Translate the following inference to logic notation: For all x, x is not poor. If it is overcast, then Joseph is a politician. For all x, x is a politician if and only if x is poor. If Joseph were a politician, then it is overcast. Therefore it is not overcast.
forall x: ~P(x). p -> Q(a). forall x: Q(x) <-> P(x). Q(a) -> p. Therefore ~p.