Translate the following inference to logic notation: For all x, if x_3 writes a letter, then x_3 is climbing a mountain. For all x, x_3 will climb a mountain if and only if x_3 will sleep. There is at least one x for which x_3 will write a letter. Therefore there is at least one x for which x_3 will sleep.
forall x: P(x) -> Q(x). forall x: Q(x) <-> R(x). exists x: P(x). Therefore exists x: R(x).