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