Translate the following inference to logic notation: There is at least one x for which z will sleep or z is not a poet. For all x, if z were a poet, then z is a scientist. For all x, if z were a scientist, then z is a poet. Therefore there is at least one x for which if z were a scientist, then z is sleeping.
exists x: P(x) or ~Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> Q(x). Therefore exists x: R(x) -> P(x).