Translate the following inference to logic notation: For all x, x_4 will go running if and only if x_4 is a musician. There is at least one x for which x_4 is not a musician. For all x, if x_4 goes running, then x_4 is climbing a mountain. For all x, if x_4 climbs a mountain, then x_4 is running. Therefore there is at least one x for which x_4 will not climb a mountain.
forall x: P(x) <-> Q(x). exists x: ~Q(x). forall x: P(x) -> R(x). forall x: R(x) -> P(x). Therefore exists x: ~R(x).