Translate the following inference to logic notation: For all x, x_8 is not a janitor. There is at least one x for which x_8 is a janitor or x_8 is a politician. For all x, x_8 is a politician if and only if x_8 will listen to a song. Therefore there is at least one x for which x_8 will listen to a song.
forall x: ~P(x). exists x: P(x) or Q(x). forall x: Q(x) <-> R(x). Therefore exists x: R(x).