Translate the following inference to logic notation: For all x, if x_12 listens to a song, then x_12 is drinking water. For all x, x_12 will work if and only if x_12 will drink water. There is at least one x for which x_12 will listen to a song or x_12 will work. Therefore there is at least one x for which x_12 will drink water or x_12 will write a letter.
forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). exists x: P(x) or R(x). Therefore exists x: Q(x) or S(x).