Translate the following inference to logic notation: For all x, x_6 will listen to a song or x_6 will climb a mountain. For all x, x_6 will not listen to a song or x_6 is a musician. For all x, x_6 will work or x_6 will not climb a mountain. For all x, if x_6 were a musician, then x_6 is working. Therefore for all x, x_6 will work.
forall x: P(x) or Q(x). forall x: ~P(x) or R(x). forall x: S(x) or ~Q(x). forall x: R(x) -> S(x). Therefore forall x: S(x).