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