Consider the training set given below for predicting lung cancer in patients based on their symptoms $($chronic cough and weight loss$)$ and other lifestyle and environmental attributes $($tobacco smoking and expo$-$ sure to radon$).$

$($a$)$ Draw a two$-$level decision tree obtained using entropy as the impurity Show your steps clearly $($i$.$e$.,$ the computation of information gain for every candidate attribute at the first and second levels of the decision tree must be shown$).(7$ points$)$

$($b$)$ Compute the training error of the decision tree. $(3$ points$)$

Tobacco Smoking

Radon Exposure

Chronic Cough

Weight Loss

Lung Cancer

Yes

Yes

Yes

No

Yes

Yes

No

Yes

No

Yes

Yes

No

Yes

Yes

Yes

Yes

No

Yes

Yes

Yes

No

Yes

No

Yes

Yes

Yes

No

No

No

No

No

No

Yes

No

No

No

No

Yes

Yes

No

No

No

Yes

No

No

No

No

No

Yes