Translate the following inference to logic notation: For all x, if x_10 were a police officer, then x_10 is happy. For all x, x_10 will cook or x_10 is not happy. For all x, x_10 will cook if and only if x_10 is a police officer. Therefore for all x, x_10 will cook if and only if x_10 is a police officer.
forall x: P(x) -> Q(x). forall x: R(x) or ~Q(x). forall x: R(x) <-> P(x). Therefore forall x: R(x) <-> P(x).