In Java XOR with three true inputs returns true. Why?

Question

The following code System.out.println("1 0 0: " + (true ^ false ^ false)); System.out.println("1 0 1: " + (true ^ false ^ true)); System.out.println("1 1 0: " + (true ^ true ^ false)); System.out.println("1 1 1: " + (true ^ true ^ true)); System.out.println("0 0 0: " + (false ^ false ^ false)); System.out.println("0 0 1: " + (false ^ false ^ true)); System.out.println("0 1 0: " + (false ^ true ^ false)); System.out.println("0 1 1: " + (false ^ true ^ true)); outputs: 1 0 0: true 1 0 1: false 1 1 0: false 1 1 1: true 0 0 0: false 0 0 1: true 0 1 0: true 0 1 1: false Why does XOR returns `true` when all three inputs are `true`? If it's valid logic how can I implement logic that returns `true` **only** if one of the input elements is `true` (no matter how many inputs I provide)?

Answer 1

XOR is associative. True ^ True will resolve to false, and then false ^ True will resolve back to true! So processing True^True^True will reduce to False ^True and then just True.

(a ^ b ^ c ) ^ ( a && b && c )

This will return true only if only one input is true.