Translate the following inference to logic notation: If it rains, then Michael is a server. For all x, if y were a server, then y is a sailor. For all x, if y were a sailor, then y is a server. For all x, y is not a sailor. Therefore it is not raining.
p -> P(a). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: ~Q(x). Therefore ~p.