Translate the following inference to logic notation: For all x, if x_2 works, then x_2 is writing a letter. For all x, x_2 will write a letter or x_2 will not sleep. For all x, x_2 will sleep or x_2 will work. Therefore for all x, x_2 will write a letter.
forall x: P(x) -> Q(x). forall x: Q(x) or ~R(x). forall x: R(x) or P(x). Therefore forall x: Q(x).