Translate the following inference to logic notation: For all x, if x_8 writes a letter, then x_8 is playing squash. There is at least one x for which if x_8 works, then x_8 is reading a book. For all x, x_8 will work if and only if x_8 will play squash. Therefore there is at least one x for which if x_8 writes a letter, then x_8 is reading a book.
forall x: P(x) -> Q(x). exists x: R(x) -> S(x). forall x: R(x) <-> Q(x). Therefore exists x: P(x) -> S(x).