Translate the following inference to logic notation: There is at least one x for which x_15 will listen to a song. For all x, x_15 is a cashier. For all x, x_15 will play a game if and only if x_15 will listen to a song. Therefore there is at least one x for which x_15 will play a game.
exists x: P(x). forall x: Q(x). forall x: R(x) <-> P(x). Therefore exists x: R(x).