Translate the following inference to logic notation: There is at least one x for which z is fast if and only if z is a server. For all x, z is a server if and only if z will write a letter. Therefore there is at least one x for which if z writes a letter, then z is fast.
exists x: P(x) <-> Q(x). forall x: Q(x) <-> R(x). Therefore exists x: R(x) -> P(x).