Translate the following inference to logic notation: For all x, x_7 is fast or x_7 will cook. For all x, x_7 is not fast. There is at least one x for which x_7 is excited or x_7 will not cook. Therefore there is at least one x for which x_7 is excited.
forall x: P(x) or Q(x). forall x: ~P(x). exists x: R(x) or ~Q(x). Therefore exists x: R(x).