Translate the following inference to logic notation: For all x, if z_4 were a writer, then z_4 is sleeping. For all x, z_4 is a writer or z_4 will not sleep. For all x, if z_4 sleeps, then z_4 is a writer. Therefore for all x, z_4 will sleep if and only if z_4 is a writer.
forall x: P(x) -> Q(x). forall x: P(x) or ~Q(x). forall x: Q(x) -> P(x). Therefore forall x: Q(x) <-> P(x).