Exclusive or
In logic, exclusive disjunction is a logical operator. The exclusive disjunction of propositions A and B is called A xor B, where "xor" stands for "exclusive or".
The operation yields the result TRUE when one, and only one, of its operands is TRUE.
For two inputs A and B, the truth table of the function is as follows.
A B | A xor B ----+-------- F F | F F T | T T F | T T T | F
It can be deduced from this table that
- (A xor B) = (A and not B) or (not A and B) = (A or B) and (not A or not B) = (A or B) and not (A and B)
The mathematical symbol for exclusive disjunction varies in the literature. In addition to the abbreviation "xor", one may see
- a plus sign ("+") or a plus sign that is modified in some way, such being put inside of a circle ("⊕"); this is used because exclusive disjunction corresponds to addition modulo 2 if F = 0 and T = 1.
- a vee that is modified in some way, such as being underlined ("∨"); this is used because exclusive disjunction is a modification of ordinary (inclusive) disjunction, which is typically denoted by a vee.
- a caret ("^"), as in the C programming language.