Translate the following inference to logic notation: There is at least one x for which x_12 is poor if and only if x_12 will climb a mountain. For all x, x_12 is a poet if and only if x_12 is an astronaut. For all x, x_12 is not a poet. For all x, x_12 is an astronaut if and only if x_12 is poor. Therefore there is at least one x for which x_12 will not climb a mountain.
exists x: P(x) <-> Q(x). forall x: R(x) <-> S(x). forall x: ~R(x). forall x: S(x) <-> P(x). Therefore exists x: ~Q(x).