1. For the following statements, deduce whether they are true or false, and provide a brief explanation. (a) If A, B are NP-Complete, then A Sp B and B Sp A. (b) If A € NP, then A & P. (c) If A is NP-Hard and A € P, then A is NP-Complete. (d) If A in NP-Complete and A can be reduced to a problem B € NP, then B is also NP- Complete. (e) P U NP-Complete= NP. (f) Suppose that P = NP. Then, there exists a polynomial time algorithm for Independent- Set. (g) Define the PALINDROME problem as checking whether an all-lowercase string is a palindrome (equal when reversed). PALINDROME is in P. (h) Define the VERTEX-COVER-MINI as a problem similar to VERTEX-COVER, but the graph G is assumed to have the property that the degree of all its vertices are at most 2. VERTEX-COVER-MINI is not in P. (i) Define the VERTEX-COVER-MINI-2 as a problem similar to VERTEX-COVER, but the graph G are assumed to be a binary tree. VERTEX-COVER-MINI-2 is not in P.