the question in algorithm and complexity. please, I need step by step solutions. thanks

Exercise 3 (Spoints Consider a graph G = (V, E). An independent set of the graph G is a set of vertices S CV such that for all x, y ES the xy is not an edge of the graph G. A set D C X is said to be a dominating set if for every x E X D there exists y E D such that xy E E. Problem 2 Dominating and Independent sets (DIS) Instance : A graph G = (V, E) and an integer k (1, X]. Question : Are there a dominating set of size > k and an independent set of size > 1. Show that DIS is in NP? 2. * Show that DIS is NP - Hard? Hint: Maximal independent set. 3. Suppose that P= NP and given a polynomial time black-box algorithm for solving the decision problem DIS. Give a polynomial time algorithm to solve the associated optimization problem. Exercise 3 (Spoints Consider a graph G = (V, E). An independent set of the graph G is a set of vertices S CV such that for all x, y ES the xy is not an edge of the graph G. A set D C X is said to be a dominating set if for every x E X D there exists y E D such that xy E E. Problem 2 Dominating and Independent sets (DIS) Instance : A graph G = (V, E) and an integer k (1, X]. Question : Are there a dominating set of size > k and an independent set of size > 1. Show that DIS is in NP? 2. * Show that DIS is NP - Hard? Hint: Maximal independent set. 3. Suppose that P= NP and given a polynomial time black-box algorithm for solving the decision problem DIS. Give a polynomial time algorithm to solve the associated optimization