Translate the following inference to logic notation: There is at least one x for which x_3 will write a letter. For all x, if x_3 plays a game, then x_3 is not writing a letter. For all x, x_3 is a musician if and only if x_3 will play a game. Therefore there is at least one x for which x_3 is not a musician.
exists x: P(x). forall x: Q(x) -> ~P(x). forall x: R(x) <-> Q(x). Therefore exists x: ~R(x).