Translate the following inference to logic notation: For all x, if y cooks, then y is fast. For all x, if y were fast, then y is cooking. For all x, y will cook if and only if y is fast. Therefore for all x, y will cook if and only if y is fast.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: P(x) <-> Q(x). Therefore forall x: P(x) <-> Q(x).