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