Translate the following inference to logic notation: For all x, x_15 is a nurse if and only if x_15 is a cashier. There is at least one x for which x_15 is a cashier if and only if x_15 is a nurse. For all x, x_15 will not play a game. For all x, if x_15 were a nurse, then x_15 is playing a game. Therefore there is at least one x for which x_15 is not a cashier.
forall x: P(x) <-> Q(x). exists x: Q(x) <-> P(x). forall x: ~R(x). forall x: P(x) -> R(x). Therefore exists x: ~Q(x).