Translate the following inference to logic notation: For all x, if y_2 drinks water, then y_2 is a cashier. There is at least one x for which y_2 is a cashier if and only if y_2 is fast. For all x, if y_2 were a cashier, then y_2 is drinking water. For all x, y_2 is not fast. Therefore there is at least one x for which y_2 will not drink water.
forall x: P(x) -> Q(x). exists x: Q(x) <-> R(x). forall x: Q(x) -> P(x). forall x: ~R(x). Therefore exists x: ~P(x).