Translate the following inference to logic notation: For all x, if x_7 were a lawyer, then x_7 is listening to a song. There is at least one x for which x_7 is a lawyer if and only if x_7 will listen to a song. Therefore there is at least one x for which if x_7 were a lawyer, then x_7 is listening to a song.
forall x: P(x) -> Q(x). exists x: P(x) <-> Q(x). Therefore exists x: P(x) -> Q(x).