Translate the following inference to logic notation: For all x, x_1 will listen to a song. For all x, x_7 is a politician if and only if x_7 is an astronaut. If Karen were a politician, then Joseph is not listening to a song. Therefore Karen is not an astronaut.
forall x: P(x). forall x: Q(x) <-> R(x). Q(a) -> ~P(b). Therefore ~R(a).