Translate the following inference to logic notation: For all x, z is a politician if and only if z is a writer. There is at least one x for which if z were a politician, then z is a writer. Therefore there is at least one x for which if z were a politician, then z is a writer.
forall x: P(x) <-> Q(x). exists x: P(x) -> Q(x). Therefore exists x: P(x) -> Q(x).