Translate the following inference to logic notation: For all x, x_3 is a sailor if and only if x_3 will sleep. For all x, if x_3 sleeps, then x_3 is a sailor. Therefore for all x, x_3 will sleep if and only if x_3 is a sailor.
forall x: P(x) <-> Q(x). forall x: Q(x) -> P(x). Therefore forall x: Q(x) <-> P(x).