Translate the following inference to logic notation: For all x, if x sleeps, then x is writing a letter. For all x, x will not sleep. For all x, if x were a nurse, then x is sleeping. For all x, if x writes a letter, then x is a nurse. Therefore for all x, x will not write a letter.
forall x: P(x) -> Q(x). forall x: ~P(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore forall x: ~Q(x).