Translate the following inference to logic notation: For all x, if z_2 cooks, then z_2 is driving a car. If Joseph drives a car, then Joseph is cooking. Joseph is driving a car if and only if Jennifer is climbing a mountain. If James writes a letter, then Joseph is cooking. Jennifer is not climbing a mountain. Therefore James is not writing a letter.
forall x: P(x) -> Q(x). Q(a) -> P(a). Q(a) <-> p. q -> P(a). ~p. Therefore ~q.