Translate the following inference to logic notation: For all x, x will listen to a song or x is not a politician. There is at least one x for which x is an office clerk if and only if x is a politician. Therefore there is at least one x for which if x were an office clerk, then x is listening to a song.
forall x: P(x) or ~Q(x). exists x: R(x) <-> Q(x). Therefore exists x: R(x) -> P(x).