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