Translate the following inference to logic notation: For all x, if z goes running, then z is writing a letter. For all x, if z writes a letter, then z is running. For all x, z will write a letter if and only if z will go running. Therefore for all x, z will go running if and only if z will write a letter.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: Q(x) <-> P(x). Therefore forall x: P(x) <-> Q(x).