Translate the following inference to logic notation: For all x, if x_1 listens to a song, then x_1 is a police officer. For all x, if x_1 were bored, then x_1 is listening to a song. There is at least one x for which x_1 is bored. Therefore there is at least one x for which x_1 is a police officer.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: R(x). Therefore exists x: Q(x).