Translate the following inference to logic notation: For all x, if x_2 sleeps, then x_2 is playing squash. For all x, if x_2 listens to a song, then x_2 is playing squash. There is at least one x for which x_2 will climb a mountain or x_2 will listen to a song. For all x, x_2 will not climb a mountain or x_2 will sleep. Therefore there is at least one x for which x_2 will play squash.
forall x: P(x) -> Q(x). forall x: R(x) -> Q(x). exists x: S(x) or R(x). forall x: ~S(x) or P(x). Therefore exists x: Q(x).