Translate the following inference to logic notation: For all x, if x_12 were a soldier, then x_12 is a bartender. For all x, if x_12 were a bartender, then x_12 is a soldier. If Karen were not a bartender, then Elisabeth is a nurse. Karen is not a soldier. Therefore Elisabeth is a nurse.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). ~Q(a) -> p. ~P(a). Therefore p.