Translate the following inference to logic notation: There is at least one x for which y is a cashier if and only if y will play a game. For all x, if y plays a game, then y is making tea. For all x, if y makes tea, then y is a cashier. Therefore there is at least one x for which y is a cashier if and only if y will make tea.
exists x: P(x) <-> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore exists x: P(x) <-> R(x).