Translate the following inference to logic notation: For all x, if x climbs a mountain, then x is running. For all x, if x goes running, then x is excited. For all x, if x were excited, then x is climbing a mountain. For all x, if x goes running, then x is climbing a mountain. Therefore for all x, x will go running if and only if x will climb a mountain.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). forall x: Q(x) -> P(x). Therefore forall x: Q(x) <-> P(x).