Translate the following inference to logic notation: For all x, x_21 is a nurse if and only if x_21 is a politician. If it is cloudy, then Thomas is a nurse. It is cloudy if and only if it is cold. Thomas is not a politician. Therefore it is not cold.
forall x: P(x) <-> Q(x). p -> P(a). p <-> q. ~Q(a). Therefore ~q.