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