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