Translate the following inference to logic notation: For all x, x_15 will not work. For all x, x_15 will work or x_15 is not sad. Charles is listening to a song if and only if it is cloudy. For all x, x_15 is sad if and only if x_15 will listen to a song. Therefore it is not cloudy.
forall x: ~P(x). forall x: P(x) or ~Q(x). R(a) <-> p. forall x: Q(x) <-> R(x). Therefore ~p.