Translate the following inference to logic notation: For all x, z will play tennis if and only if z is a cashier. For all x, z will play tennis if and only if z is a bartender. There is at least one x for which if z were a bartender, then z is playing tennis. Therefore there is at least one x for which if z were a bartender, then z is a cashier.
forall x: P(x) <-> Q(x). forall x: P(x) <-> R(x). exists x: R(x) -> P(x). Therefore exists x: R(x) -> Q(x).