Translate the following inference to logic notation: For all x, y_3 will listen to a song or y_3 is an office clerk. There is at least one x for which if y_3 listens to a song, then y_3 is climbing a mountain. For all x, y_3 will climb a mountain or y_3 is not a politician. For all x, if y_3 were an office clerk, then y_3 is a politician. Therefore there is at least one x for which y_3 will climb a mountain.
forall x: P(x) or Q(x). exists x: P(x) -> R(x). forall x: R(x) or ~S(x). forall x: Q(x) -> S(x). Therefore exists x: R(x).