Translate the following inference to logic notation: For all x, x_5 will work. For all x, x_5 will sleep if and only if x_5 will work. For all x, if x_5 were a janitor, then x_5 is sleeping. Therefore for all x, x_5 will sleep.
forall x: P(x). forall x: Q(x) <-> P(x). forall x: R(x) -> Q(x). Therefore forall x: Q(x).