Translate the following inference to logic notation: There is at least one x for which x is not a nurse. For all x, x will write a letter or x is not a scientist. For all x, if x writes a letter, then x is a nurse. For all x, if x were a nurse, then x is writing a letter. Therefore there is at least one x for which x is not a scientist.
exists x: ~P(x). forall x: Q(x) or ~R(x). forall x: Q(x) -> P(x). forall x: P(x) -> Q(x). Therefore exists x: ~R(x).