Translate the following inference to logic notation: For all x, if x_8 cooks, then x_8 is fast. For all x, if x_8 were fast, then x_8 is cooking. If it is cloudy, then Thomas is fast. Therefore if it is cloudy, then Thomas is cooking.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). p -> Q(a). Therefore p -> P(a).