Translate the following inference to logic notation: There is at least one x for which if x_6 plays a game, then x_6 is taking a plane. For all x, if x_6 takes a plane, then x_6 is playing a game. For all x, x_6 will make tea if and only if x_6 will take a plane. For all x, x_6 will not make tea. Therefore there is at least one x for which x_6 will not play a game.
exists x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: R(x) <-> Q(x). forall x: ~R(x). Therefore exists x: ~P(x).