Translate the following inference to logic notation: For all x, y will cook if and only if y is a mechanic. There is at least one x for which y is a mechanic if and only if y will work. For all x, y will not cook. Therefore there is at least one x for which y will not work.
forall x: P(x) <-> Q(x). exists x: Q(x) <-> R(x). forall x: ~P(x). Therefore exists x: ~R(x).