Translate the following inference to logic notation: There is at least one x for which if z sleeps, then z is an office clerk. For all x, if z were a doctor, then z is an office clerk. For all x, if z were an office clerk, then z is a doctor. For all x, z will sleep or z is a doctor. Therefore there is at least one x for which z is an office clerk.
exists x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: Q(x) -> R(x). forall x: P(x) or R(x). Therefore exists x: Q(x).