Translate the following inference to logic notation: For all x, y will play a game or y is not a poet. There is at least one x for which if y plays a game, then y is reading a book. For all x, if y reads a book, then y is a poet. Therefore there is at least one x for which y is a poet if and only if y will read a book.
forall x: P(x) or ~Q(x). exists x: P(x) -> R(x). forall x: R(x) -> Q(x). Therefore exists x: Q(x) <-> R(x).