A method to design a decision tree is to use the concept of the mutual information. Specifically, we find

the feature X$,$ which maximizes the mutual information I$($X; C$)$ with the class C$,$ and use it in the root node.

Suppose that you find the optimal feature X$.$ A friend of yours told you that she made a better feature Y

from X using the relation Y $=12$X and improved the classification performance. Did she tell you a lie

or a truth?