Translate the following inference to logic notation: For all x, if z_4 were an astronaut, then z_4 is listening to a song. For all x, z_4 is an astronaut or z_4 is not a cashier. For all x, if z_4 plays a game, then z_4 is a cashier. Therefore for all x, if z_4 plays a game, then z_4 is listening to a song.
forall x: P(x) -> Q(x). forall x: P(x) or ~R(x). forall x: S(x) -> R(x). Therefore forall x: S(x) -> Q(x).