Translate the following inference to logic notation: For all x, x_15 will play a game if and only if x_15 is a scientist. There is at least one x for which x_15 is a musician if and only if x_15 will play a game. For all x, if x_15 were a musician, then x_15 is a scientist. Therefore there is at least one x for which if x_15 were a musician, then x_15 is playing a game.
forall x: P(x) <-> Q(x). exists x: R(x) <-> P(x). forall x: R(x) -> Q(x). Therefore exists x: R(x) -> P(x).