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