Translate the following inference to logic notation: For all x, if y_3 drinks water, then y_3 is happy. There is at least one x for which y_3 is a cashier or y_3 is not happy. For all x, if y_3 were a cashier, then y_3 is drinking water. Therefore there is at least one x for which y_3 is a cashier if and only if y_3 is happy.
forall x: P(x) -> Q(x). exists x: R(x) or ~Q(x). forall x: R(x) -> P(x). Therefore exists x: R(x) <-> Q(x).