Translate the following inference to logic notation: For all x, x_5 will listen to a song. There is at least one x for which x_5 is a mechanic if and only if x_5 will listen to a song. Therefore there is at least one x for which x_5 is a mechanic.
forall x: P(x). exists x: Q(x) <-> P(x). Therefore exists x: Q(x).