Translate the following inference to logic notation: For all x, if x_9 listens to a song, then x_9 is a soldier. For all x, x_9 will play a game or x_9 is an electrician. There is at least one x for which x_9 will play a game if and only if x_9 will listen to a song. For all x, if x_9 were an electrician, then x_9 is a soldier. Therefore there is at least one x for which x_9 is a soldier.
forall x: P(x) -> Q(x). forall x: R(x) or S(x). exists x: R(x) <-> P(x). forall x: S(x) -> Q(x). Therefore exists x: Q(x).