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