Translate the following inference to logic notation: For all x, if z were sad, then z is a musician. For all x, if z were a musician, then z is sad. For all x, if z were sad, then z is sleeping. For all x, if z sleeps, then z is a musician. Therefore for all x, z is sad if and only if z will sleep.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: P(x) -> R(x). forall x: R(x) -> Q(x). Therefore forall x: P(x) <-> R(x).