Let G = (V,E) be a simple graph with |V| 2. The complement graph G of...

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Let G = (V,E) be a simple graph with |V| 2. The complement graph G of G is the simple graph whose vertex set is V and whose edge set consists of all the edges that have as endpoints nonadjacent vertices in G. State whether the following statements are Correct or Incorrect and provide a proof. (a) (15 points) If G is disconnected, then is connected. (b) (5 points) If G is connected, then is disconnected. Let G = (V,E) be a simple graph with |V| 2. The complement graph G of G is the simple graph whose vertex set is V and whose edge set consists of all the edges that have as endpoints nonadjacent vertices in G. State whether the following statements are Correct or Incorrect and provide a proof. (a) (15 points) If G is disconnected, then is connected. (b) (5 points) If G is connected, then is disconnected.