Translate the following inference to logic notation: For all x, y_1 is a nurse or y_1 will not cook. For all x, if y_1 were a nurse, then y_1 is cooking. For all x, if y_1 cooks, then y_1 is a nurse. Therefore for all x, if y_1 were a nurse, then y_1 is cooking.
forall x: P(x) or ~Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore forall x: P(x) -> Q(x).