https://www.geeksforgeeks.org/given-a-set-find-xor-of-the-xors-of-all-subsets/
The question is to find XOR of the XOR’s of all subsets. i.e if the set is {1,2,3}. All subsets are : [{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}]. Find the XOR of each of the subset and then find the XOR of every subset result.
This is a very simple question to solve if we get the first step (and only step) right. The solution is XOR is always 0 when n > 1 and Set[0] when n is 1.
The logic goes simple. Let us consider n’th element, it can be included in all subsets of remaining (n-1) elements. The number of subsets for (n-1) elements is equal to 2(n-1) which is always even when n>1. Thus, in the XOR result, every element is included even number of times and XOR of even occurrences of any number is 0.
