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