Translate the following inference to logic notation: For all x, x_8 is not an astronaut. For all x, x_8 will work if and only if x_8 is an astronaut. For all x, x_8 will cook or x_8 is a soldier. For all x, x_8 will cook if and only if x_8 will work. Therefore for all x, x_8 is a soldier.
forall x: ~P(x). forall x: Q(x) <-> P(x). forall x: R(x) or S(x). forall x: R(x) <-> Q(x). Therefore forall x: S(x).