Translate the following inference to logic notation: For all x, x_21 will listen to a song if and only if x_21 is a poet. Joseph is working if and only if it is raining. It is raining if and only if William is a poet. William is not listening to a song. Therefore Joseph is not working or Jessica is a janitor.
forall x: P(x) <-> Q(x). p <-> q. q <-> Q(a). ~P(a). Therefore ~p or r.