Consider the following data set for a binary class problem. (a) Calculate the information gain when splitting on A and B. Which attribute would the decision tree induction algorithm choose? (b) Calculate the gain in the Gini index when splitting on A and B. Which attribute would the decision tree induction algorithm choose? (c) Consider both entropy and the Gini index are monotonously increasing on the range [0, 0.5] and they are both monotonously decreasing on the range [0.5, 1]. Is it possible that information gain and the gain in the Gini index favor different attributes? Explain