Translate the following inference to logic notation: For all x, if x_7 listens to a song, then x_7 is playing a game. There is at least one x for which if x_7 cooks, then x_7 is happy. For all x, x_7 will cook or x_7 will not play a game. Therefore there is at least one x for which if x_7 listens to a song, then x_7 is happy.
forall x: P(x) -> Q(x). exists x: R(x) -> S(x). forall x: R(x) or ~Q(x). Therefore exists x: P(x) -> S(x).