Translate the following inference to logic notation: For all x, x_8 will listen to a song if and only if x_8 will play squash. For all x, x_8 will play squash or x_1 will go running. For all x, x_8 will not listen to a song. Therefore there is at least one x for which x_1 will go running.
forall x: P(x) <-> Q(x). forall x: Q(x) or R(x). forall x: ~P(x). Therefore exists x: R(x).