Translate the following inference to logic notation: For all x, if y_4 cooks, then y_4 is a soldier. For all x, if y_4 were a soldier, then y_4 is cooking. Therefore for all x, if y_4 cooks, then y_4 is a soldier.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore forall x: P(x) -> Q(x).