Translate the following inference to logic notation: There is at least one x for which if x_11 climbs a mountain, then x_11 is sleeping. For all x, x_11 will climb a mountain or x_11 will not play squash. For all x, x_11 will play squash if and only if x_11 will sleep. Therefore there is at least one x for which x_11 will climb a mountain if and only if x_11 will play squash.
exists x: P(x) -> Q(x). forall x: P(x) or ~R(x). forall x: R(x) <-> Q(x). Therefore exists x: P(x) <-> R(x).