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