9. Show that Theorem 8.37 is best possible in the following sense.

(a) There exist sets A, Bin R such that (A U B)O #- AO U BO.

(b) There exist sets A, B in R such that A n B #- An B.

"

(c) There exist sets A, Bin R such that 8(A U B) #- 8A U 8B and 8(A n B) #-

8AU8B.