Translate the following inference to logic notation: There is at least one x for which x_3 will go running or x_3 will not read a book. For all x, if x_3 goes running, then x_3 is reading a book. Therefore there is at least one x for which x_3 will go running if and only if x_3 will read a book.
exists x: P(x) or ~Q(x). forall x: P(x) -> Q(x). Therefore exists x: P(x) <-> Q(x).