Translate the following inference to logic notation: For all x, if z_2 were fast, then z_2 is happy. There is at least one x for which z_2 will cook if and only if z_2 is happy. For all x, if z_2 were happy, then z_2 is fast. Therefore there is at least one x for which if z_2 were fast, then z_2 is cooking.
forall x: P(x) -> Q(x). exists x: R(x) <-> Q(x). forall x: Q(x) -> P(x). Therefore exists x: P(x) -> R(x).