The exclusive disjunction is an operation on two statements that creates another statement that is true only if input statements are different (ie. one is true and the other is false). This is similar to the disjunction except for that when both inputs are true the exclusive disjunction outputs false whereas the disjunction outputs true.
The exclusive disjunction can also be thought of as outputting second input if the first is false and negates the second input if the first is true. The exclusive disjunction is usually represented by a
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | F |
The exclusive disjunction can be written as:
Alternatively, it can be written as: