Translate the following inference to logic notation: William is a cashier if and only if Sarah is a taxi driver. For all x, y will listen to a song if and only if y is a taxi driver. If Sarah listens to a song, then William is a cashier. Therefore Sarah is a taxi driver if and only if William is a cashier.
p <-> P(a). forall x: Q(x) <-> P(x). Q(a) -> p. Therefore P(a) <-> p.