Translate the following inference to logic notation: For all x, x_7 will cook if and only if x_7 will sleep. For all x, x_7 is a scientist and x_7 is a nurse. For all x, if x_7 sleeps, then x_7 is not a scientist. Therefore for all x, x_7 will not cook.
forall x: P(x) <-> Q(x). forall x: R(x) and S(x). forall x: Q(x) -> ~R(x). Therefore forall x: ~P(x).