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