Translate the following inference to logic notation: For all x, if z_3 works, then z_3 is sleeping. For all x, if z_3 sleeps, then z_3 is working. For all x, z_3 will work if and only if z_3 will sleep. Therefore for all x, z_3 will work if and only if z_3 will sleep.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: P(x) <-> Q(x). Therefore forall x: P(x) <-> Q(x).