Consider the data set in Figure $1$ where $$A$,$B$$ and $$C$$ are binary features with values $$T$($i$.$e$.,$ True$)$ or $$F$($i$.$e$.,$ False$).$

Figure $1.$ Data Set.

Suppose that you are using the features $$A$,$B$$ and $$C$$ to build a decision tree which classify $$Y$$ as $$T$$ or $$F$.$

$1)$ Use the error rate$/$purity of splitting to decide which feature should be used in the root node. Your answer should include the computation of the error rates of splitting.