Translate the following inference to logic notation: For all x, if x_5 were a janitor, then x_5 is cooking. For all x, x_5 will not play a game. For all x, x_5 will cook if and only if x_5 will play a game. For all x, if x_5 cooks, then x_5 is a janitor. Therefore for all x, x_5 is not a janitor.
forall x: P(x) -> Q(x). forall x: ~R(x). forall x: Q(x) <-> R(x). forall x: Q(x) -> P(x). Therefore forall x: ~P(x).