How could we prove it using Shanon Information Theory?

Problem 1.2 (30 points). Consider each of the the following encryption schemes and state whether the scheme is perfectly secret or not. Justify your answer by giving a de- tailed proof if your answer is Yes, a counterexample if your answer is No. 1. An encryption scheme whose plaintext space consists of the integers M = {0, ,8) and key generation algorithm chooss a uniform key from the key space 0,9 Suppose Enck (m) = k + m mod 9 and Deale) = c-k mod 9. 2. An encryption scheme whose plaintext space is M = {m E {0.1}') given that the last bit of m is 0 and key generation algorithm chooses a uniform key from the key space (0, 1}(-1. Suppose Ena(m)-m (k10) and Dea(c) c D (kl)