Translate the following inference to logic notation: For all x, x_11 will play a game if and only if x_11 will read a book. For all x, x_11 will play a game or x_11 will not read a book. For all x, if x_11 reads a book, then x_11 is playing a game. Therefore for all x, x_11 will play a game if and only if x_11 will read a book.
forall x: P(x) <-> Q(x). forall x: P(x) or ~Q(x). forall x: Q(x) -> P(x). Therefore forall x: P(x) <-> Q(x).