Translate the following inference to logic notation: For all x, if x_9 works, then x_9 is sleeping. For all x, if x_9 sleeps, then x_9 is an office clerk. For all x, if x_9 sleeps, then x_9 is working. For all x, if x_9 were an office clerk, then x_9 is working. Therefore for all x, x_9 will sleep if and only if x_9 is an office clerk.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: Q(x) -> P(x). forall x: R(x) -> P(x). Therefore forall x: Q(x) <-> R(x).