Translate the following inference to logic notation: For all x, x_12 is a bartender or x_12 is not bored. For all x, x_12 is a cashier if and only if x_12 is a bartender. There is at least one x for which if x_12 were a cashier, then x_12 is bored. Therefore there is at least one x for which x_12 is a cashier if and only if x_12 is bored.
forall x: P(x) or ~Q(x). forall x: R(x) <-> P(x). exists x: R(x) -> Q(x). Therefore exists x: R(x) <-> Q(x).