Translate the following inference to logic notation: There is at least one x for which x_4 will climb a mountain if and only if x_4 will go running. For all x, x_4 will climb a mountain if and only if x_4 will go running. Therefore there is at least one x for which x_4 will climb a mountain if and only if x_4 will go running.
exists x: P(x) <-> Q(x). forall x: P(x) <-> Q(x). Therefore exists x: P(x) <-> Q(x).