H 9. Define a set S recursively as follows: I. BASE: 1 € S, 3 e S, 5 e S, 7 e S, 9 E S II. RECURSION: If s = S and tЄS then a. stЄ S c. 4s € S e. 8s € S b. 2s € S d. 6s € S III. RESTRICTION: Nothing is in S other than objects defined in I and II above. Use structural induction to prove that every string in S rep- resents an odd integer.