Translate the following inference to logic notation: For all x, x_1 will play a game. For all x, if x_1 were a musician, then x_1 is not playing a game. For all x, x_1 is a nurse if and only if x_1 is a musician. Therefore for all x, x_1 is not a nurse.
forall x: P(x). forall x: Q(x) -> ~P(x). forall x: R(x) <-> Q(x). Therefore forall x: ~R(x).