Translate the following inference to logic notation: For all x, if x_2 were a soldier, then x_2 is not cooking. For all x, x_2 will cook. For all x, x_2 will work if and only if x_2 is a soldier. Therefore for all x, x_2 will not work.
forall x: P(x) -> ~Q(x). forall x: Q(x). forall x: R(x) <-> P(x). Therefore forall x: ~R(x).