Translate the following inference to logic notation: There is at least one x for which if x_6 were a server, then x_6 is working. For all x, if x_6 writes a letter, then x_6 is a server. For all x, x_6 will work if and only if x_6 will write a letter. Therefore there is at least one x for which x_6 will write a letter if and only if x_6 will work.
exists x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: Q(x) <-> R(x). Therefore exists x: R(x) <-> Q(x).