Translate the following inference to logic notation: For all x, x_12 is a musician if and only if x_12 will listen to a song. Richard is listening to a song or Richard is not a musician. Therefore Richard is listening to a song if and only if Richard is a musician.
forall x: P(x) <-> Q(x). Q(a) or ~P(a). Therefore Q(a) <-> P(a).