Translate the following inference to logic notation: Barbara is a janitor if and only if Thomas is cooking. For all x, if y_1 were rich, then y_1 is a janitor. Thomas is not cooking. For all x, if y_1 were a janitor, then y_1 is rich. Therefore Barbara is not rich.
P(a) <-> p. forall x: Q(x) -> P(x). ~p. forall x: P(x) -> Q(x). Therefore ~Q(a).