Translate the following inference to logic notation: There is at least one x for which z_4 is a janitor if and only if z_4 is fast. For all x, if z_4 were fast, then z_4 is a janitor. Therefore there is at least one x for which if z_4 were a janitor, then z_4 is fast.
exists x: P(x) <-> Q(x). forall x: Q(x) -> P(x). Therefore exists x: P(x) -> Q(x).