Translate the following inference to logic notation: For all x, y_1 will work or y_1 will not take a plane. There is at least one x for which y_1 will work if and only if y_1 will take a plane. Therefore there is at least one x for which y_1 will work if and only if y_1 will take a plane.
forall x: P(x) or ~Q(x). exists x: P(x) <-> Q(x). Therefore exists x: P(x) <-> Q(x).