Translate the following inference to logic notation: For all x, y_1 is a janitor or y_1 will not sleep. There is at least one x for which y_1 is an artist if and only if y_1 is a janitor. Therefore there is at least one x for which if y_1 sleeps, then y_1 is an artist.
forall x: P(x) or ~Q(x). exists x: R(x) <-> P(x). Therefore exists x: Q(x) -> R(x).