Translate the following inference to logic notation: For all x, if x_11 were a soldier, then x_11 is playing a game. For all x, x_11 is an astronaut if and only if x_11 will play a game. There is at least one x for which if x_11 were an astronaut, then x_11 is playing a game. Therefore there is at least one x for which if x_11 were a soldier, then x_11 is an astronaut.
forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). exists x: R(x) -> Q(x). Therefore exists x: P(x) -> R(x).