Translate the following inference to logic notation: Robert is cooking if and only if Joseph is listening to a song. If Joseph listens to a song, then Patricia is a writer. Michael is running if and only if Robert is cooking. If Patricia were a writer, then Michael is running. Therefore Joseph is listening to a song if and only if Robert is cooking.
p <-> q. q -> r. s <-> p. r -> s. Therefore q <-> p.