I was going through the Andrew Ng's notes for Decision Trees. It has one section explaining the usage of categorical variables using Decision Trees in which I am not able to understand this part
" A caveat to the above is that we must take care to not allow a variable to have too many categories. For a set of categories S, our set of possible questions is the power set P(S), of cardinality 2^|S| . Thus, a large number of categories makes question selection computationally intractable. "
Q1 -> How is the possible set of questions is $2^{|S|}$ ? It should be equal to the non-leaf nodes in the decision tree .
Link to Andrew Ng notes on Decision Tree : http://cs229.stanford.edu/notes/cs229-notes-dt.pdf
Can you please give some clarification on it .