Translate the following inference to logic notation: There is at least one x for which if x_8 were a bartender, then x_8 is working. For all x, if x_8 were a bartender, then x_8 is working. For all x, x_8 will work if and only if x_8 is a bartender. Therefore there is at least one x for which x_8 is a bartender if and only if x_8 will work.
exists x: P(x) -> Q(x). forall x: P(x) -> Q(x). forall x: Q(x) <-> P(x). Therefore exists x: P(x) <-> Q(x).