Translate the following inference to logic notation: For all x, x_1 will read a book if and only if x_1 will go running. For all x, x_1 will go running if and only if x_1 will read a book. Therefore for all x, if x_1 goes running, then x_1 is reading a book.
forall x: P(x) <-> Q(x). forall x: Q(x) <-> P(x). Therefore forall x: Q(x) -> P(x).