Translate the following inference to logic notation: For all x, y_4 is an astronaut if and only if y_4 will cook. For all x, y_4 will cook or y_4 will not take a plane. For all x, y_4 will take a plane or y_4 is an astronaut. Therefore for all x, y_4 will cook.
forall x: P(x) <-> Q(x). forall x: Q(x) or ~R(x). forall x: R(x) or P(x). Therefore forall x: Q(x).