Translate the following inference to logic notation: For all x, if x_1 were happy, then x_1 is writing a letter. For all x, if x_1 writes a letter, then x_1 is excited. There is at least one x for which if x_1 climbs a mountain, then x_1 is happy. Therefore there is at least one x for which if x_1 climbs a mountain, then x_1 is excited.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: S(x) -> P(x). Therefore exists x: S(x) -> R(x).