Translate the following inference to logic notation: For all x, x_5 will not listen to a song. For all x, x_5 will play a game if and only if x_5 will climb a mountain. For all x, if x_5 climbs a mountain, then x_5 is listening to a song. Therefore for all x, x_5 will not play a game.
forall x: ~P(x). forall x: Q(x) <-> R(x). forall x: R(x) -> P(x). Therefore forall x: ~Q(x).