Translate the following inference to logic notation: For all x, z is not a nurse. Sarah is listening to a song if and only if Richard is running. Richard is running if and only if Susan is an office clerk. For all x, z is a nurse if and only if z will listen to a song. Therefore Susan is not an office clerk.
forall x: ~P(x). Q(a) <-> p. p <-> q. forall x: P(x) <-> Q(x). Therefore ~q.