Translate the following inference to logic notation: There is at least one x for which if x_8 cooks, then x_8 is making tea. For all x, x_8 is a nurse if and only if x_8 will make tea. For all x, x_8 is not a nurse. Therefore there is at least one x for which x_8 will not cook.
exists x: P(x) -> Q(x). forall x: R(x) <-> Q(x). forall x: ~R(x). Therefore exists x: ~P(x).