Translate the following inference to logic notation: For all x, x_9 will cook if and only if x_9 is a mechanic. For all x, if x_9 cooks, then x_9 is a mechanic. For all x, if x_9 were a mechanic, then x_9 is cooking. Therefore for all x, x_9 will cook if and only if x_9 is a mechanic.
forall x: P(x) <-> Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore forall x: P(x) <-> Q(x).