Translate the following inference to logic notation: For all x, x_7 is a carpenter. For all x, if x_7 were a carpenter, then x_7 is a cashier. There is at least one x for which x_7 is a cashier if and only if x_7 is a police officer. Therefore there is at least one x for which x_7 is a cashier.
forall x: P(x). forall x: P(x) -> Q(x). exists x: Q(x) <-> R(x). Therefore exists x: Q(x).