exclusive or

• exclusive-or, XOR, xor, EOR, eor

exclusive + or.

exclusive or (plural exclusive ors)

1. (logic, computing) Exclusive disjunction: the use of or to indicate that of two predicates, one is true and one is false (without specifying which is which); contrasted with inclusive or, which does not imply that one must be false.
2. (logic, computing, more generally) Exclusive disjunction: the use of or to indicate that of two or more predicates, an odd number are true (without specifying which or how many); contrasted with inclusive or, which indicates only that one or more is true.
3. (logic, computing) An exclusive disjunction; the result of applying the above-described exclusive or to two or more predicates; contrasted with an inclusive or, which is the result of applying an inclusive or.

• Denoted ⊕.
• (the result): In an expression of formal logic, the phrase exclusive or (or hyphenated as exclusive-or) may appear between the predicates, much like a conjunction:

  (x ∧ ¬y) ${\displaystyle \lor }$ (¬x ∧ y) ↔ x ⊕ y, which reads: x exclusive-or y.

• inclusive or