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