Translate the following inference to logic notation: Patricia is not playing a game. For all x, if x_3 plays a game, then x_3 is a nurse. For all x, if x_3 were a nurse, then x_3 is playing a game. Therefore Patricia is not a nurse.
~P(a). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore ~Q(a).