Translate the following inference to logic notation: For all x, x_5 will listen to a song if and only if x_5 is a scientist. For all x, x_5 is a scientist. For all x, x_5 will not listen to a song. Therefore for all x, x_5 will sleep.
forall x: P(x) <-> Q(x). forall x: Q(x). forall x: ~P(x). Therefore forall x: R(x).