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