Translate the following inference to logic notation: For all x, x_14 is a nurse if and only if x_14 will sleep. If Joseph sleeps, then it is late. If it is late, then Joseph is a nurse. Therefore if Joseph sleeps, then Joseph is a nurse.
forall x: P(x) <-> Q(x). Q(a) -> p. p -> P(a). Therefore Q(a) -> P(a).