Translate the following inference to logic notation: There is at least one x for which y is excited or y will not play tennis. For all x, y will play tennis or y will not cook. For all x, if y were excited, then y is cooking. Therefore there is at least one x for which y will cook if and only if y will play tennis.
exists x: P(x) or ~Q(x). forall x: Q(x) or ~R(x). forall x: P(x) -> R(x). Therefore exists x: R(x) <-> Q(x).