Translate the following inference to logic notation: For all x, if x were a writer, then x is playing a game. For all x, x is a nurse if and only if x will play a game. For all x, x is not a nurse. There is at least one x for which if x plays a game, then x is a writer. Therefore there is at least one x for which x is not a writer.
forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). forall x: ~R(x). exists x: Q(x) -> P(x). Therefore exists x: ~P(x).