Translate the following inference to logic notation: For all x, if x_9 were a nurse, then x_9 is sad. For all x, if x_9 were sad, then x_9 is a nurse. For all x, x_9 is sad or x_9 is not a nurse. Therefore for all x, x_9 is a nurse if and only if x_9 is sad.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: Q(x) or ~P(x). Therefore forall x: P(x) <-> Q(x).