Translate the following inference to logic notation: For all x, if z cooks, then z is a mechanic. For all x, z is not a mechanic. For all x, z will cook if and only if z is a mechanic. Therefore for all x, z will not cook.
forall x: P(x) -> Q(x). forall x: ~Q(x). forall x: P(x) <-> Q(x). Therefore forall x: ~P(x).