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