5 were an office clerk, then x_5 is a lawyer. For all x, if x_5 were a scientist, then x_5 is an office clerk. For all x, x_5 is a scientist or x_5 is not a lawyer. Therefore for all x, x_5 is a lawyer if and only if x_5 is a scientist.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: R(x) or ~Q(x). Therefore forall x: Q(x) <-> R(x).