Consider the following data set for a binary class problem.

NOTE: Solve any calculation required using Python.

(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) Figure 4.13 shows that entropy and the Gini index are both 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.

A B Class Label T F T F