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