A dataset $($samples$)$ is given below, representing as an information table. The attributes named Hair, Breathes, and Legs are its conditional attributes. The attributed named Species is its decision attribute. Create a decision tree based on the dataset, applying ID$3$ algorithm.

$1.$ When selecting the most appropriate conditional attribute for each node, you need to provide the answers of the following items:

a$.(15$ points$)$ The entropy for the present information table;

b$.(15$ points$)$ For each conditional attribute, the entropy of each conditional attribute value;

c$.(15$ points$)$ The information gain of each conditional attribute value;

d$.(15$ points$)$ The name of the conditional attribute to be selected and why.

$2.(10$ points$)$ Draw the decision tree.

$3.(30$ points$)$ Write down all decision rules that can be derived from the decision tree.