Translate the following inference to logic notation: For all x, if y takes a plane, then y is running. For all x, if y cooks, then y is taking a plane. For all x, y will cook if and only if y will go running. Therefore for all x, y will cook if and only if y will take a plane.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: R(x) <-> Q(x). Therefore forall x: R(x) <-> P(x).