Translate the following inference to logic notation: For all x, if x_10 plays a game, then x_10 is listening to a song. For all x, x_10 is a politician. There is at least one x for which if x_10 were a politician, then x_10 is listening to a song. For all x, x_10 will play a game if and only if x_10 is a server. Therefore there is at least one x for which x_10 will listen to a song.
forall x: P(x) -> Q(x). forall x: R(x). exists x: R(x) -> Q(x). forall x: P(x) <-> S(x). Therefore exists x: Q(x).