Translate the following inference to logic notation: For all x, y_1 is a lawyer if and only if y_1 is a nurse. There is at least one x for which y_1 is a nurse if and only if y_1 is a lawyer. Therefore there is at least one x for which if y_1 were a nurse, then y_1 is a lawyer.
forall x: P(x) <-> Q(x). exists x: Q(x) <-> P(x). Therefore exists x: Q(x) -> P(x).