Translate the following inference to logic notation: For all x, x_10 is bored or x_10 is a nurse. For all x, if x_10 writes a letter, then x_10 is a scientist. For all x, x_10 is not bored. There is at least one x for which if x_10 were a scientist, then x_10 is not a nurse. Therefore there is at least one x for which x_10 will not write a letter.
forall x: P(x) or Q(x). forall x: R(x) -> S(x). forall x: ~P(x). exists x: S(x) -> ~Q(x). Therefore exists x: ~R(x).