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