Translate the following inference to logic notation: For all x, z_2 is a carpenter if and only if z_2 will sleep. For all x, if z_2 were a carpenter, then z_2 is sleeping. Therefore for all x, if z_2 were a carpenter, then z_2 is sleeping.
forall x: P(x) <-> Q(x). forall x: P(x) -> Q(x). Therefore forall x: P(x) -> Q(x).