a$)$ Calculate the entropy

Entropy$(S)={?}^{\text{d}\text{e}\text{f}}{\displaystyle \underset{i=1}{\overset{c}{}}}{p}_{i}lo{g}_2(\frac{1}{p_i})={\displaystyle \underset{i=1}{\overset{c}{}}}-p_{i}lo{g}_2(p_i)$

Where $p_i$ is the proportion of $S$ belonging to class i$.$ Also note that $lo{g}_2(x)=\frac{lo{g}_{10}(x)}{lo{g}_{10}(2)}.$

b$)$ Construct the decision tree structure from the above examples, which would be learned by the ID$3$ algorithm.

c$)$ Show the value of the information gain for each candidate attribute at each step in the construction of the tree.

In your report you need to include all details of the tree construction process following steps $1-3.$