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