Translate the following inference to logic notation: For all x, x_7 will work. For all x, x_7 will work if and only if x_7 is an astronaut. For all x, if x_7 were an astronaut, then x_7 is playing squash. Therefore for all x, x_7 will play squash.
forall x: P(x). forall x: P(x) <-> Q(x). forall x: Q(x) -> R(x). Therefore forall x: R(x).