Translate the following inference to logic notation: There is at least one x for which x will sleep or x will not cook. For all x, if x were an artist, then x is drinking water. For all x, x will drink water if and only if x will cook. Therefore there is at least one x for which if x were an artist, then x is sleeping.
exists x: P(x) or ~Q(x). forall x: R(x) -> S(x). forall x: S(x) <-> Q(x). Therefore exists x: R(x) -> P(x).