Translate the following inference to logic notation: If it is cold, then Sarah is writing a letter. Sarah is not sleeping. For all x, if x_12 writes a letter, then x_12 is sleeping. If Sarah sleeps, then it is cold. Therefore it is not cold.
p -> P(a). ~Q(a). forall x: P(x) -> Q(x). Q(a) -> p. Therefore ~p.