Translate the following inference to logic notation: For all x, x will drink water if and only if x will read a book. For all x, if x reads a book, then x is listening to a song. Therefore for all x, if x drinks water, then x is listening to a song.
forall x: P(x) <-> Q(x). forall x: Q(x) -> R(x). Therefore forall x: P(x) -> R(x).