Translate the following inference to logic notation: There is at least one x for which y will play squash if and only if y will take a plane. For all x, y will cook if and only if y will play squash. For all x, if y cooks, then y is taking a plane. Therefore there is at least one x for which if y plays squash, then y is taking a plane.
exists x: P(x) <-> Q(x). forall x: R(x) <-> P(x). forall x: R(x) -> Q(x). Therefore exists x: P(x) -> Q(x).