Translate the following inference to logic notation: For all x, if x were rich, then x is cooking. For all x, x is not rich. For all x, if x cooks, then x is rich. Michael is sleeping if and only if Richard is cooking. Therefore Michael is not sleeping.
forall x: P(x) -> Q(x). forall x: ~P(x). forall x: Q(x) -> P(x). p <-> Q(a). Therefore ~p.