Translate the following inference to logic notation: For all x, z_1 is an office clerk. For all x, z_1 is fast if and only if z_1 is an office clerk. There is at least one x for which if z_1 listens to a song, then z_1 is fast. Therefore there is at least one x for which z_1 is fast.
forall x: P(x). forall x: Q(x) <-> P(x). exists x: R(x) -> Q(x). Therefore exists x: Q(x).