Translate the following inference to logic notation: If it is cloudy, then Elisabeth is listening to a song. William is a nurse or Richard is not an artist. If Elisabeth listens to a song, then Richard is an artist. If William were a nurse, then it is cloudy. Therefore Elisabeth is listening to a song if and only if William is a nurse.
p -> q. r or ~s. q -> s. r -> p. Therefore q <-> r.