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