Translate the following inference to logic notation: For all x, x is a nurse. For all x, if x were a politician, then x is not a nurse. For all x, x is a politician if and only if x is excited. Therefore for all x, x is not excited.
forall x: P(x). forall x: Q(x) -> ~P(x). forall x: Q(x) <-> R(x). Therefore forall x: ~R(x).