For a set S, define the following languages: S^MT = "Middle Thirds of S" = {y: for some x and z such that |x| = |y| = |z|, xyz is in S} S^OT = "Outer Thirds of S" = {xz: for some y such that |x| = |y| = |z|, xyz is in S} A. Prove that if S is regular, then so is S^MT. B. Give an example of a regular set S for which S^OT is regular. C. Give an example of a regular set S for which S^OT is not regular.