# Given a set, find XOR of the XOR’s of all subsets.

• Difficulty Level : Easy
• Last Updated : 04 Nov, 2021

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.
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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 when n is 1.

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## C++

 `// C++ program to find XOR of XOR's of all subsets``#include ``using` `namespace` `std;` `// Returns XOR of all XOR's of given subset``int` `findXOR(``int` `Set[], ``int` `n)``{``    ``// XOR is 1 only when n is 1, else 0``    ``if` `(n == 1)``       ``return` `Set;``    ``else``       ``return` `0;``}` `// Driver program``int` `main()``{``    ``int` `Set[] = {1, 2, 3};``    ``int` `n = ``sizeof``(Set)/``sizeof``(Set);``    ``cout << ``"XOR of XOR's of all subsets is "``         ``<< findXOR(Set, n);``    ``return` `0;``}`

## Java

 `// Java program to find XOR of``// XOR's of all subsets``import` `java.util.*;` `class` `GFG {``    ` `// Returns XOR of all XOR's of given subset``static` `int` `findXOR(``int` `Set[], ``int` `n) {``    ` `    ``// XOR is 1 only when n is 1, else 0``    ``if` `(n == ``1``)``    ``return` `Set[``0``];``    ``else``    ``return` `0``;``}` `// Driver code``public` `static` `void` `main(String arg[])``{``    ``int` `Set[] = {``1``, ``2``, ``3``};``    ``int` `n = Set.length;``    ``System.out.print(``"XOR of XOR's of all subsets is "` `+``                                        ``findXOR(Set, n));``}``}` `// This code is contributed by Anant Agarwal.`

## Python3

 `# Python program to find``# XOR of XOR's of all subsets` `# Returns XOR of all``# XOR's of given subset``def` `findXOR(``Set``, n):` `    ``# XOR is 1 only when``    ``# n is 1, else 0``    ``if` `(n ``=``=` `1``):``         ``return` `Set``[``0``]``    ``else``:``         ``return` `0``    ` `# Driver code` `Set` `=` `[``1``, ``2``, ``3``]``n ``=` `len``(``Set``)` `print``(``"XOR of XOR's of all subsets is "``,``         ``findXOR(``Set``, n));` `# This code is contributed``# by Anant Agarwal.`

## C#

 `// C# program to find XOR of``// XOR's of all subsets``using` `System;` `class` `GFG {``    ` `// Returns XOR of all``// XOR's of given subset``static` `int` `findXOR(``int` `[]Set, ``int` `n)``{``    ` `    ``// XOR is 1 only when n``    ``// is 1, else 0``    ``if` `(n == 1)``    ``return` `Set;``    ``else``    ``return` `0;``}` `// Driver code``public` `static` `void` `Main()``{``    ``int` `[]Set = {1, 2, 3};``    ``int` `n = Set.Length;``    ``Console.Write(``"XOR of XOR's of all subsets is "` `+``                                    ``findXOR(Set, n));``}``}` `// This code is contributed by nitin mittal`

## PHP

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## Javascript

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Output:

`XOR of XOR's of all subsets is 0`

Time Complexity: O(1)

Auxiliary Space: O(1)

Related Problem :
Sum of XOR of all possible subsets
How does this work?
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.