Translate the following inference to logic notation: For all x, x_12 is an astronaut if and only if x_12 is rich. For all x, x_12 is an astronaut if and only if x_12 will climb a mountain. For all x, if x_12 were an astronaut, then x_12 is climbing a mountain. Therefore for all x, if x_12 climbs a mountain, then x_12 is rich.
forall x: P(x) <-> Q(x). forall x: P(x) <-> R(x). forall x: P(x) -> R(x). Therefore forall x: R(x) -> Q(x).