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