Translate the following inference to logic notation: For all x, x_11 is fast or x_11 will not take a plane. There is at least one x for which x_11 will not cook or x_11 will take a plane. For all x, x_11 is fast if and only if x_11 is rich. For all x, x_11 will cook or x_11 is rich. Therefore there is at least one x for which x_11 is fast.
forall x: P(x) or ~Q(x). exists x: ~R(x) or Q(x). forall x: P(x) <-> S(x). forall x: R(x) or S(x). Therefore exists x: P(x).