Translate the following inference to logic notation: For all x, y is a lawyer if and only if y will listen to a song. For all x, y will listen to a song if and only if y is a lawyer. Therefore for all x, if y listens to a song, then y is a lawyer.
forall x: P(x) <-> Q(x). forall x: Q(x) <-> P(x). Therefore forall x: Q(x) -> P(x).