Translate the following inference to logic notation: For all x, x_1 will not listen to a song. For all x, x_1 is a politician if and only if x_1 is a musician. For all x, if x_1 were a politician, then x_1 is listening to a song. There is at least one x for which x_1 is a musician if and only if x_1 is a politician. Therefore there is at least one x for which x_1 is not a musician.
forall x: ~P(x). forall x: Q(x) <-> R(x). forall x: Q(x) -> P(x). exists x: R(x) <-> Q(x). Therefore exists x: ~R(x).