Translate the following inference to logic notation: For all x, if x_9 were a musician, then x_9 is listening to a song. For all x, if x_9 were a server, then x_9 is a musician. For all x, if x_9 listens to a song, then x_9 is a musician. For all x, if x_9 listens to a song, then x_9 is a server. Therefore for all x, x_9 will listen to a song if and only if x_9 is a server.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> P(x). forall x: Q(x) -> R(x). Therefore forall x: Q(x) <-> R(x).