I want to state this by saying that this is homework.
I am given a set of binary input variables Q, which will be used to classify the output of Y, which is also binary.
The first part of the question: no more, how many examples do you need to list all possible combinations of Q? Currently, I think that since it asks for the maximum, I will need Q, since it is possible that all values before Q-1 are the same for instance 1, and the element in Q is 0.
The second part of the question: no more than how many leaf nodes can a tree give to examples Z?
My current answer is that in most cases the tree has two leaf nodes, one of which represents true and one represents false, since it deals with binary inputs and binary outputs.
Is this the right way to study this problem or am I generalizing my answers too deeply?
Edit
Having looked at Cameron's answer, I will now return my first answer to 2 ^ Q and describe his example Q = 3, I would get 2 ^ 3 or 8 (2 * 2 * 2). Please correct if this is incorrect.
Edit # 2
The second part of the question seems that it should be (2 ^ Q) * Z or provide an example: (2 ^ 3) * 3) or 8 * 3 = 24 leaf nodes. To repeat, if I have 3 inputs that are binary, I would first take 2 ^ 3 and get 8 now, I want to go to 3 examples. So I have to get 8 * 3 or 24.
Edit # 3
In retrospect, it seems that no matter how many examples I use, the number of leaf nodes should never increase, since it depends on the tree.