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