Translate the following inference to logic notation: For all x, x_5 will cook if and only if x_5 is a soldier. For all x, if x_5 cooks, then x_5 is rich. For all x, if x_5 were rich, then x_5 is a soldier. Therefore for all x, x_5 will cook if and only if x_5 is a soldier.
forall x: P(x) <-> Q(x). forall x: P(x) -> R(x). forall x: R(x) -> Q(x). Therefore forall x: P(x) <-> Q(x).