Translate the following inference to logic notation: For all x, x_8 will not climb a mountain. There is at least one x for which x_8 will listen to a song. For all x, x_8 is a politician or x_8 is a server. For all x, x_8 is a politician if and only if x_8 will climb a mountain. Therefore there is at least one x for which x_8 is a server and x_8 will listen to a song.
forall x: ~P(x). exists x: Q(x). forall x: R(x) or S(x). forall x: R(x) <-> P(x). Therefore exists x: S(x) and Q(x).