Translate the following inference to logic notation: For all x, if z_2 were a musician, then z_2 is running. For all x, if z_2 goes running, then z_2 is a musician. There is at least one x for which z_2 will go running if and only if z_2 will play a game. For all x, z_2 will not play a game. Therefore there is at least one x for which z_2 is not a musician.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: Q(x) <-> R(x). forall x: ~R(x). Therefore exists x: ~P(x).