TASK $1(60$ points$)1$a $(20$ points$)$ Suppose that a decision tree is trained on $1000$ training examples, and achieves $90\%$ accuracy on the training examples. What is the smallest and largest accuracy that this decision tree can possibly achieve on a test set of $1000$ examples? Justify your answer. You can assume there are only two classes$\mathrm{.}1$b $(20$ points$).$ Suppose that a decision tree is trained on $1000$ training examples, and achieves $80\%$ accuracy on the training examples. What is the smallest and largest possible value for the entropy at a leaf node of this decision tree? Remember that entropy is measured on the training set. You can assume there are only two classes$\mathrm{.}1$c $(20$ points$).$ Suppose that a decision tree is trained on $1000$ training examples, and achieves $100\%$ accuracy on the training examples. What is the smallest and largest possible value for the entropy at a leaf node of this decision tree? Again, remember that entropy is measured on the training set. You can assume there are only two classes.