Problem 3 Prove that class P is closed under a. [5 points] Union. [Hint: Let Mi and M2 be deterministic TMs that decide languages A and B in polynomial time. Construct a new deterministic TM M that decides Au B in polynomial time .] b. [5 points] Complement. Hint: Let M be a deterministic TM that decides lan- guage A in polynomial time. Construct a new deterministic TM M' that decides 4 in polynomial time.]