Translate the following inference to logic notation: There is at least one x for which y_3 will read a book if and only if y_3 is sad. For all x, y_3 is sad if and only if y_3 will read a book. Therefore there is at least one x for which y_3 is sad if and only if y_3 will read a book.
exists x: P(x) <-> Q(x). forall x: Q(x) <-> P(x). Therefore exists x: Q(x) <-> P(x).