Translate the following inference to logic notation: For all x, x_13 is a cashier if and only if x_13 will play squash. For all x, if x_13 were a cashier, then x_13 is playing squash. There is at least one x for which x_13 is not a cashier. For all x, if x_13 listens to a song, then x_13 is playing squash. Therefore there is at least one x for which x_13 will not listen to a song.
forall x: P(x) <-> Q(x). forall x: P(x) -> Q(x). exists x: ~P(x). forall x: R(x) -> Q(x). Therefore exists x: ~R(x).