Translate the following inference to logic notation: For all x, if x_5 works, then x_5 is sleeping. For all x, x_5 is a writer if and only if x_5 is happy. For all x, if x_5 sleeps, then x_5 is happy. Therefore for all x, if x_5 works, then x_5 is a writer.
forall x: P(x) -> Q(x). forall x: R(x) <-> S(x). forall x: Q(x) -> S(x). Therefore forall x: P(x) -> R(x).