Suppose we collected the following Dataset A during 2016.

Table 1. Dataset A.

Index of Records	Rain	Sprinkler	WetGrass
1	No	No	No
2	No	Yes	Yes
3	No	No	No
4	No	Yes	Yes
5	Yes	No	Yes
6	No	Yes	Yes
7	No	No	No
8	Yes	Yes	Yes
9	No	No	No
10	No	Yes	No
11	Yes	No	No
12	No	No	No
13	No	No	No
14	No	Yes	Yes
15	Yes	No	Yes
16	No	No	No

We also collected another Dataset B during 2017.

Table 2. Dataset B.

Index of Records	Rain	Sprinkler	WetGrass
1	No	No	Yes
2	No	No	No
3	No	Yes	No
4	No	Yes	Yes
5	Yes	Yes	Yes
6	No	Yes	No
7	No	No	No
8	Yes	No	Yes
9	No	Yes	Yes
10	No	No	No

These two datasets A and B are independent. We are going to train and test a few classifiers by using these two datasets. That is, given two attributes Rain and Sprinkler, we want to predict if WetGrass is Yes or No.

Problem 1 (20 points). Please illustrate how to construct a full decision tree (using all the attributes Rain and Sprinkler) by using the information gain criteria on the training Dataset A in Table 1.