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