Translate the following inference to logic notation: For all x, z is a police officer or z is bored. For all x, z is an office clerk. For all x, if z were bored, then z is listening to a song. For all x, z will listen to a song or z is not a police officer. Therefore for all x, z will listen to a song and z is an office clerk.
forall x: P(x) or Q(x). forall x: R(x). forall x: Q(x) -> S(x). forall x: S(x) or ~P(x). Therefore forall x: S(x) and R(x).