Translate the following inference to logic notation: For all x, if y_4 cooks, then y_4 is taking a plane. For all x, y_4 will not take a plane. There is at least one x for which y_4 will take a plane if and only if y_4 will cook. Therefore there is at least one x for which y_4 will not cook.
forall x: P(x) -> Q(x). forall x: ~Q(x). exists x: Q(x) <-> P(x). Therefore exists x: ~P(x).