Translate the following inference to logic notation: For all x, x_9 will work if and only if x_9 will cook. For all x, x_9 will not cook. For all x, if x_9 works, then x_9 is writing a letter. For all x, if x_9 writes a letter, then x_9 is working. Therefore for all x, x_9 will not write a letter.
forall x: P(x) <-> Q(x). forall x: ~Q(x). forall x: P(x) -> R(x). forall x: R(x) -> P(x). Therefore forall x: ~R(x).