Translate the following inference to logic notation: For all x, z_1 will listen to a song. For all x, if z_1 were happy, then z_1 is not listening to a song. There is at least one x for which z_1 is an office clerk if and only if z_1 is happy. Therefore there is at least one x for which z_1 is not an office clerk.
forall x: P(x). forall x: Q(x) -> ~P(x). exists x: R(x) <-> Q(x). Therefore exists x: ~R(x).