Translate the following inference to logic notation: For all x, y is a bartender or y will not sleep. For all x, if y plays tennis, then y is sleeping. For all x, y will sleep if and only if y will play tennis. Therefore for all x, if y plays tennis, then y is a bartender.
forall x: P(x) or ~Q(x). forall x: R(x) -> Q(x). forall x: Q(x) <-> R(x). Therefore forall x: R(x) -> P(x).