Translate the following inference to logic notation: There is at least one x for which y will listen to a song if and only if y is an office clerk. For all x, y is an office clerk or y will not listen to a song. Therefore there is at least one x for which y will listen to a song if and only if y is an office clerk.
exists x: P(x) <-> Q(x). forall x: Q(x) or ~P(x). Therefore exists x: P(x) <-> Q(x).