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