Translate the following inference to logic notation: For all x, if x_7 goes running, then x_7 is a carpenter. For all x, x_7 is a carpenter if and only if x_7 is an astronaut. For all x, if x_7 were an astronaut, then x_7 is running. Therefore for all x, x_7 will go running if and only if x_7 is an astronaut.
forall x: P(x) -> Q(x). forall x: Q(x) <-> R(x). forall x: R(x) -> P(x). Therefore forall x: P(x) <-> R(x).