9.J. If A is any subset of R', let A denote the union of all open sets which are contained in A; the set A is called the interior of A. Note that A is an open set; prove that it is the largest open set contained in A. Prove that As A, (A) = A (ANB) = An B', (R') = R. Give an example to show that (A UB) = AUB may not hold.