How do you generate all subsets of a set using backtracking?

At each position in the input, make a binary decision: include the current element or exclude it. Start with an empty subset and recurse through the elements. When you include an element, add it to the current subset and recurse to the next position. After that recursive call returns, remove the element to backtrack and recurse without it. When you reach past the last element, the current subset is one valid result. This generates all two to the power of n subsets. The decision tree has n levels with two branches each.