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