Translate the following inference to logic notation: For all x, if x_2 cooks, then x_2 is playing tennis. There is at least one x for which if x_2 plays tennis, then x_2 is cooking. For all x, if x_2 plays tennis, then x_2 is playing a game. Therefore there is at least one x for which if x_2 cooks, then x_2 is playing a game.
forall x: P(x) -> Q(x). exists x: Q(x) -> P(x). forall x: Q(x) -> R(x). Therefore exists x: P(x) -> R(x).