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