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