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