Translate the following inference to logic notation: If Barbara plays squash, then Barbara is listening to a song. For all x, x_7 will play squash or x_7 will not listen to a song. Therefore Barbara is listening to a song if and only if Barbara is playing squash.
P(a) -> Q(a). forall x: P(x) or ~Q(x). Therefore Q(a) <-> P(a).